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## Big Ideas 4th Grade Chapter 4 Multiply by Two-Digit Numbers Solution Key

Students can easily understand the concepts in-depth with the help of Big Ideas Math Answers Grade 4 Chapter 4 Multiply by Two-Digit Numbers. We have provided all the questions, answers, along with explanations. Also, most of the explanations are given with images for the best learning for students. In order to become a math expert, you must refer to the Big Ideas Multiply by Two-Digit Numbers chapter. Verify the step-by-step procedure to solve a problem to make your preparation easy.

**Lesson 1: Multiply by Tens**

**Lesson 2: Estimate Products**

**Lesson 3: Use Area Models to Multiply Two-Digit Numbers**

- Lesson 4.3 Use Area Models to Multiply Two-Digit Numbers
- Use Area Models to Multiply Two-Digit Numbers Homework & Practice 4.3

**Lesson 4: Use the Distributive Property to Multiply Two-Digit Numbers**

- Lesson 4.4 Use the Distributive Property to Multiply Two-Digit Numbers
- Use the Distributive Property to Multiply Two-Digit Numbers Homework & Practice 4.4

**Lesson 5: Use Partial Products to Multiply Two-Digit Numbers**

- Lesson 4.5 Use Partial Products to Multiply Two-Digit Numbers
- Use Partial Products to Multiply Two-Digit Numbers Homework & Practice 4.5

**Lesson 6: Multiply Two-Digit Numbers**

**Lesson 7: Practice Multiplication Strategies**

- Lesson 4.7 Practice Multiplication Strategies
- Practice Multiplication Strategies Homework & Practice 4.7

**Lesson 8: Problem Solving: Multiplication with Two-Digit Numbers**

- Lesson 4.8 Problem Solving: Multiplication with Two-Digit Numbers
- Problem Solving: Multiplication with Two-Digit Numbers Homework & Practice 4.8

**Performance Task**

- Multiply by Two-Digit Numbers Performance Task
- Multiply by Two-Digit Numbers Activity
- Multiply by Two-Digit Numbers Chapter Practice
- 4.3 Use Area Models to Multiply Two-Digit Numbers
- 4.4 Use Distributive Property to Multiply Two-Digit Numbers
- 4.5 Use Partial Products to Multiply Two-Digit Numbers
- 4.6 Multiply Two-Digit Numbers
- 4.7 Practice Multiplication Strategies

### Lesson 4.1 Multiply by Tens

**Explore and Grow**

Model each product. Draw each model.

What pattern do you notice in the products?

Answer:

The Place- value method. From the above pattern, we can conclude that the result has different place-values of 6

Explanation:

The position of 3 is different in the given 4 multiplications.

So,

2 × 3 = 6

2 × 30 = 60

2 × 300 = 600

2 × 3000 = 6,000

From the above pattern, we can conclude that the result has different place-values of 6

**Repeated Reasoning**

How can the pattern above help you find 20 × 30?

Answer:

20 × 30 = 600

Explanation:

You can think of 20 as two tens and 30 as Three tens.

So,

20 × 30 = 2 × 1 ten × 3 × 1 ten = 2 tens × 2 × 3 = 6 × 2 tens = 600

**Think and Grow: Multiply by Multiples of Tens**

You can use place value and properties to multiply two-digit numbers by multiples of ten.

**Example**

Find 40 × 20.

One Way: Use place value.

40 × 20 = 40 × ____ tens

= ____ tens

= _____

So, 40 × 20 = _____.

Answer:

800

Explanation:

By using the Place-value method,

40 × 20 = 40 × 2 tens

= 80 tens

= 800

So, 40 × 20 = 800

Another Way: Use the Associative Property of Multiplication.

40 × 20 = 40 × (2 × 10) Rewrite 20 as 2 × 10.

= (40 × 2) × 10 Associative Property of Multiplication

= ____ × 10

= ____

So, 40 × 20 = _____.

Answer:

800

Explanation:

By using the Associative Property of Multiplication,

40 × 20 = 40 × (2 × 10)

= (40 × 2) × 10

= 80 × 10

= 800

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Find 12 × 30.

One Way: Use place value

12 × 30 = 12 × _____ tens

= ____ tens

= _____

So, 12 × 30 = _____.

Answer:

360

Explanation:

Using the Place-value method,

12 × 30 = 12 × 3 tens

= 36 tens

= 360

So, 12 × 30 = 360

Another Way: Use the Associative Property of Multiplication

12 × 30 = 12 × (3 × 10) Rewrite 30 as 3 × 10.

= (12 × 3) × 10 Associative Property of Multiplication

= ____ × 10

= _____

So, 12 × 30 = ____.

Answer: 360

Explanation:

By using the Associative Property of Multiplication,

12 × 30 = 12 × (3 × 10)

= (12 × 3) × 10

= 36 × 10

= 360

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

**Show and Grow**

**Find the product.**

Question 1.

70 × 40 = _____

Answer:

2800

Explanation:

By using the Associative Property of Multiplication,

70 × 40 = 70 × (4 × 10)

= (70 × 4) × 10

= 280 × 10

= 2800

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 2.

50 × 80 = ____

Answer:

4,000

Explanation:

By using the Associative Property of Multiplication,

50 × 80 = 50 × (8 × 10)

= (50 × 8) × 10

= 400 × 10

= 4000

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 3.

24 × 90 = _____

Answer:

2160

Explanation:

By using the Associative Property of Multiplication,

24 × 90 = 24 × (9 × 10)

= (24 × 9) × 10

= (8 × 3 × 9) × 10

= 216 × 10

= 2160

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 4.

45 × 60 = _____

Answer:

2700

Explanation:

By using the Associative Property of Multiplication,

45 × 60 = 45 × (6 × 10)

= (45 × 6) × 10

= (5 × 9 × 6) × 10

= 270 × 10

= 2700

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

**Apply and Grow: Practice**

**Find the product.**

Question 5.

90 × 10 = _____

Answer:

900

Explanation:

By using the place-value method,

90 × 10 = 10 × 9 tens

= 90 tens

= 900

So,

90 × 10 = 900

Question 6.

40 × 60 = ____

Answer:

2400

Explaination:

By using the place-value method,

40 × 60 = 40 × 6 tens

= 4 tens × 6 tens

= 24 × tens × tens

= 2400

So,

40 × 60 = 2400

Question 7.

20 × 70 = _____

Answer: 1400

Explanation:

By using the place-value method,

70 × 20 = 70 × 2 tens

= 7 tens × 2 tens

= 14 × tens × tens

= 1400

So,

70 × 20 = 1400

Question 8.

11 × 30 = ____

Answer: 330

Explanation:

By using the place-value method,

11 × 30 = 11 × 3 tens

= 33 tens

= 330

So,

11 × 30 = 330

Question 9.

12 × 40 = ____

Answer: 480

Explanation:

By using the place-value method,

12 × 40 = 12 × 4 tens

= 48 tens

= 480

So,

12 × 40 = 480

Question 10.

15 × 50 = _____

Answer: 750

Explanation:

By using the place-value method,

15 ×50 = 15 × 5 tens

= 75 tens

= 750

So,

15 × 50 = 750

Question 11.

30 × 13 = _____

Answer: 390

Explanation:

By using the place-value method,

13 × 30 = 13 × 3 tens

= 39 tens

= 390

So,

13 × 30 = 390

Question 12.

10 × 76 = _____

Answer: 760

Explanation:

By using the place-value method,

10 × 76 = 76 × 1 ten

= 76 tens

= 760

So,

76 × 10 = 760

Question 13.

40 × 25 = ____

Answer: 1,000

Explanation:

By using the place-value method,

25 × 40 = 25 × 4 tens

= 5 × 5× 4 tens

= 100 tens

= 1,000

So,

25 × 40 = 1,000

**Find the missing factor.**

Question 14.

50 × ____ = 1,500

Answer: 30

Explanation;

Let the missing number be X

So, 50 × X = 1,500

X = 1,500 / 50 = 30

Hence, the value of X is: 30

Question 15.

20 × ____ = 1,800

Answer: 90

Explanation;

Let the missing number be X

So, 20 × X = 1,800

X = 1,800 /20 = 90

Hence, the value of X is: 90

Question 16.

60 × ___ = 4,200

Answer: 70

Explanation;

Let the missing number be X

So, 60 × X = 4,200

X = 4,200 / 60 = 70

Hence, the value of X is: 70

Question 17.

____ × 80 = 6,400

Answer: 80

Explanation;

Let the missing number be X

So, X × 80 = 6,400

X = 6,400 / 80 = 80

Hence, the value of X is: 80

Question 18.

____ × 90 = 3,600

Answer: 40

Explanation;

Let the missing number be X

So, X × 90 = 3,600

X = 3,600 / 90 = 40

Hence, the value of X is: 40

Question 19.

____ × 70 = 3,500

Answer: 50

Explanation;

Let the missing number be X

So, X × 70 = 3,500

X = 3,500 / 70 = 50

Hence, the value of X is: 50

**Compare.**

Question 20.

Answer: 60 × 30 is equal to 1,800

Explanation:

60 × 30 = 1,800

Given numbers are: 1,800 and 1,800

By comparing 2 values, we can conclude that 1,800 is equal to 1,800

Question 21.

Answer: 480 is greater than 460

Explanation:

40 × 12 = 480

Given numbers are: 480 and 460

By comparing 2 values, we can conclude that480 is greater than 460

Question 22.

Answer: 2,250 is less than 2,340

Explanation:

25 × 90 = 2,250

Given numbers are 2,250 and 2,340

By comparing 2 values, we can conclude that 2,250 is less than 2,340

Question 23.

It takes 10 days to film 1 episode of a television show. How many days will it take to film a 20-episode season?

Answer: 200 days

Explanation:

Given that it takes 10 days to film 1 episode of a Television show.

So,

The number of days it will take to film a 20-episode season is: 20 × 10 = 200 days

Question 24.

**Reasoning**

What is Descartes’s number? Explain.

Answer:

Question 25.

**YOU BE THE TEACHER**

Newton says that the product of two multiples of ten will always have exactly two zeros. Is he correct? Explain.

Answer: He is correct

Explanation:

Let us suppose 2 numbers 10 and 20 which are the two multiples of 10.

Now,

10 × 20 = 200

According to Newton, the product of two multiples of ten will always have exactly two zeroes.

So, from the above multiplication, we can say that Newton is correct.

**Think and Grow: Modeling Real Life**

**Example**

Food drive volunteers collect 1,328 cans of food. The volunteers have50 boxes. Each box holds 20 cans. How many cans will fit in the boxes?

Multiply to find how many cans will fit in the boxes.

20 × 50 = 50 × (5 × 10)

Rewrite 50 as 5 × 10.

= (20 × 5) × 10 Associative Property of Multiplication

= 100 × 10

= 1,000

So, 1,000 cans fit in the boxes.

Subtract the number of cans that will fit in the boxes from the total number of cans collected.

The cans that can not fit in the boxes = 1,328 – 1,000 = 328

So,

328 cans will not fit in the boxes.

**Show and Grow**

Question 26

A library has 2,124 new books. The library has 40 empty shelves. Each shelf holds 35 books. How many not books

will fit on the empty shelves?

Answer: 724

Explanation:

Multiply to find how many books will hold on the shelves.

40 × 35 = 35 × (4 × 10)

Rewrite 40 as 5 × 10.

= (35 × 4) × 10 **Associative Property of Multiplication**

= 140 × 10

= 1,400

So, 1,400 cans fit in the boxes.

Subtract the number of books that will hold on the shelves from the total number of books collected.

The number of books that will not hold on the shelves = 2,124 – 1,400 = 724

So,

724 books will not hold on the shelves

Question 27.

An apartment building has 15 floors. Each floor is 10 feet tall. An office building has 30 floors. Each floor is 13 feet tall. How much taller is the office building than the apartment building?

Answer: 240 feet

Explanation:

Given that an apartment has 15 floors and in that, each floor is 10 feet tall.

So, the height of the apartment = 15 × 10 = 150 feet

Given that an office building has 30 floors and in that, each floor is 13 feet tall.

So, the height of the office building = 30 × 13 = 390 feet

Now, to calculate how much taller an office building than the apartment, we have to subtract both the heights of the apartment and the office building.

So,

The difference in height between the office building and the apartment = 390 feet – 150 feet = 240 feet.

From the above, we can conclude that the office building is 240 feet taller than the apartment.

Question 28.

You burn 35 calories each hour you spend reading and 50 calories each hour you spend playing board games. In 2

weeks, you spend14 hours reading and 28 hours playing board games. How many calories do you burn reading

and playing board games?

Answer:

The calories burned during reading in 2 weeks = 490 calories

The calories burned during playing board games = 1400 calories

Explanation:

Given that,

The calories burned during reading is: 35 calories each hour

The calories burned during playing board games is: 50 calories each hour

It is also given that In 2 weeks,

the time spend on reading and Playing Board Games are 14 hours and 28 hours

So, to calculate the calorie consumption in these 2 weeks, we have to multiply the number of hours and the number of calories.

So,

The calories burned during reading in 2 weeks = 490 calories

The calories burned during playing board games in 2 weeks = 1400 calories

### Multiply by Tens Homework & Practice 4.1

**Find the product.**

Question 1.

30 × 10 = _____

Answer: 300

Explanation:

The product of multiply by tens can be done in 2 ways. They are:

A) The place-value method B) The Associative Property of Multiplication

A) By using the place-value method:

30 × 10 = 10 × 3 tens

= 1 ten × 3 tens

= 3 × 1 ten × 1 ten

= 3 × 100

= 300

B) The Associative Property of Multiplication:

30 × 10 = 3 × (10 × 10)

= (3 × 10) × 10

= 30 × 10

= 300

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 2.

20 × 90 = _____

Answer: 1800

Explanation:

The product of multiply by tens can be done in 2 ways. They are:

A) The place-value method B) The Associative Property of Multiplication

A) By using the place-value method:

20 × 90 = 20 × 9 tens

= 2 tens × 9 tens

= 18 × 1 ten × 1 ten

= 18 × 100

= 1800

B) The Associative Property of Multiplication:

20 × 90 = 20 × (9 × 10)

= (20 × 9) × 10

=(5 × 4 × 9) × 10

= 180 × 10

= 1800

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 3.

50 × 70 = _____

Answer: 3500

Explanation:

The product of multiply by tens can be done in 2 ways. They are:

A) The place-value method B) The Associative Property of Multiplication

A) By using the place-value method:

50 × 70 = 50 × 7 tens

= 5 tens × 7 tens

= 35 × 1 ten × 1 ten

= 35 × 100

= 3500

B) The Associative Property of Multiplication:

50 × 70 = 50 × (7 × 10)

= (50 × 7) × 10

=(5 × 10 × 7) × 10

= 350 × 10

= 3500

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 4.

40 × 13 = ______

Answer: 520

Explanation:

The product of multiply by tens can be done in 2 ways. They are:

A) The place-value method B) The Associative Property of Multiplication

A) By using the place-value method:

40 × 13 = 13 × 4 tens

= 13 × 4 tens

= 52 × 1 ten

= 52 × 10

= 520

B) The Associative Property of Multiplication:

40 × 13 = 13 × (4 × 10)

= (13 × 4) × 10

=(13 ×2× 2) × 10

= 54 × 10

= 540

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 5.

27 × 60 = _____

Answer: 1620

Explanation:

The product of multiply by tens can be done in 2 ways. They are:

A) The place-value method B) The Associative Property of Multiplication

A) By using the place-value method:

27 × 60 = 27 × 6 tens

= 3 × 9 × 6 tens

= 162 × 1 ten

= 162 × 10

= 1620

B) The Associative Property of Multiplication:

27 × 60 = 27 × (6 × 10)

= (27 × 6) × 10

=(6 × 3 × 9) × 10

= 162 × 10

= 1620

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 6.

80 × 56 = _____

Answer: 4480

Explanation:

The product of multiply by tens can be done in 2 ways. They are:

A) The place-value method B) The Associative Property of Multiplication

A) By using the place-value method:

80 × 56 = 56 × 8 tens

= 7 × 8 × 8 tens

= 448 × 1 ten

= 448 × 10

= 4480

B) The Associative Property of Multiplication:

56 × 80 = 56 × (8 × 10)

= (56 × 8) × 10

=(8 × 7 × 8) × 10

= 448 × 10

= 4480

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

**Find the missing factor.**

Question 7.

70 × ____ = 2,100

Answer: 30

Explanation:

Let the missing number be X

So, 70 × X = 2,100

X = 2,100 / 70 = 30

Hence, the value of X is: 30

Question 8.

____ × 10 = 900

Answer: 90

Let the missing number be X

So, X × 10 = 900

X = 900 / 10 =90

Hence, the value of X is: 90

Question 9.

40 × ____ = 1,600

Answer: 40

Let the missing number be X

So, 40 × X = 1,600

X = 1,600 / 40 = 40

Hence, the value of X is: 40

Question 10.

____ × 20 = 1,600

Answer: 80

Let the missing number be X

So, X× 20 = 1,600

X = 1,600 / 20 = 80

Hence, the value of X is: 80

Question 11.

30 × ____ = 1,800

Answer: 60

Let the missing number be X

So, 30 × X = 1,800

X = 1,800 / 30 = 60

Hence, the value of X is: 60

Question 12.

____ × 50 = 3,000

Answer: 60

Let the missing number be X

So, X × 50 = 3,000

X = 3,000 / 50 = 60

Hence, the value of X is: 60

**Compare.**

Question 13.

Answer: 7,200 is less than 8,100

Explanation:

90 × 80 = 7,200

Given numbers are: 7,200 and 8,100

By comparing 2 values, we can conclude that 7,200 is less than 8,100

Question 14.

Answer: 1,200 is greater than 1,020

Explanation:

60 ×17 = 1,020

Given numbers are: 1,200 and 1,020

By comparing 2 values, we can conclude that 1,200 is greater than 1,020

Question 15.

Answer: 2,380 is equal to 2,380

Explanation:

34 × 70 = 2,380

Given numbers are:2,380 and 2,380

By comparing the 2 values, we can conclude that 2,380 is equal to2,380

Question 16.

A shallow moonquake occurs 20 kilometers below the moon’s surface. A deep moonquake occurs 35 times deeper than a shallow moonquake. How many kilometers below the surface does the deep moonquake occur?

Answer: 15 kilometers

Explanation:

Given that a shallow moonquake occurred 20 kilometers below the moon’s surface and a deep moonquake occurs 35 meters deeper than a shallow moonquake.

Now, to calculate how much distance the deep moonquake occurred from the surface, we have to subtract the distance that a shallow moonquake occurred from the deep moonquake occurred.

Hence,

The distance below the surface the deep moonquake occurred = 30 – 25 = 15 kilometers

Question 17.

**Structure**

Write the multiplication equation represented by the number line.

Answer:

Question 18.

**Writing**

Explain how you can use 20 × 10 = 200 to find 20 × 12.

Answer: By using the Associative Property of Multiplication,

20 × 10 = 10 × (2 × 10)

= (10 × 2) × 10

= 20 × 10

= 200

By using the same method, we can also find the value of 20 × 12.

Now,

By using the Associative Property of Multiplication,

20 × 12 = 12 × (2 × 10)

= (12 × 2) × 10

= 24 × 10

= 240

* Note*:

**Associative Property of Multiplication**

Take 3 numbers a, b, c.

By using Associative Property, we can write

a × (b × c) = (a × b) × c

Question 19.

**DIG DEEPER!**

The product of a number and twice that number is 800. What are the numbers?

Answer: 20, 40

Explanation:

Let the number be X

Given that,

X × 2X = 800

Take X as a common multiple.

Hence,

X × X ( 1 × 2) = 800

X × X × 2 = 800

X × X = 800/2 = 400

X × X = 20 × 20

From the above, we can conclude that the value of X is 20

Hence, the value of twice the X is 20 × 2 = 40

So,

The numbers that can give the product 800 are 20, 40

Question 20.

**Modeling Real Life**

There are 506 new plants in a greenhouse. A worker programs a robot to arrange the plants into14 rows with 30 plants in each row. How many plants will fit in the rows?

Answer: 420

Explanation:

Given that there are 506 new plants in a greenhouse and a robot can arrange the plants into 14 rows with 30 plants each.

So, to find how many plants will fit in the row, we have to multiply 14 and 30( Since the robot arranges the plants in rows)

Now, By using the Associative Property of Multiplication,

14 × 30 = 14 × (3 × 10)

= (14 × 3) × 10

= (2 × 7 × 3) × 10

= 42 × 10

= 420

From the above, we can conclude that 420 plants will fit in the row.

Question 21.

**Modeling Real Life**

The world’s largest pool is 13 meters longer than the total length of 20 Olympic pools. An Olympic pool is 50 meters long. How long is the world’s largest pool?

Answer: 1013 meters

Explanation: Given that an Olympic pool has a length of 50 meters. But, there are 20 Olympic pools.

So, to find the total length of the Olympic Pool, we have to multiply the number of pools and the length of each pool.

By using the Associative Property of Multiplication,

50 × 20 = 50 × (2 × 10)

= (50 × 2) × 10

= ( 5 × 10 × 2) × 10

= 100 × 10

= 1,000 meters

So, the total length of the 20 Olympic pools = 1,000 meters

The

Question also mentions that the world’s largest pool is 13 meters longer than the total length of 20 Olympic pools.

Hence,

The length of the World’s largest pool = 1,000 + 13 = 1,013 meters.

So, the length of the World’s largest pool is 1,013 meters

**Review & Refresh**

**Find the value of the underlined digit.**

Question 22.

52,618

Answer: The place-value of 8 in the given number is: 8

Explanation:

We can find the position of any given number by using the place- value method.

From this, we can conclude that the place-value of 8 is: 8

Question 23.

379,021

Answer: The place-value of 7 in the given number is: 70,000

Explanation:

We can find the position of any given number by using the place- value method.

From this, we can conclude that the place-value of 7 in the given number is: 70,000

Explanation:

Question 24.

203,557

Answer: The place-value of 2 in the given number is: 200,000

Explanation:

We can find the position of any given number by using the place- value method.

From this, we can conclude that the place-value of 2 in the given number is: 200,000

Question 25.

497,384

Answer: The place-value of 3 in the given number is: 300

Explanation:

We can find the position of any given number by using the place- value method.

From this, we can conclude that the place-value of 3 in the given number is: 300

### Lesson 4.2 Estimate Products

**Explore and Grow**

Choose an expression to estimate each product. Write the expression. You may use an expression more than once.

Compare your answers with a partner. Did you choose the same expressions?

Answer:

Let your Expression be 20 ×25.

The given Partner Expressions are:

A) 21 × 24 B) 26 × 38 C) 23 × 17 D) 42 × 23

By Comparing your Expression and your Partner Expression,

A) 500 is less than 504.

Explanation:

Let your Expression be 20 ×25.

By using the Associative Property of Multiplication,

20 × 25 = 25 × ( 2 × 10)

= (25 × 2) × 10

= (5 × 5 × 2) × 10

= 50 × 10

= 500

The given Partner Expressions are:

A) 21 × 24 B) 26 × 38 C) 23 × 17 D) 42 × 23

We can calculate the partner Expressions by Simplifying the given Expressions.

A)

21 × 24 = 3 × 7 × 3 × 8

= 9 × 56

= 504

By comparing your Expression with your Partner Expression, 500 is less than 504.

B)

26 × 38 = 13 × 2 × 19 × 2

= 4× 247

= 988

By comparing your Expression with your Partner Expression, 500 is less than 988.

C)

23 × 17

=391

By comparing your Expression with your Partner Expression, 500 is greater than 391.

D)

42 × 23 = 7 × 2 ×3 × 23

= 966

By comparing your Expression with your Partner Expression, 500 is less than 966.

**Construct Arguments**

Which estimated product do you think will be closer to the product of 29 and 37? Explain your reasoning.

Answer: 1,000 will be closer to 1,073

Explanation:

Given Product is

29 × 37 = 1,073

Given Expressions are:

25 × 40 = 1,000

30 × 40 = 1,200

Compare the given Product and the Expressions.

By comparison, we can conclude that 1,073 is close to 1,000.

**Think and Grow: Estimate Products**

You can estimate products using rounding or compatible numbers. Compatible numbers are numbers that are easy to multiply and are close to the actual numbers.

**Example**

Use rounding to estimate 57 × 38.

Step 1: Round each factor to the nearest ten.

Step 2: Multiply.

60 × 40 = 60 × 4 tens

= 240 tens

= 2400

So, 57 × 38 is about 2400.

**Example**

Use compatible numbers to estimate 24 × 31.

Step 1: Choose compatible numbers.

Step 2: Multiply.

25 × 30 = 25 × 3 tens

= 75 tens

= 750

So, 24 × 31 is about 750.

**Show and Grow**

**Use rounding to estimate the product.**

Question 1.

27 × 50

Answer: 1500

Explanation:

**Let 27 be Rounded to 30.**

Now, we have to find the result of 30 × 50.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

30 × 50 = 30 × (5 × 10)

= (30 × 5) × 10

= ( 3 × 10 × 5) × 10

= 150 × 10

= 1,500

B) By using the place-value method,

30 × 50 = 30 × 5 tens

= 3 tens × 5 tens

= 15 × 1 ten × 1ten

= 15 × 10 × 10

= 1500

So,

27 × 50 can be rounded to 1,500

Question 2.

42 × 14

Answer: 600

Explanation:

**Let 42 be Rounded to 40**

**Let 14 be Rounded to 15**

Now, we have to find the result of 40 × 15.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

40 × 15 = 15 × (4 × 10)

= (15 × 4) × 10

= ( 3 × 4 × 5) × 10

= 60 × 10

= 600

B) By using the place-value method,

40 × 15 = 15 × 4 tens

= 60 tens

= 60 × 10

= 600

So,

42 × 16 can be rounded to 600

Question 3.

61 × 73

Answer: 4,200

Explanation:

**Let 61 be Rounded to 60**

**Let 73 be Rounded to 70**

Now, we have to find the result of 60 × 70.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

60 × 70 = 60 × (7 × 10)

= (60 × 7) × 10

= ( 6 × 10 × 7) × 10

= 420 × 10

= 4,200

B) By using the place-value method,

60 × 70 = 60 × 7 tens

= 6 tens ×7 tens

= 42 × 1 ten × 1ten

= 42 × 10 × 10

= 4,200

So,

61 ×73 can be rounded to 4,200

**Use compatible numbers to estimate the product.**

Question 4.

19 × 26

Answer: 500

Explanation:

**Let 19 be Rounded to 20**

**Let 26 be Rounded to 25**

Now, we have to find the result of 20 × 25.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

20 × 25 = 25 × (2 × 10)

= (25 × 2) × 10

= ( 5 × 5 ×2) × 10

= 50 × 10

= 500

B) By using the place-value method,

20 × 25 = 25 × 2 tens

= 50 tens

= 50 × 1 ten

= 50 × 10

= 500

So,

19 ×26 can be rounded to 500

Question 5.

23 × 78

Answer: 2,000

Explanation:

**Let 23 be Rounded to 25**

**Let 78 be Rounded to 80**

Now, we have to find the result of 25 × 80.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

25 × 80 = 25 × (8 × 10)

= (25 × 8) × 10

= ( 5× 5 × 8) × 10

= 200 × 10

= 2,000

B) By using the place-value method,

25 × 80 = 25 × 8 tens

= 200 tens

= 200 × 10

= 2,000

So,

23 ×78 can be rounded to 2,000

Question 6.

74 × 20

Answer: 1,500

Explanation:

**Let 74 be Rounded to 75**

Now, we have to find the result of 75 × 20.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

75 × 20 = 75 × (2 × 10)

= (75 × 2) × 10

= ( 5 × 5 × 3 × 2) × 10

= 150 × 10

= 1,500

B) By using the place-value method,

75× 20 = 75 ×2 tens

= 150 tens

= 150× 10

= 1,500

So,

74 ×20 can be rounded to 1,500

**Apply and Grow: Practice**

**Estimate the product.**

Question 7.

41 × 73

Answer: 2,800

Explanation:

**Let 41 be Rounded to 40**

**Let 73 be Rounded to 70**

Now, we have to find the result of 40 × 70.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

40 × 70 = 40 × (7 × 10)

= (40 × 7) × 10

= ( 4 × 10 × 7) × 10

= 280 × 10

= 2,800

B) By using the place-value method,

40 × 70 = 40 × 7 tens

= 4 tens ×7 tens

= 28 × 1 ten × 1ten

= 28 × 10 × 10

= 2,800

So,

41 ×73 can be rounded to 2,800

Question 8.

52 × 84

Answer: 4,250

Explanation:

**Let 52 be Rounded to 50**

**Let 84 be Rounded to 85**

Now, we have to find the result of 50 × 85.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

50 × 85 = 85 × (5× 10)

= (85 × 5) × 10

= ( 17× 5 × 5) × 10

= 425 × 10

= 4,250

B) By using the place-value method,

50 × 85 = 85 × 5 tens

= 425 tens

= 425 × 10

= 4,250

So,

52 ×84 can be rounded to 4,250

Question 9.

26 × 68

Answer: 1,750

Explanation:

**Let 26 be Rounded to 25**

**Let 68 be Rounded to 70**

Now, we have to find the result of 25 × 70.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

25 × 70 = 25 × (7 × 10)

= (25 × 7) × 10

= ( 5 × 5 × 7) × 10

= 175 × 10

= 1,750

B) By using the place-value method,

25 × 70 = 25 × 7 tens

= 175 tens

= 175 × 10

= 1,750

So,

26 ×68 can be rounded to 1,750

Question 10.

38 × 17

Answer: 600

Explanation:

**Let 38 be Rounded to 40**

**Let 17 be Rounded to 15**

Now, we have to find the result of 40 × 15.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

15 × 40 = 15 × (4× 10)

= (15 × 4) × 10

= ( 5 × 3 × 4) × 10

= 60 × 10

= 600

B) By using the place-value method,

15 × 40 = 15 × 4 tens

= 60 tens

= 60 × 10

= 600

So,

38 ×17 can be rounded to 600

Question 11.

75 × 24

Answer: 1,875

Explanation:

**Let 24 be Rounded to 25**

Now, we have to find the result of 25 × 75.

We can find the Product by using the simplification method.

25 × 75

= 5 × 5 × 25 × 3

= 5 × 5× 5 × 5 × 3

= 25 × 25 × 3

= 625 × 3

= 1,875

So,

38 × 17 can be Rounded to 1,875

Question 12.

93 × 53

Answer: 4,500

Explanation:

**Let 93 be Rounded to 90**

**Let 53 be Rounded to 50**

Now, we have to find the result of 90 × 50.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

90 × 50 = 90 × (5 × 10)

= (90 × 5) × 10

= ( 5 × 2 × 9 × 5) × 10

= 450 × 10

= 4,500

B) By using the place-value method,

90 × 50 = 90 × 5 tens

= 9 tens × 5 tens

= 45 × 1 ten × 1 ten

= 45 × 10 × 10

= 4,500

So,

93 ×53 can be rounded to 4,500

Question 13.

44 × 78

Answer: 3,600

Explanation:

**Let 44 be Rounded to 45**

**Let 78 be Rounded to 80**

Now, we have to find the result of 45 × 80.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

45 × 80 = 45 × (8 × 10)

= (45 × 8) × 10

= ( 5 × 2 × 9 × 4) × 10

= 360 × 10

= 3,600

B) By using the place-value method,

45 × 80 = 45 × 8 tens

= 5 × 9 × 8 tens

= 45 × 8 × 10

= 360 × 10

= 3,600

So,

44 ×78 can be rounded to 4,500

Question 14.

21 × 33

Answer: 600

Explanation:

**Let 21 be Rounded to 20**

**Let 33 be Rounded to 30**

Now, we have to find the result of 20 × 30.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

20 × 30 = 20 × (3× 10)

= (20 × 3) × 10

= ( 5× 4 × 3) × 10

= 60 × 10

= 600

B) By using the place-value method,

20 × 30 = 30 × 2 tens

= 3 tens × 2 tens

= 6 × 10 × 10

= 600

So,

21 ×33 can be rounded to 600

Question 15.

45 × 45

Answer: 2,500

Explanation:

**Let 45 be Rounded to 50**

Now, we have to find the result of 50 × 50.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

50 × 50 = 50 × (5× 10)

= (50 × 5) × 10

= ( 10× 5 × 5) × 10

= 250 × 10

= 2,500

B) By using the place-value method,

50 × 50 = 50 × 5 tens

= 250 tens

= 25 × 10 × 10

= 2,500

So,

45 ×45 can be rounded to 2,500

**Open-Ended**

Write two possible factors that can be estimated as shown.

Question 16.

2,400

Answer:

Explanation:

The given number is: 2,400

The Products of 24 are:

4 × 6 = 24

6 × 4 =24

From the above two products, we can conclude that the two possible numbers that can give the product 2,400 are: 40, 60

Question 17.

1,200

Answer:

Explanation:

Explanation:

The given number is: 1,200

The Products of 12 are:

3 × 4 =12

4 × 3 =12

6 ×2 =12

2 ×6 =12

From the above two products, we can conclude that the two possible numbers that can give the product 2,400 are: 40, 30, and 20, 60

Question 18.

**DIG DEEPER!**

You use 50 × 30 to estimate 46 × 29. Will your estimate be greater than or less than the actual product? Explain.

Answer: We will Estimate the Product greater than the actual Product

Explanation:

Given Product is: 46 × 29

Explanation:

**Let 46 be Rounded to 50**

**Let 29 be Rounded to 30**

Now, we have to find the result of 50 × 30.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

50 × 30 = 50 × (3 × 10)

= (50 × 3) × 10

= ( 5 × 10 × 3) × 10

= 150 × 10

= 1,500

B) By using the place-value method,

50 × 30 = 30 × 5 tens

= 150 tens

= 150× 10

= 1,500

So,

46 ×29 can be rounded to 1,500

Question 19.

**YOU BE THE TEACHER**

Your friend uses rounding to estimate 15 × 72. She gets a product of 700. Is your friend’s estimate correct?

Explain.

Answer: No

Explanation:

Your friend is going to estimate 15 × 72 and she gets a product 700.

So, According to her Product, the Possible rounded off numbers to get the product 700 are 10 and 70

So, your Friend’s estimate is not correct.

Now,

**Let 72 be Rounded to 70**

Now, we have to find the result of 15 × 70.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

15 × 70 = 15 × (7 × 10)

= (15 × 7) × 10

= (3 × 5 × 7) × 10

= 105 × 10

= 1,050

B) By using the place-value method,

15 × 70 = 15 × 7 tens

= 105 tens

= 105 × 10

= 1,050

So,

15 ×72 can be rounded to 1,050

**Think and Grow: Modeling Real Life**

**Example**

About how much does 1 year of phone service cost?

Think: What do you know? What do you need to find? How will you solve it?

There are 12 months in 1 year, so multiply the price per month by 12.

12 × 24 = 288

Estimate the product.

Answer:

**Show and Grow**

Question 20.

Use the table above. About how much does 1 year of Internet service cost? About how much does 1 year of cable television service cost?

Answer:

Internet Service cost: $540

Cable television service cost: $1068

Explanation:

In the given table,

The Internet cost and cable television service costs are given per month.

For 1 year, there are 12 months.

So,

The cost of Internet service for a year is: 12 × $45 = $ 540

The cost of cable television service for a year is: 12 × $89 = 1068

Question 21.

A giant panda eats 28 pounds of food each day. An orca eats 17 times as much food as the panda eats each day. About how much food does the orca eat each day?

Answer: 476 Pounds

Explanation:

Given that a giant panda eats 28 pounds of food each day and an Orca eats 17 times as much food as the panda eats each day.

So,

The amount of food eaten by an Orca = 17 × The amount of food eaten by panda

= 17 × 28 = 476 pounds

### Estimate Products Homework & Practice 4.2

**Use rounding to estimate the product.**

Question 1.

42 × 13

Answer: 600

Explanation:

**Let 42 be Rounded to 40**

**Let 13 be Rounded to 15**

Now, we have to find the result of 40 × 15.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

40 × 15 = 15 × (4 × 10)

= (15 × 4) × 10

= ( 3 × 4 × 5) × 10

= 60 × 10

= 600

B) By using the place-value method,

40 × 15 = 15 × 4 tens

= 60 tens

= 60 × 10

= 600

So,

42 × 13 can be rounded to 600

Question 2.

56 × 59

Answer: 3,300

Explanation:

**Let 56 be Rounded to 55**

**Let 59 be Rounded to 60**

Now, we have to find the result of 55 × 60.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

55 × 60 = 55 × (6 × 10)

= (55 × 6) × 10

= ( 5 × 11 × 6) × 10

= 330 × 10

= 3,300

B) By using the place-value method,

55 × 60 = 55 × 6 tens

= 330 tens

= 330 × 10

= 3,300

So,

42 × 16 can be rounded to 600

Question 3.

19 × 91

Answer: 1,800

Explanation:

**Let 19 be Rounded to 20**

**Let91 be Rounded to 90**

Now, we have to find the result of 20 × 90.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

20 × 90 = 20 × (9× 10)

= (20 × 9) × 10

= ( 5 × 4 × 9) × 10

= 180 × 10

= 1,800

B) By using the place-value method,

20 × 90 = 20 × 9 tens

= 2 tens × 9 tens

= 18 × 1 ten × 1 ten

=18 × 10 × 10

= 18 × 100

= 1,800

So,

19 × 91 can be rounded to 1,800

**Use compatible numbers to estimate the product.**

Question 4.

23 × 78

Answer: 2,000

Explanation:

**Let 23 be Rounded to 25**

**Let 78 be Rounded to 80**

Now, we have to find the result of 25 × 80.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

25 × 80 = 25 × (8 × 10)

= (25 × 8) × 10

= ( 5 × 5 × 8) × 10

= 200 × 10

= 2,000

B) By using the place-value method,

25 × 80 = 25 × 8 tens

= 200 tens

= 200 × 10

= 2,000

So,

23 × 78 can be rounded to 2,000

Question 5.

67 × 45

Answer:3,150

Explanation:

**Let 67 be Rounded to 70**

Now, we have to find the result of 70 × 45.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

45 × 70 = 45 × (7 × 10)

= (45 × 7) × 10

= ( 5 × 9 × 7) × 10

= 315 × 10

= 3,150

B) By using the place-value method,

45 × 70 = 45 × 7 tens

= 315 tens

= 315 × 10

= 3,150

So,

67 × 45 can be rounded to 3,150

Question 6.

19 × 24

Answer: 500

Explanation;

**Let 19 be Rounded to 20**

**Let 24 be Rounded to 25**

Now, we have to find the result of 25 × 20.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

20 × 25 =25 × (2 × 10)

= (25 × 2) × 10

= ( 5 × 5 × 2) × 10

= 50 × 10

= 500

B) By using the place-value method,

25 × 20 = 25 × 2 tens

= 50 tens

= 50 × 10

= 500

So,

19 × 24 can be rounded to 500

**Estimate the product.**

Question 7.

84 × 78

Answer: 6,800

Explanation:

**Let 84 be Rounded to 85**

**Let 78 be Rounded to 80**

Now, we have to find the result of 85 × 80.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

85 × 80 = 85 × (8 × 10)

= (85 × 8) × 10

= ( 5 × 17 × 8) × 10

= 680 × 10

= 6,800

B) By using the place-value method,

85 × 80 = 85 × 8 tens

= 680 tens

= 680 × 10

= 6,800

So,

84 × 78 can be rounded to 600

Question 8.

92 × 34

Answer: 3,150

Explanation:

**Let 92 be Rounded to 90**

**Let 34 be Rounded to 35**

Now, we have to find the result of 90 × 35.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

90 × 35 = 35 × (9 × 10)

= (35 × 9) × 10

= ( 5 × 7 × 9) × 10

= 315 × 10

= 3,150

B) By using the place-value method,

90 × 35 = 35 × 9 tens

= 315 tens

= 315 × 10

= 3,150

So,

92 × 34 can be rounded to 3,150

Question 9.

57 × 81

Answer: 4,800

Explanation:

**Let 57 be Rounded to 60**

**Let 81 be Rounded to 80**

Now, we have to find the result of 80 × 60.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

80 × 60 = 80 × (6 × 10)

= (80 × 6) × 10

= ( 8 × 10 × 6) × 10

= 480 × 10

= 4,800

B) By using the place-value method,

80 × 60 = 80 × 6 tens

= 480 tens

= 480 × 10

= 4,800

So,

57 × 81 can be rounded to 600

**Open-Ended**

Write two possible factors that could be estimated as shown.

Question 10.

6,400

Answer:

Explanation:

The Products of 64 are:

8 × 8 = 64

16 × 4 =64

From the above two products, we can conclude that the two possible numbers that can give the product 6,400 are: 80,80 and. 160,40

Question 11.

1,600

Answer:

Explanation:

The Products of 16 are:

4 × 4 = 16

8 × 2 =16

From the above two products, we can conclude that the two possible numbers that can give the product 1,600 are: 40, 40 and, 80,20

Question 12.

**Reasoning**

Are both Newton’s and Descartes’s estimates reasonable? Explain.

Answer: Both Newton’s and Descartes’s estimates are reasonable

Explanation:

According to Newton,

**The estimated values of 27 and 68 are 30 and 70**

According to Descartes,

**The estimated values of 27 and 68 are 25 and 70**

According to Newton:

27 × 68 = 2,100

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

30 × 70 = 30 × (7 × 10)

= (30 × 7) × 10

= ( 3 × 10 × 7) × 10

= 210 × 10

= 2,100

B) By using the place-value method,

30× 70 = 30 ×7 tens

= 210 tens

= 210 × 10

= 2,100

So,

27 × 68 can be rounded to 2,100 ( According to Newton)

According to Descartes:

27 × 68 = 1,750

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

25 × 70 = 25 × (7 × 10)

= (25 × 7) × 10

= ( 5 × 5 × 7) × 10

= 175 × 10

= 1,750

B) By using the place-value method,

25× 70 = 25 ×7 tens

= 175 tens

= 175 × 10

= 1,750

So,

27 × 68 can be rounded to 1,750 ( According to Descartes)

Question 13.

**DIG DEEPER!**

You use 90 × 30 to estimate 92 × 34. Will your estimate be greater than or less than the actual product? Explain.

Answer: No

Your friend is going to estimate 92 × 34 and she gets a product 2,700.

So, your Friend’s estimate is not correct.

Now,

**Let 34 be Rounded to 35**

**Let 92 be Rounded to 90**

Now, we have to find the result of 35 × 90.

We can find the product of multiples of ten by using two methods. They are:

A) The place-value method B) Associative Property of Multiplication

A) By using the Associative Property of Multiplication,

35 × 90 = 35 × (9 × 10)

= (35 × 9) × 10

= (9× 5 × 7) × 10

= 315 × 10

= 3,150

B) By using the place-value method,

35 × 90 = 35 × 9 tens

= 315 tens

= 315 × 10

= 3,150

So,

92 ×34 can be rounded to 3,150

Question 14.

**Modeling Real Life**

About how many hours of darkness does Barrow, Alaska have in December?

Answer: 744 hours

Explanation:

From the above table,

The days of darkness in Barrow, Alaska are 31 days.

We know that there are 24 hours in a day.

So,

The number of hours of darkness does Barrow, Alaska have in December = 31 × 24 = 744 hours

**Review & Refresh**

Question 15.

Round 253,490 to the nearest ten thousand.

Answer: 250,000

Explanation;

The position of a given number is dependent on the place-value of that number.

So,

When 253,490 rounded off to the nearest ten thousand, the result ts **250,000**

Question 16.

Round 628,496 to the nearest hundred thousand.

Answer: 630,000

Explanation;

The position of a given number is dependent on the place-value of that number.

So,

When 628,496 rounded off to the nearest ten thousand, the result ts **630,000**

### Lesson 4.3 Use Area Models to Multiply Two-Digit Numbers

**Explore and Grow**

Draw an area model that represents 15 × 18. Then break apart your model into smaller rectangles.

What is the total area of your model? Explain how you found your answer.

Answer: The Total Area of your Model = 400

Explanation:

Count the number of boxes in both the vertical and horizontal directions.

Since all the sides of the figure look the same, take any 1 row in the vertical direction and horizontal direction and count the number of boxes in it.

After counting, you get

The number of boxes in a row present in the vertical direction is: 20

The number of boxes in a row present in the horizontal direction is: 20

So, we can find the total area of your model by multiplying the number of boxes in both the vertical and horizontal directions. ( Remember, there is no need to count all the boxes in both directions since the figure has an equal number of boxes on all sides)

So,

The total area of your model = 20 × 20 = 400

**Reasoning**

Compare with a partner. Do you get the same answer? Explain.

Answer: Yes

Explanation:

My Partner counted the number of boxes in the middle of the model in both vertical and horizontal directions.

He got,

The number of boxes in a row present in the vertical direction is: 20

The number of boxes in a row present in the horizontal direction is: 20

So,

The total area of my partner’s model = 20 × 20 = 400

So,

My partner and I got the same answer.

**Think and Grow: Use Area Models to Multiply**

**Example**

Use an area model and partial products to find 12 × 14.

Model the expression. Break apart 12 as 10 + 2 and 14 as 10 + 4.

Answer: 168

Explanation:

So, **12 × 14 = 168**

**Show and Grow**

**Use the area model to find the product.**

Question 1.

17 × 15 = _____

Answer: 255

Explanation:

So, **17 × 15 = 255**

Question 2.

34 × 22 = _____

Answer: 748

Explanation:

So, 34 × 22 = 748

**Apply and Grow: Practice**

**Use the area model to find the product.**

Question 3.

13 × 19 = _____

Answer: 247

Explanation:

So, **13 × 19 = 247**

Now,

100 + 90 + 30 + 27 = 247

So,

** 13 × 19 = 247**

Question 4.

25 × 39 = ____

Answer: 975

Explanation:

Now,

600 + 150 + 180 + 45 = 975

So,

** 25 × 39 = 975**

**Draw an area model to find the product.**

Question 5.

11 × 13 = ______

Answer: 143

Explanation:

By using the Partial Products method,

10 × 6 + 3 × 6 + 10 × 5 + 3 × 5

= 60 + 18 + 50 + 15 = 143

So,

** 11 × 13 = 143**

Question 6.

23 × 26 = ______

Answer: 598

Explanation:

By using the Partial products method,

20 × 20 + 3 × 20 + 20 × 6 + 3 × 6

= 400 + 60 + 120 + 18 = 598

So, ** 23 × 26 = 598**

Question 7.

27 × 45 = ______

Answer: 1,215

Explanation:

By using the partial products method,

20 × 20 + 7 × 20 + 20 × 25 + 7 ×25

= 400 + 140 +500 + 175 = 1,215

So, **27 × 45 = 1,215**

Question 8. Perseid meteors travel 59 kilometers each second. How far does a perseid meteor travel in 15 seconds?

Answer: 885 kilometers

Explanation:

Given that the Perseid meteors travel 59 kilometers each second.

So,

The distance traveled by the Perseid meteors in 15 seconds = 59 × 15 = 885 kilometers

From the above,

We can conclude that the **Perseid meteors travel 885 kilometers in 15 seconds.**

Question 9.

**DIG DEEPER!**

Write the multiplication equation represented by the area model.

Answer:

Explanation:

Using the Partial Products Model,

40 × 30 + 40 × 2 + 3 × 30 + 3 × 2

= 1,200 + 80 + 90 + 6 = 1,376

**So, the multiplication equation represented by area model = 43 × 32**

**Think and Grow: Modeling Real Life**

**Example**

A wind farm has 8 rows of new wind turbines and 3 rows of old wind turbines. Each row has 16 turbines. How many turbines does the wind farm have?

Answer: Add the number of rows of new turbines to the number of rows of old turbines

8 + 3 =11

So,

There are11 rows of turbines.

Multiply the number of rows by the number in each row.

So, the wind farm has 176 turbines.

**Show and Grow**

Question 10.

You can type 19 words per minute. Your cousin can type 33 words per minute. How many more words can your cousin type in 15 minutes than you?

Answer: 210 words

Explanation:

Given that you can type 19 words per minute and your cousin can type 33 words per minute.

So,

The number of words you can type in 15 minutes = 19 × 15 = 285

The number of words your cousin can type in 15 minutes = 495

Hence,

**The number of words you have to type more than your cousin in 15 minutes = 495 – 285 = 310 words**

Question 11.

A store owner buys 24 packs of solar eclipse glasses. Each pack has 12 glasses. The store did not sell 18 of the glasses. How many of the glasses did the store sell?

Answer: 270 glasses

Explanation:

Given that a store Owner buys 24 packs of solar eclipse glasses and each pack has 12 glasses.

So,

the total number of glasses that a store owner buy = 24 × 12 = 288 glasses

But,

It is also given that the store owner did not sell 18 glasses.

**Hence, the total number of glasses the store owner sold = 288 – 18 = 270 glasses**

### Use Area Models to Multiply Two-Digit Numbers Homework & Practice 4.3

**Use the area model to find the product.**

Question 1.

12 × 13 = ______

Answer: 156

Explanation:

By using the partial products method,

10 × 10 + 2 ×10 + 10 × 3 + 2 ×3

= 100 + 20 +30 + 6 = 156

So, **12 × 13 = 156**

Question 2.

38 × 24 = _____

Answer: 912

Explanation:

By using the Partial products method,

30 × 20 + 8 × 20 + 30 × 4 + 8 × 4

= 600 + 160 + 120 + 32 = 912

So, ** 38 × 24 = 912**

**Use the area model to find the product.**

Question 3.

19 × 18 = ____

Answer: 342

Explanation:

By using the partial products method,

10 × 10 +8 × 10 + 10 × 9 +9 ×8

= 100 + 80 +90 + 72 = 342

So, **19 × 18 = 342**

Question 4.

23 × 25 = _____

Answer: 575

Explanation:

By using the partial products method,

20 × 20 +5 × 20 + 3 × 20 +3 ×5

= 400 + 100 +60 + 15 = 575

So, **23 × 25 = 575**

**Draw an area model to find the product.**

Question 5.

26 × 31 = _____

Answer: 806

Explanation:

By using the partial products method,

20 × 30 +6× 30 + 1 × 20 +6 ×1

= 600 + 180 +20 + 6 = 806

So, **26 × 31 = 806**

Question 6.

22 × 47 = ______

Answer: 1,034

Explanation:

By using the partial products method,

20 × 40 +2×40 + 7 × 20 +2 ×7

= 800 + 80 +140 + 14 = 1,034

So, **22 × 47 = 1,034**

Question 7.

**YOU BE THE TEACHER**

Your friend finds 12 × 42. Is your friend correct? Explain.

Answer: Yes, your friend is correct.

Explanation:

By using the partial products method,

10 × 40 +2×10 + 2 × 40 +2 ×2

= 400 + 20 +80 + 4 = 504

So, **12 × 42 = 504**

Question 8.

**Writing**

Explain how to use an area model and partial products to multiply two-digit numbers.

Answer:

Let the Partial Products are: a, b, c, d

By using the Partial Products method,

a × c + b × c + a × d + b × d

= ac + bc + ad + bd

So, by using the above method, we can find the product of 2- digit numbers.

Question 9.

**Modeling Real Life**

A mega-arcade has 9 rows of single-player games and 5 rows of multi-player games. Each row has 24 games. How many games does the arcade have?

Answer: The arcade has 336 games

Explanation:

Given that a mega arcade has 9 rows of single-player games and 5 rows of multi-player games.

So,

Total number of rows present in the arcade = 9 + 5 = 14

It is also given that each row has 24 games.

So,

The total number of games present in the arcade = 14 × 24 = 336

By using the partial products method,

10 × 20 +4 × 20 + 10 × 4 + 4 ×4

= 200 + 80 +40 + 16 = 336

So, **14 × 24 = 336**

**Review & Refresh**

**Find the sum. Check whether your answer is reasonable.**

Question 10.

Answer: 84,016

Explanation:

To find the sum, add the digits starting from the Right-most position. If there is “Carry”, then add that carry to the result of the next Position value.

Question 11.

Answer: 71,585

Explanation:

To find the sum, add the digits starting from the Right-most position. If there is “Carry”, then add that carry to the result of the next Position value. (As shown in the above figure)

Question 12.

Answer: 569,821

Explanation:

To find the sum, add the digits starting from the Right-most position. If there is “Carry”, then add that carry to the result of the next Position value. (As shown in the above figure)

### Lesson 4.4 Use the Distributive Property to Multiply Two-Digit Numbers

**Explore and Grow**

Use as few base ten blocks as possible to create an area model for 13 × 24. Draw to show your model.

Color your model to show four smaller rectangles. Label the partial products.

Answer:

By using the partial products method,

10 × 20 +3 × 20 + 4 × 3 + 10 ×4

= 200 + 60 +12 + 40 = 312

So, **13 × 24 = 312**

**Reasoning**

How do you think the Distributive Property relates to your area model? Explain.

Answer:

Distributive Property of Multiplication:

Let there are 3 numbers a, b, c.

The Distributive property is given as:

a × (b + c) = ( a × b) + ( a × c)

SO, by using the above property, we can conclude that the Distributive Property relates to your area model.

**Think and Grow: Use the Distributive Property to Multiply**

**Example**

Find 17 × 25.

One Way: Use an area model and partial products.

**Show and Grow**

Question 1.

Use the area model and the Distributive Property to find 32 × 19.

Answer: 608

Explanation:

Using the Distributive Property, we can find the product of 32 × 19

32 × 19 = 32 × ( 10 + 9)

= ( 32 × 10 ) + ( 32 × 9)

= ( 30 + 2 ) × 10 + ( 30 + 2 ) × 9

= ( 30 × 10 ) + ( 2 × 10 ) + ( 30 × 9 ) + ( 2 × 9)

= 300 + 20 + 270 + 18

= 608

So, **32 × 19 = 608**

**Apply and Grow: Practice**

Question 2.

Use the area model and the Distributive Property to find 34 × 26.

Answer: 884

Explanation:

Using the Distributive Property, we can find the product of 34 × 26

34 × 26 = 34 × ( 20 + 6)

= ( 34 × 20 ) + ( 34 × 6)

= ( 30 + 4 ) × 20 + ( 30 + 4 ) × 6

= ( 30 × 20 ) + ( 4 × 20 ) + ( 30 × 6 ) + ( 4 × 6)

= 600 + 80 + 180 + 24

= 884

So, **34 × 26 = 884**

**Use the Distributive Property to find the product.**

Question 3.

28 × 47 = 28 × (40 + 7)

= (28 × 40) + (28 × 7)

= (20 + 8) × 40 + (20 + 8) × 7

= (20 × 40) + (8 × 40) + (20 × 7) + (8 × 7)

= 800 + 320 + 140 + 56

=1,316

So, 28 × 47 = 1,316

Answer: **28 × 47 = 1,316**

Question 4.

39 × 41 = _____

Answer:

39 × 41 = 39 × (40 + 1)

= (39 × 40) + (39 × 1)

= (30 + 9) × 40 + (30 + 9) × 1

= (30 × 40) + (9 × 40) + (30 × 1) + (9 ×1)

=1,200 + 360 + 30 + 9

=1,599

So, **39 × 41 = 1,599**

Question 5.

74 × 12 = ______

Answer:

74 × 12 = 74 × (10 + 2)

= (74 × 10) + (74 × 2)

= (70 + 4) × 10 + (70 + 4) × 2

= (70 × 10) + (4 × 10) + (70 × 2) + (4 ×2)

=700 + 40 + 140 + 8

=888

So, **74 × 12 = 888**

Question 6.

83 × 65 = _____

Answer:

83 × 65 = 83 × (60 + 5)

= (83 × 60) + (83 × 5)

= (80 + 3) × 60 + (80 + 3) ×5

= (80 × 60) + (3 × 60) + (80 × 5) + (3 ×5)

=4,800 + 180 + 400 + 15

=5,395

So, **83 × 65 = 5,395**

Question 7.

**Which One Doesn’t Belong?**

Which expression does not belong with the other three?

Answer:

Let the given Expressions be ordered as A), B), C) and D)

From the Order, we can say that Expression C) does not belong to the other three.

Explanation:

The given Expressions are:

A) ( 40 + 7) × 52

B) ( 40 + 7) × (50 + 2)

C) ( 40 × 7) × ( 50 × 2)

D) 47 × ( 50 + 2)

The given Expressions are written using the Distributive Property of Multiplication.

The Distributive property is given as:

a × (b + c) = ( a × b) + ( a × c)

So, from the above Property, we can conclude that **Expression C) does not belong to the other three**.

**Think and Grow: Modeling Real Life**

**Example**

The dunk tank at a school fair needs 350 gallons of water. There are 27 students in a class. Each student pours13 gallons of water into the tank. Is there enough water in the dunk tank?

Find how many gallons of water the students put in the dunk tank.

Given that there are 350 gallons at a school fair.

But, we got 351 gallons of water.

So, there is 1 gallon enough water in the dunk tank.

**Show and Grow**

Question 8.

An event coordinator orders 35 boxes of T-shirts to give away at a baseball game. There are 48 T-shirts in each box. If 2,134 fans attend the game, will each fan get a T-shirt?

Answer: No, each fan will not get a T-shirt.

Explanation:

Given that an event coordinator orders 35 boxes of T-shirts to give away at a baseball game and there are 48 T-shirts in each box.

So, we will get the total number of T-shirts due to the Product of 35 × 48.

We will get the product by using the Distributive Property of Multiplication.

35 × 48 = 35 × (40 + 8)

= (35 × 40) + (35 × 8)

= (30 + 5) × 40 + (30 + 5) × 8

= (30 × 40) + (5 × 40) + (30 × 8) + (8 ×5)

=1,200 + 20 + 240 + 40

=1,680

So, **35× 48 = 1,680**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 9.

A horse owner must provide 4,046 square meters of pasture for each horse. Is the pasture large enough for 2 horses? Explain.

Answer: Yes, the pasture is large enough for 2 horses.

Explanation:

Given that a horse owner must provide 4,046 square meters for each horse.

But, it is also given that the area of pasture is 86 × 96 square meters.

We have to find the Product of 86 × 96 by using the Distributive Property of Multiplication..

86 × 96 = 86 × (90 + 6)

= (86 × 90) + (86 × 6)

= (80 + 6) × 90 + (80 + 6) × 6

= (80 × 90) + (6 × 90) + (80 × 6) + (6 ×6)

=7,200 + 540 + 480 + 36

=8,256

So, **86× 96 = 8,256**

By comparing the area of the pasture of each horse and the Product, we can conclude that the pasture is large enough for the 2 horses.

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

### Use the Distributive Property to Multiply Two-Digit Numbers Homework & Practice 4.4

Question 1.

Use the area model and the Distributive Property to find 45 × 21.

Answer: 945

Explanation: By using the Distributive Property of Multiplication,

45 × 21 = 45 × (20 + 1)

= (45 × 20) + (45 × 1)

= (40 + 5) × 20 + (40 + 5) ×1

= (20 × 40) + (5 × 20) + (40 × 1) + (1 ×5)

=800 + 100 + 40 + 5

=945

So, **45× 21 = 945**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 2.

Use the Distributive Property to find the product.

34 × 49 = 34 × (40 + 9)

= (34 × 40) + (34 × 9)

= (30 + 4) × 40 + (30 + 4) × 9

= (30 × 40) + (4 × 40) + (30 × 9) + (4 × 9)

= 1,200 +160 + 270 + 36

= 1,666

**So, 34 × 49 =1,666**

Question 3.

14 × 27 = ______

Answer: 378

Explanation: Using the Distributive Property of Multiplication,

14 × 27 = 14 × (20 + 7)

= (14 × 20) + (14 × 7)

= (10 + 4) × 20 + (10 + 4) × 7

= (10 × 20) + (4 × 20) + (10 × 7) + (4 ×7)

=200 + 80 + 70 + 28

=378

So, **14× 27 = 378**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 4.

38 × 31 = ______

Answer: 1,178

Explanation: Using the Distributive Property of Multiplication,

38 × 31 = 38 × (30 + 1)

= (38 × 30) + (38 × 1)

= (30 + 8) × 30 + (30 + 8) ×1

= (30 × 30) + (8× 30) + (30 × 1) + (8 ×1)

=900 + 240 + 30 + 8

=1,178

So, **38× 31 = 1,178**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 5.

58 × 26 = ______

Answer: 1,508

Explanation: Using the Distributive Property of Multiplication,

58 × 26 = 58 × (20 + 6)

= (58 × 20) + (58 × 6)

= (50 + 8) × 20 + (50 + 8) × 6

= (50 × 20) + (8 × 20) + (50 × 6) + (8 ×6)

=1,000 + 160 + 300 + 48

=1,508

So, **58× 26 = 1,508**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 6.

56 × 32 = ______

Answer: 1,792

Explanation: Using the Distributive Property of Multiplication,

56 × 32 = 56 × (30 + 2)

= (56 × 30) + (56× 2)

= (50 + 6) × 30 + (50 + 6) × 2

= (30 × 50) + (6 × 30) + (50 × 2) + (6 ×2)

=1,500 + 180 + 100 + 12

=1,792

So, **56× 32 = 1,792**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 7.

87 × 23 = ______

Answer: 2,001

Explanation: Using the Distributive Property of Multiplication,

87 × 23 = 87 × (20 + 3)

= (87 × 20) + (87 × 3)

= (80 + 7) × 20 + (80 + 7) × 3

= (80 × 20) + (7 × 20) + (3 × 80) + (7 ×3)

=1,600 + 140 + 240 + 21

=2,001

So, **87× 23 = 2,001**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 8.

95 × 81 = ______

Answer: 7,695

Explanation: Using the Distributive Property of Multiplication,

95 × 81 = 95 × (80 + 1)

= (95 × 80) + (95 × 1)

= (90 + 5) × 80 + (90 + 5) × 1

= (90 × 80) + (5 × 80) + (90 × 1) + (1 ×5)

=7,200 + 400 + 90 + 5

=7,695

So, **95× 81 = 7,695**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 9.

**DIG DEEPER!**

Find 42 × 78 by breaking apart 42 first.

Answer: 3,276

Explanation: Using the Distributive Property of Multiplication,

42 × 78 = 78 × (40 + 2)

= (78 × 40) + (78 × 2)

= (70 + 8) × 40 + (70 + 8) × 2

= (70 × 40) + (8 × 40) + (70 × 8) + (8 ×2)

=2,800 + 320 + 560 + 16

=3,276

So, **42× 78 = 3,276**

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

Question 10.

**Modeling Real Life**

The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?

Answer: The 29 real elephants would reach the top of the building even when they stand on top of each other.

Explanation:

Give that the Elephant Building is 335 feet high. It is also given that a real Asian Elephant is 12 feet tall and there are 29 real elephants.

So, we have to find the height of 29 real elephants. We can find it using the product of 29 × 12.

We find the product by using the Distributive Property of Multiplication.

29 × 12 = 12 × (20 + 9)

= (12 × 20) + (12 × 9)

= (10 + 2) × 20 + (10 + 2) × 9

= (10 × 20) + (2 × 20) + (10 × 9) + (2 ×9)

=200 + 40 + 90 + 18

=348

So, **29× 12 = 348**

We get the result of the Product as 348 feet but given that the Elephant Building is 335 feet high.

From this, we can conclude that if 29 real elephants could stand on top of each other, they would reach the top of the building

**Note:**

**The Distributive property is given as:**

**a × (b + c) = ( a × b) + ( a × c)**

**Review & Refresh**

**Find the difference. Then check your answer.**

Question 11.

Answer: 25,259

Explanation:

The difference between the multi-digit numbers can be found by the difference taken from the left-most digit. If the number we want to subtract is less than the number to be subtracted, then we will take the carry from the Previous digit and the Previous digit contains 1 less number.

Question 12.

Answer: 53,162

Explanation:

The difference between the multi-digit numbers can be found by the difference taken from the left-most digit. If the number we want to subtract is less than the number to be subtracted, then we will take the carry from the Previous digit and the Previous digit contains 1 less number.

Question 13.

Answer: 140,938

Explanation:

The difference between the multi-digit numbers can be found by the difference taken from the left-most digit. If the number we want to subtract is less than the number to be subtracted, then we will take the carry from the Previous digit and the Previous digit contains 1 less number.

### Lesson 4.5 Use Partial Products to Multiply Two-Digit Numbers

**Explore and Grow**

How can you use the rectangles to find 24 × 53? Complete the equation.

24 × 53 = _____

Answer: 1,272

Explanation:

By using the partial products method,

24 × 53 = 50 × 20 +3 × 20 + 4 × 3 + 50 ×4

= 1,000 + 60 +12 + 200 = 1,272

So, **53 × 24 = 1,272**

**Reasoning**

What does the area of each rectangle represent.

Answer:

**Think and Grow: Use Partial Products to Multiply Two-DigitNumbers**

**Example**

Use place value and partial products to find 27 × 48.

Estimate: **30 × 50 = 1,500**

So, **27 × 48 =1296**

Check: Because **1,296** is close to the estimate, **1,500**, the answer is reasonable.

**Show and Grow**

**Find the product. Check whether your answer is reasonable.**

Question 1.

Estimate: ______

Answer: 585

Explanation:

Using the Partial Products method,

39 × 15 = ( 30 + 9) × ( 10 + 5)

= 30 × 10 + 9 × 10 + 30 × 5 + 9 × 5

= 300 + 90 + 150 + 45

= 585

Estimate:

**Let 39 be Rounded to 40.**

So, **40 × 15 = 600**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 2.

Estimate: ______

Answer: 5,166

Explanation:

Using the Partial Products method,

82 × 63 = ( 80 + 2) × ( 60 + 3)

= 80 × 60 + 2 × 60 + 80 × 3 + 2 × 3

= 4,800 + 120 + 240 + 6

= 5,166

Estimate:

**Let 82 be Rounded to 80.**

**Let 63 be Rounded to 65.**

So, 8**0 × 65 = 5,200**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 3.

Estimate: _______

Answer: 3,976

Explanation:

Using the Partial Products method,

56 × 71 = ( 50 + 6) × ( 70 + 1)

= 50 × 70 + 1 × 50 + 70 × 6 + 6 × 1

= 3,500 + 50 + 420 + 6

= 3,976

Estimate:

**Let 56 be Rounded to 55.**

**Let 71 be Rounded to 70.**

So,** 55 × 70 = 3,850**

As the Estimate and the actual answer are not near, the answer is not reasonable.

**Apply and Grow: Practice**

**Find the product. Check whether your answer is reasonable.**

Question 4.

Estimate: _____

Answer: 364

Explanation:

Using the Partial Products method,

14 × 26 = ( 10 + 4) × ( 20 + 6)

= 10 × 20 + 10 × 6 + 20 × 4 + 4 × 6

= 200 + 60 + 80 + 24

= 364

Estimate:

**Let 26 be Rounded to 25.**

**Let 14 be Rounded to 15.**

So, 25** × 15 = 375**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 5.

Estimate: _____

Answer: 1,767

Explanation:

Using the Partial Products method,

57 × 31 = ( 50 + 7) × ( 30 + 1)

= 50 × 30 + 1 × 50 + 30 × 7 + 7 ×1

= 1,500 + 50 + 210 + 7

= 1,767

Estimate:

**Let 57 be Rounded to 55. (or) Let 57 be Rounded to 60.**

**Let 31 be Rounded to 30.**

So, 3**0 × 55 = 1,650 (or) 30 × 60 = 1,800**

As the Estimate and the actual answer are near, the answer is reasonable. ( Depending on the Estimate value).

Question 6.

Estimate: _______

Answer: 2,116

Explanation:

Using the Partial Products method,

23 × 92 = ( 20 +3) × ( 90 + 2)

= 20 × 90 + 2 × 20 + 90 × 3 + 3 ×2

= 1,800 + 40 + 270 + 6

= 2,116

Estimate:

**Let 23 be Rounded to 25.**

**Let 92 be Rounded to 90.**

So, 9**0 × 25 = 2,250 **

As the Estimate and the actual answer are near, the answer is reasonable.

Question 7.

Estimate: ______

13 × 98 = ______

Answer: 1,274

Explanation:

Using the Partial Products method,

13 × 98 = ( 10 + 3) × ( 90 +8)

= 10 × 90 + 3 × 90 + 10 × 8 + 3 ×8

= 900 + 270 + 80 + 24

= 1,274

Estimate:

**Let 13 be Rounded to 15.**

**Let 98 be Rounded to 100.**

So, 15** × 100 = 1,500 **

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 8.

Estimate: ______

65 × 22 = ______

Answer: 1,430

Explanation:

Using the Partial Products method,

65 × 22 = ( 60 + 5) × ( 20 + 2)

= 60 × 20 + 60 × 2 + 20 × 5 + 5 ×2

= 1,200 + 120 + 100 + 10

= 1,430

Estimate:

**Let 22 be Rounded to 20.**

So, **20 × 65 = 1,300**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 9.

Estimate: ______

72 × 81 = _____

Answer: 5,832

Explanation:

Using the Partial Products method,

72 × 81 = ( 70 + 2) × (80 + 1)

= 70 × 80 + 1 × 70 + 80 × 2 + 2 ×1

= 5,600 + 70 + 160 + 2

= 5,832

Estimate:

**Let 72 be Rounded to 70.**

**Let 81 be Rounded to 80.**

So, 7**0 × 80 = 5,600**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 10.

A farmer has 58 cows. Each cow produces 29 liters of milk. How many liters of milk do the cows produce in all?

Answer: 1,682 liters

Explanation:

Given that a farmer has 58 cows and each cow gives 29 liters of milk.

So, to find the total quantity of milk, we have to find the Product of 58 × 29 by using the Partial Products method.

Now,

Using the Partial Products method,

58 × 29 = ( 50 + 8) × ( 20 + 9)

= 50 × 20 + 9 × 50 + 20 ×8 + 8 ×9

= 1,000 + 450 + 160 + 72

= 1,682

From the above value, we can conclude that the total quantity of milk produces is 1,682 liters.

Question 11.

**Number Sense**

How much greater is the product of 12 and 82 than the product of 11 and 82? Explain how you know without multiplying.

Answer: The product of 12 and 82 * is greater than 82* than the product of 11 and 82.

Explanation:

The given Products are

A) product of 12 and 82 B) product of 11 and 82

From the above, we can see that both the products have “82” as a Common number. So, find the difference between the remaining 2 numbers and we find that difference as ‘1’.

From this, we can conclude that the product of 12 and 82 * is greater than 82* than the product of 11 and 82.

To verify this, we can find the products using the Partial Products method.

Now,

12 × 82 = ( 10 + 2) × ( 80 +2)

= 10 × 80 + 10 × 2 + 80 × 2 + 2 ×2

= 800 + 20 + 160 + 4

= 984

11 × 82 = ( 10 + 1) × ( 80 + 2)

= 10 × 80 + 10 × 2 + 80 ×1 + 2 × 1

= 800 + 20 + 80 + 2

= 902

Now,

**984 – 902 = 82**

By multiplication also, we can conclude that the product of 12 and 82

*than the product of 11 and 82.*

**is greater than 82**Question 12.

**DIG DEEPER!**

Write the multiplication equation shown by the partial products.

200 + 60 + 50 + 15

Answer: **13 × 25**

Explanation:

By using the Partial Products method,

200 + 60 + 50 + 15

= 20 × 10 + 20 × 3 + 5 ×10 + 5 × 3

= ( 10 + 3) × 20 +( 10 + 3) × 5

= ( 10 + 3) × ( 20 + 5)

=** 13 × 25**

**Think and Grow: Modeling Real Life**

**Example**

How many hours does a koala sleep in 2 weeks?

Find how many hours a koala sleeps each day.

We know that,

1 week = 7 days

So,

2 weeks = 2 × 7 days = 14 days

Hence,

A koala sleeps 308 hours in 2 weeks.

**Show and Grow**

Question 13.

Use the table above. How many hours does a python sleep in 3 weeks?

Answer: 378 hours

Explanation:

From the above table, we can conclude that the python sleeps for 18 hours a day.

We know that,

1 week = 7 days

So,

3 weeks = 3 × 7 = 21 days

Hence, to find how many hours a python sleep in 3 weeks, we have to find the product of 18 × 21.

Using the Partial Products method,

18 × 21 = ( 10 + 8) × ( 20 +1)

= 10 × 20 + 10 × 1 + 20 × 8 + 8 ×1

= 200 + 10 + 160 + 8

= 378

Hence, from the above,

we can conclude that the python sleeps for 378 hours in 3 weeks.

Question 14.

You have 12 packets of pea seeds and23 packets of cucumber seeds. How many fewer pea seeds do you have than cucumber seeds?

Answer: 102 pea seeds are less than cucumber seeds

Explanation:

Given that there are 12 packets of pea seeds and 23 packets of cucumber seeds.

From the table,

The number of seeds in each packet of pea seeds = 12 × 6 = 72

The number of seeds in each packet of cucumber = 12 × 3 = 36 + 6 = 42

So,

The total number of seeds in pea = 72 × 12

The total number of seeds in cucumber = 42 × 23

By using the Partial Products method,

72 × 12 = ( 10 + 2) × ( 70 +2)

= 10 × 70 + 10 × 2 + 2 × 70 + 2 ×2

= 700 + 20 + 140 + 4

= 864

42 × 23 = ( 40 + 2) × ( 20 +3)

= 40 × 20 + 40 × 3 + 20 × 2 + 2 ×3

= 800 + 120 + 40 + 6

= 966

So,

**The number of pea seeds less than the cucumber seeds = 966 – 864 = 102 seeds**

### Use Partial Products to Multiply Two-Digit Numbers Homework & Practice 4.5

**Find the product. Check whether your answer is reasonable.**

Question 1.

Estimate: _______

Answer: 442

Explanation:

Using the Partial Products method,

17 × 26 = ( 10 + 7) × ( 20 + 6)

= 10 × 20 + 10 × 6 + 20 × 7 + 7 × 6

= 200 + 140 + 60 + 24

= 424

Estimate:

**Let 17 be Rounded to 15.**

**Let 26 be Rounded to 25.**

So, **25 × 15 = 375**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 2.

Estimate: _____

Answer: 2,356

Explanation:

Using the Partial Products method,

38 × 62 = ( 30 + 8) × ( 60 + 2)

= 30 × 60 + 30 × 2 + 60 × 8 + 8 × 2

= 1,800 + 60 + 480 + 16

= 2,356

Estimate:

**Let 38 be Rounded to 40.**

**Let 62 be Rounded to 60.**

So, **40 × 60 = 2,400**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 3.

Estimate: ______

Answer: 3,913

Explanation:

Using the Partial Products method,

91 × 43 = ( 90 + 1) × ( 40 + 3)

= 90 × 40 + 90 × 3 + 40 × 1 + 3 × 1

= 3,600 + 270 + 40 + 3

= 3,913

Estimate:

**Let 91 be Rounded to 90.**

**Let 43 be Rounded to 45.**

So, **90 × 45 = 4,050**

As the Estimate and the actual answer are not near, the answer is not reasonable.

**Find the product. Check whether your answer is reasonable.**

Question 4.

Estimate: _____

Answer: 3,774

Explanation:

Using the Partial Products method,

51 × 74 = ( 50 + 1) × ( 70 + 4)

= 50 × 70 + 50 × 4 + 70 × 1 + 4 × 1

= 3,500 + 200 + 70 + 4

= 3,774

Estimate:

**Let 51 be Rounded to 50.**

**Let 74 be Rounded to 75.**

So, **50 × 75 = 3,750**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 5.

Estimate: ______

Answer: 532

Explanation:

Using the Partial Products method,

28 × 19 = ( 20 + 8) × ( 10 + 9)

= 10 × 20 + 20 × 9 + 10 × 8 + 9 × 8

= 200 + 180 + 80 + 72

= 532

Estimate:

**Let 28 be Rounded to 30.**

**Let 19 be Rounded to 20.**

So, **30 × 15 = 600**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 6.

Estimate: ______

Answer: 1,575

Explanation:

Using the Partial Products method,

35 × 45 = ( 30 + 5) × ( 40 + 5)

= 30 × 40 + 30 × 5 + 40 × 5 + 5 × 5

= 1,200 + 150 + 200 + 25

= 1,575

There is no need for Estimate because they are already rounded numbers. So, the answer is reasonable.

Question 7.

Estimate: ______

82 × 63 = ______

Answer: 5,166

Explanation:

Using the Partial Products method,

82 × 63 = ( 80 + 2) × ( 60 + 3)

= 80 × 60 + 80 × 3 + 60 × 2 + 2 × 3

= 4,800 + 240 + 120 + 6

= 5,166

Estimate:

**Let 82 be Rounded to 80.**

**Let 63 be Rounded to 65.**

So, **80 × 65 = 5,200**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 8.

Estimate: ______

36 × 93 = ______

Answer: 3,348

Explanation:

Using the Partial Products method,

36 × 93 = ( 30 + 6) × ( 90 + 3)

= 30 × 90 + 30 × 3 + 90 × 6 + 3 × 6

= 2,700 + 90 + 540 + 18

= 3,348

Estimate:

**Let 36 be Rounded to 35.**

**Let 93 be Rounded to 95.**

So, **35 × 95 = 3,325**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 9.

Estimate: _______

57 × 22 = ______

Answer: 1,254

Explanation:

Using the Partial Products method,

57 × 22 = ( 50 + 7) × ( 20 + 2)

= 50 × 20 + 50 × 2 + 20 × 7 + 7 × 2

= 1,000 + 100 + 140 + 14

= 1,254

Estimate:

**Let 57 be Rounded to 55.**

**Let 22 be Rounded to 20.**

So, **55 × 20 = 1,100**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 10.

**DIG DEEPER!**

Find the missing digits. Then find the product.

Answer: The missing digits are 1, 1

Explanation:

Using the Partial Products method,

100 + 50 + 60 + 30

= 10 × 10 + 10 × 5 + 10 × 6 + 5 × 6

= 10( 10 + 5) + 6( 10 + 5)

= ( 10 + 5) × ( 10 + 6)

= 15 × 16

So,

From the above, we can conclude that the missing digits are: 1, 1

Question 11.

**Modeling Real Life**

If Newton meets his goal each month, how many liters of water will he drink in 1 year?

Answer: 396 liters of water

Explanation;

Given,

Each ♦ = 6 liters

From this,

Half ♦ = 3 liters

From the above table,

Monthly water Intake by Newton = 6 × 5 + 3 = 33 liters

So, The yearly intake by Newton can find out by the product of 33 × 12. ( Since a year has 12 months)

Using the Partial Products method,

33 × 12 = ( 30 + 3) × ( 10 + 2)

= 30 × 10 + 30 × 2 + 10 × 3 + 3 × 2

= 300 + 60 + 30 + 6

= 396 liters

From the above,

**we can conclude that the yearly intake by Newton is: 396 liters**

Question 12.

**Modeling Real Life**

Use the table in Exercise 11. If you and Descartes each meet your goal each month, how many more liters will you drink in 1 year than Descartes?

Answer: 468 liters

Explanation;

From the above table,

Given that,

The monthly intake of water by you = 6 × 7 + 3 = 45 liters

The monthly intake of water by Descartes = 6 liters

We know that 1 year consists of 12 months.

So,

The yearly intake of water by Descartes = 12 × 6 = 72 liters

The yearly intake of water by you = 45 × 12

We have to find 45 × 12 using the Partial Products method.

45 × 12 = ( 40 + 5) × ( 10 +2)

= 10 × 40 + 40 × 2 + 5 × 10 + 5 ×2

= 400 + 80 + 50 + 10

= 540 liters

Hence,

**The amount of water you drink more than Descartes = 540 – 72 = 468 liters**

**Review & Refresh**

**Add or subtract. Then check your answer.**

Question 13.

512,006 + 318,071 = ______

Answer: 830,077

Explanation:

To find the sum, add the digits starting from the Right-most position. If there is “Carry”, then add that carry to the result of the next Position value.

Question 14.

746,620 – 529,706 = ______

Answer: 216,914

The difference between the multi-digit numbers can be found by the difference taken from the left-most digit. If the number we want to subtract is less than the number to be subtracted, then we will take the carry from the Previous digit and the Previous digit contains 1 less number.

### Lesson 4.6 Multiply Two-Digit Numbers

**Explore and Grow**

Use base ten blocks to model each product. Draw each model.

Answer:

**Reasoning**

How are the models related to the product 17 × 13?

Answer:

The above model shows the pattern of the Partial Products method.

According to the Partial Products method,

(10 +7) × (10 + 3 ) ( As in the above model)

= 17 × 13

**Think and Grow: Multiply Two-Digit Numbers**

**Show and Grow**

**Find the product. Check whether your answer is reasonable.**

Question 1.

Estimate: ______

Answer: 1,312

Explanation: Using the Partial Products method,

41 × 32 = ( 40 + 1) × ( 30 +2)

= 30 × 40 + 40 × 2 + 1 × 30 + 1 ×2

= 1,200 + 80 + 30 + 2

= 1,312

Estimate:

**Let 41 be Rounded to 40.**

**Let 32 be Rounded to 30.**

So, **40 × 30 = 1,200**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 2.

Estimate: _____

Answer: 2,392

Explanation: Using the Partial Products method,

52 × 46 = ( 50 + 2) × ( 40 +6)

= 50 × 40 + 50 × 6 +2 × 40 + 6 ×2

= 2,000 + 300 + 80 + 12

= 2,392

Estimate:

**Let 52 be Rounded to 50.**

**Let 46 be Rounded to 45.**

So, **45 × 50 = 2,250**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 3.

Estimate: ______

Answer: 2,730

Explanation: Using the Partial Products method,

78 × 35 = ( 70 + 8) × ( 30 +5)

= 30 × 70 + 70 × 5 + 8 × 30 + 8 ×5

= 2,100 + 350 + 240 + 40

= 2,730

Estimate:

**Let 78 be Rounded to 80.**

So, **35 × 80 = 2,800**

As the Estimate and the actual answer are near, the answer is reasonable.

**Apply and Grow: Practice**

**Find the product. Check whether your answer is reasonable.**

Question 4.

Estimate: _____

Answer: 516

Explanation: Using the Partial Products method,

12 × 43 = ( 10 + 2) × ( 40 +3)

= 10 × 40 + 10 × 3 + 2 × 40 + 3 ×2

= 400 + 30 + 80 + 6

= 516

Estimate:

**Let 12 be Rounded to 10.**

**Let 43 be Rounded to 45.**

So, **45 × 10 = 450**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 5.

Estimate: ______

Answer: 1,992

Explanation: Using the Partial Products method,

83 × 24 = ( 80 + 3) × ( 20 +4)

= 80 × 20 + 80 × 4 + 3 × 20 + 3 ×4

= 1,600 + 320 + 60 + 12

= 1,992

Estimate:

**Let 83 be Rounded to 85.**

**Let 24 be Rounded to 25.**

So, **85 × 25 = 2,152**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 6.

Estimate: _____

Answer: 4,484

Explanation: Using the Partial Products method,

59 × 76 = ( 50 + 9) × ( 70 +6)

= 50 × 70 + 50 × 6 + 9 × 70 + 9 ×6

= 3,500 + 300 + 630 + 54

= 4,484

EStimate:

**Let 59 be Rounded to 60.**

**Let 76 be Rounded to 75.**

So, **60 × 75 = 4,500**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 7.

Estimate: ______

22 × 41 = ______

Answer: 902

Explanation: Using the Partial Products method,

41 × 22 = ( 40 + 1) × ( 20 +2)

= 20 × 40 + 40 × 2 + 1 × 20 + 1 ×2

= 800 + 80 + 20 + 2

= 902

Estimate:

**Let 41 be Rounded to 40.**

**Let 22 be Rounded to 20.**

So, **40 × 20 = 800**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 8.

Estimate: _____

94 × 32 = ______

Answer: 3,008

Explanation: Using the Partial Products method,

94 × 32 = ( 90 + 4) × ( 30 +2)

= 30 × 90 + 90 × 2 + 4 × 30 + 4 ×2

= 2,700 + 180 + 120 + 8

= 3,008

Estimate:

**Let 94 be Rounded to 95.**

**Let 32 be Rounded to 30.**

So, **95 × 30 = 2,850**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 9.

Estimate: _____

63 × 54 = _____

Answer: 3,402

Explanation: Using the Partial Products method,

63 × 54 = ( 60 + 3) × ( 50 +4)

= 60 × 50 + 60 × 4 + 3 × 50 + 3 ×4

= 3,000 + 240 + 150 + 12

= 3,402

Estimate:

**Let 63 be Rounded to 65.**

**Let 54 be Rounded to 55.**

So, **55 × 65 = 3,575**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 10.

Newton eats 14 treats each week. Each treat has 33 calories. How many treat calories does Newton eat each week?

Answer: 462 treat calories

Explanation:

Given that Newton eats 14 treats each week and each treat has 33 calories.

So, to find the total number of treat calories, we have to find the product of 14 × 33 by using the Partial Products method.

14 × 33 = ( 10 + 4) × ( 30 +3)

= 10 × 30 + 10 × 3 + 30 × 4 + 3 ×4

= 300 + 30 + 120 + 12

= 462

From the above,

we can conclude that Newton eats 462 treat calories each week.

Question 11.

**YOU BE THE TEACHER**

Your friend finds 43 × 26. Is he correct? Explain.

Answer: Your friend is not correct.

Explanation:

First, we will find 43 × 26 by using the Partial Products method.

43 × 26 = ( 40 + 3) × ( 20 +6)

= 40 × 20 + 40 × 6 + 20 × 3 + 3 ×6

= 800 + 240 + 60 + 18

= **860 + 258**

= 1,118

Fro the above, we can conclude that **258 must be placed instead of 248**

Question 12.

**Open-Ended**

Use 4 cards to write 2 two-digit numbers that have a product that is close to, but not greater than, 1,200.

_______ × ______

Answer:

**Think and Grow: Modeling Real Life**

**Example**

There are 16 hours in 1 day on Neptune. There are 88 times as many hours in 1 day on Mercury as 1 day on Neptune. There are 5,832 hours in 1 day on Venus. Are there more hours in 1 day on Mercury or 1 day on Venus?

Multiply to find how many hours Compare if there are in 1 day on Mercury.

Using the Multiplication method,

So, there are 1,408 hours on Mercury in 1 day

It is also given that there are 5,832 hours on venus in 1 day.

So, to compare how many hours are more on Mercury when compared to venus = 5,832 – 1,408 = 4,424 hours.

So, there are more hours in 1 day on Venus.

**Show and Grow**

Question 13.

A ninja lantern-shark is 18 inches longer than a whale. A whale-shark is 16 times as long as the ninja lantern-shark. A hammerhead shark is 228 inches long. Is the whale shark ? or the hammerhead shark longer?

Answer: The whale-shark is longer when compared to the hammerhead shark.

Explanation:

Given that a ninja lantern-shark is 18 inches long and a whale shark is 16 times longer than the ninja lantern-shark

So, to find the total length of a whale shark, we have to find the product of 18 × 16 using the Partial Products method.

18 × 16 = ( 10 + 8) × ( 10 +6)

= 10 × 10 + 10 × 6 + 10 × 8 + 8 ×6

= 100 + 60 + 80 + 48

= 288 inches

It is also given that the hammerhead shark is 228 inches long.

From the above, we can conclude that the whale shark is longer than the hammerhead shark.

Question 14.

There are 24 science classrooms in a school district. Each classroom receives 3 hot plates. Each hot plate costs $56. How much do all of the hot plates cost?

Answer: $4,032

Explanation:

Given that there are 24 science classrooms in a school district and each classroom receives 3 hot plates.

So, the total number of hot plates received in a school district = 24 × 3 = 72 hot plates

It is also given that each hot plate costs $56.

So, to find the total cost of the hot plates we have to find the product of 56 × 72 using the Partial Products method.

56 × 72 = (50 + 6) × ( 70 +2)

= 50 × 70 + 50 × 2 + 70 × 6 + 2 ×6

= 3,500 + 100 + 420 + 12

= $4,032

From the above, we can conclude that the cost of all the hotplates in a school district is: $4,032

Question 15.

Fourteen adults and 68 students visit the art museum. What is the total cost of admission?

Answer: $1,656

Explanation:

From the above table,

we can see that

the admission price of an adult is: $26

the admission price of a student is: $19

It is also given that there are 14 adults and 68 students.

So,

the total admission cost of the adults is: 14 × 26

the total admission cost of the children is: 68 × 19

Using the Partial Products method,

14 × 26 = (20 + 6) × ( 10 +4)

= 20 × 10 + 20 × 4 + 10 × 6 + 4 ×6

= 200 + 80 + 60 + 24

= $364

Using the Partial Products method,

68 × 19 = (60 + 8) × ( 10 +9)

= 60 × 10 + 60 × 9 + 10 × 8 + 8 ×9

= 600 + 540 + 80 + 72

= $1,292

Hence,

**The total cost of admission (Both adults and children) = 364 + 1,292 = $1,656**

### Multiply Two-Digit Numbers Homework & Practice 4.6

**Find the product. Check whether your answer is reasonable.**

Question 1.

Estimate: ______

Answer: 1,196

Explanation: Using the Partial Products method,

31 × 92 = ( 30 + 1) × ( 90 +2)

= 30 × 90 + 30 × 2 + 1 × 90 + 1 ×2

= 2,700 + 60 + 90 + 2

= 2,852

Estimate:

**Let 31 be Rounded to 30.**

**Let 92 be Rounded to 90.**

So, **30 × 90 = 2,700**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 2.

Estimate: ______

Answer: 3,456

Explanation: Using the Partial Products method,

48 × 72 = ( 40 + 8) × ( 70 +2)

= 70 × 40 + 40 × 2 + 8 × 70 + 8 ×2

= 2,800 + 80 + 560 + 16

= 3,456

Estimate:

**Let 48 be Rounded to 50.**

**Let 72 be Rounded to 70.**

So, **50 × 70 = 3,500**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 3.

Estimate: _____

Answer: 1,290

Explanation: Using the Partial Products method,

15 × 86 = ( 10 + 5) × ( 80 +6)

= 10 × 80 + 10 × 6 + 5 × 80 + 5 × 6

= 800 + 60 + 400 + 30

= 1,290

Estimate:

**Let 86 be Rounded to 85.**

So, **85 × 15 = 1,275**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 4.

Estimate: ______

Answer: 4,374

Explanation: Using the Partial Products method,

81 × 54 = ( 80 + 1) × ( 50 +4)

= 80 × 50 + 80 × 4 + 1 × 50 + 1 × 4

= 4,000 + 320 + 50 + 4

= 4,374

Estimate:

**Let 81 be Rounded to 80.**

**Let 54 be Rounded to 55.**

So, **55 × 80 = 4,400**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 5.

Estimate: ______

Answer: 1,426

Explanation: Using the Partial Products method,

23 × 62 = ( 20 + 3) × ( 60 +2)

= 20 × 60 + 20 × 2 + 3 × 60 + 3 ×2

= 1,200 + 40 + 180 + 6

= 1,426

Estimate:

**Let 23 be Rounded to 25.**

**Let 62 be Rounded to 60.**

So, **25 × 60 = 1,500**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 6.

Estimate: _____

Answer: 5,335

Explanation: Using the Partial Products method,

97 × 55 = ( 90 + 7) × ( 50 +5)

= 90 × 50 + 90 × 5 + 7 × 50 + 7 × 5

= 4,500 + 450 + 350 + 35

= 5,335

Estimate:

**Let 97 be Rounded to 95.**

So, **55 × 95 = 5,225**

As the Estimate and the actual answer are near, the answer is reasonable.

**Find the product. Check whether your answer is reasonable.**

Question 7.

Estimate: ______

51 × 62 = ______

Answer: 3,162

Explanation: Using the Partial Products method,

51 × 62 = ( 50 +1) × ( 60 +2)

= 60 × 50 + 50 × 2 + 1 × 60 + 1 × 2

= 3,000 + 100 + 60 + 2

= 3,162

Estimate:

**Let 51 be Rounded to 50.**

**Let 62 be Rounded to 60.**

So, **50 × 60 = 3,000**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 8.

Estimate: ______

37 × 13 = ______

Answer: 481

Explanation: Using the Partial Products method,

37 × 13 = ( 10 +3) × ( 30 +7)

= 10 × 30 + 10 × 7 + 3 × 30 + 3 × 7

= 300 + 70 + 90 + 21

= 481

Estimate:

**Let 37 be Rounded to 40.**

**Let 13 be Rounded to 15.**

So, **40 × 15= 600**

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 9.

Estimate: _______

49 × 78 = ______

Answer: 3,822

Explanation: Using the Partial Products method,

49 × 78 = ( 40 +9) × ( 70 +8)

= 40 × 70 + 40 × 8 + 9 × 70 + 9 × 8

= 2,800 + 320 + 630 + 72

= 3,822

Estimate:

**Let 49 be Rounded to 50.**

**Let 78 be Rounded to 80.**

So, **50 × 80 = 4,000**

As the Estimate and the actual answer are near, the answer is reasonable.

Question 10.

Newton plays 21 basketball games. He scores 12 points each game. How many points does he score in all?

Answer: He scored 252 points.

Explanation:

Given that Newton plays 21 basketball games and he scores 12 points each game.

So, to find the total number of points in all games, we have to find the product of 21 × 12

By using the Partial Products method,

21 × 12 = ( 20 +1) × ( 10 + 2)

= 20 × 10 + 20 × 2 + 1 × 10 + 1 × 2

= 200 + 40 + 10 + 2

= 252 points

Hence,

From the above, **we can conclude that Newton had scored 252 points in 21 basketball games.**

Question 11.

**DIG DEEPER!**

When you use regrouping to multiply two-digit numbers, why does the second partial product always end in 0?

Answer: Because we divide the partial Products in terms of 10 only.

Ex:

13 × 15 = ( 10 + 3) × (10 + 5)

Question 12.

**Number Sense**

Find the missing digits.

Answer: The missing numbers are: 6, 7, 0 and 1

Explanation:

By using the Partial Products method,

34 × 65 = ( 30 +4) × ( 60 + 5)

= 30 × 60 + 30 × 5 + 4 × 60 + 4 × 5

= 1,800 + 150 + 240 + 20

= 2,040 + **170**

= **2,210**

So,

From the above, we can conclude that the missing numbers are: 6, 7, 0 and 1

Question 13.

**Modeling Real Life**

A tiger dives 12 feet underwater. An otter dives 25 times deeper than the tiger. A walrus dives 262 feet underwater. Does the otter or walrus dive deeper?

Answer: Otter drives deeper than the Walrus.

Explanation:

Given that a tiger dives 12 feet underwater and an otter dives 25 times deeper than the tiger.

So,

The total distance dived by otter = 25 × 12 feet

By using the Partial Products method,

25 × 12 = ( 20 +5) × ( 10 + 2)

= 20 × 10 + 20 × 2 + 5 × 10 + 2 × 5

= 200 + 40 + 50 + 10

= **300**

It is also given that a walrus dives 262 feet underwater.

From the above,

we can conclude that the otter dives deeper than the walrus.

**Review & Refresh**

Question 14.

Complete the table.

Answer:

A) 6,835

Word Form: Six thousand, eight hundred thirty-five

Expanded Form: 6,000 + 800 + 30 + 5

Explanation:

Any number can be written in 3 forms. They are:

A) Standard Form B) Word Form C) Expanded Form

So, we can write the given form in the remaining 2 forms.

B) 70,000 + 4,000 + 100 + 2

Standard Form: 74,102

Word Form: Seventy-four thousand, One hundred two

Explanation:

Any number can be written in 3 forms. They are:

A) Standard Form B) Word Form C) Expanded Form

So, we can write the given form in the remaining 2 forms.

C) Five hundred one thousand, three hundred twenty-nine

Standard Form: 501,329

Expanded Form: 500,000 +0 + 1,000 + 100 + 0 + 2

Explanation:

Any number can be written in 3 forms. They are:

A) Standard Form B) Word Form C) Expanded Form

So, we can write the given form in the remaining 2 forms.

### Lesson 4.7 Practice Multiplication Strategies

**Explore and Grow**

Choose any strategy to find 60 × 80.

Answer: The strategy to find 60 × 80 is: Associative Property of Multiplication

Explanation: By using the Associative Property of Multiplication,

60 ×80 =60 × (8 × 10)

= (60 × 8) × 10

= (6 × 10 × 8) × 10

= 480 × 10

= 4,800

Choose any strategy to find 72 × 13.

Answer: The strategy to find 72 × 13 is: Distributive Property

Explanation:

72 × 13 = 72 × ( 10 + 3)

= ( 72 × 10 ) + ( 72 ×3)

= ( 70 + 2 ) × 10 + ( 70 + 2 ) × 3

= ( 70 × 10 ) + ( 2 × 10 ) + ( 70 × 3 ) + ( 2 × 3)

= 700 + 20 + 210 + 6

= 936

So, **72 × 13 = 936**

**Reasoning**

Explain why you chose your strategies. Compare your strategies to your partner’s strategies. How are they the same or different?

Answer:

**Think and Grow: Practice Multiplication Strategies**

**Example**

Find 62 × 40.

One Way: Use place value.

62 × 40 = 62 × 4 tens

=248 tens

= 248 × 10

= 2,480

So, 62 × 40 = 2,480.

Another Way: Use an area model and partial products.

So, 62 × 40 =2,480 .

**Example**

Find 56 × 83.

One Way: Use place value and partial products.

So, 56 × 83 = 4,648.

Another Way: Use regrouping

Multiply 56 by 3 ones. Then multiply 56 by 8 tens. Regroup if necessary.

So, 56 × 83 = 4,648.

**Show and Grow**

**Find the product.**

Question 1.

90 × 37 = _____

Answer: 3,330

Explanation: Using the Associative Property of Multiplication,

37 × 90 = 37 × (9 × 10)

= (37 × 9) × 10

= (3 × 3 × 37) × 10

= 333 × 10

= 3,330

Question 2.

78 × 21 = ______

Answer: 1,638

Explanation: Using the Distributive Property,

78 × 21 = 78 × ( 20 + 1)

= ( 78 × 20 ) + ( 78 × 1)

= ( 70 + 8 ) × 20 + ( 70 + 8 ) × 1

= ( 70 × 20 ) + ( 8 × 20 ) + ( 70 × 1 ) + ( 8 × 1)

= 1,400 + 160 + 70 + 8

= 1,638

So, **78 × 21 = 1,638**

Question 3.

14 × 49 = _____

Answer: 686

Explanation: Using the Associative Property of Multiplication,

14 × 49 = 14 × ( 40 + 9)

= ( 14 × 40 ) + ( 14 × 9)

= ( 10 + 4 ) × 40 + ( 10 + 4 ) × 9

= ( 40 × 10 ) + ( 4 × 40 ) + ( 10 × 9 ) + ( 4 × 9)

= 400 + 160 + 90 + 36

= 686

So, **14 × 49 = 686**

**Apply and Grow: Practice**

**Find the product.**

Question 4.

74 × 30 = _____

Answer: 2,220

Explanation: Using the Associative Property of Multiplication,

74 × 30 = 74 ( 3 × 10)

= ( 74 × 3) × 10

= 222 × 10

= 2,220

So, **74 × 30 = 2,220**

Question 5.

51 × 86 = _____

Answer: 4,386

Explanation: Using the Distributive Property ,

51 × 86 = 51 × ( 80 + 6)

= ( 51 × 80 ) + ( 51 × 6)

= ( 50 + 1 ) × 80 + ( 50 + 1 ) × 6

= ( 50 × 80 ) + ( 1 × 80 ) + ( 50 × 6 ) + ( 1 × 6)

= 4,000 + 80 + 300 + 6

= 4,386

So, **51 × 86 = 4,386**

Question 6.

40 × 29 = ______

Answer: 1,160

Explanation: Using the Associative Property of Multiplication,

40 × 29 = 29 × (4 × 10)

= (29 × 4) × 10

= (29× 2 × 2) × 10

= 116 × 10

= 1,160

Question 7.

92 × 80 = _____

Answer: 7,360

Explanation: Using the Associative Property of Multiplication,

92 × 80 = 92 × (8 × 10)

= (92 × 8) × 10

= (92 × 2 × 4) × 10

= 736 × 10

= 7,360

Question 8.

41 × 17 = ______

Answer: 697

Explanation: Using the Distributive Property,

41 × 17 = 41 × ( 10 + 7)

= ( 41 × 10 ) + ( 41 × 7)

= ( 40 + 1 ) × 10 + ( 40 + 1 ) × 7

= ( 40 × 10 ) + ( 1 × 10 ) + ( 40 × 7 ) + ( 1 × 7)

= 400 + 10 + 280 + 7

= 697

So, **41 × 17 = 697**

Question 9.

60 × 53 = _____

Answer: 3,180

Explanation: By using the Associative Property of Multiplication,

60 × 53 = 53 × (6 × 10)

= (53 × 6) × 10

= (53× 3 × 2) × 10

= 318 × 10

= 3,180

**Logic**

Find the missing factor.

Question 10.

Answer: The missing number is: 41

Explanation:

In the given figure, the partial fractions are given.

The 1st partial fraction represents the multiplication with the unit digit and the 2nd partial fraction represents the multiplication with the tens digit.

The first partial fraction will come when 72 is multiplied with 1 and the 2nd partial fraction will come when 72 is multiplied with 4.

So, the missing number is: 41

Question 11.

Answer: The missing number is: 34

Explanation:

In the given figure, the partial fractions are given.

The 1st partial fraction represents the multiplication with the unit digit and the 2nd partial fraction represents the multiplication with the tens digit.

The first partial fraction will come when 65 is multiplied with 4 and the 2nd partial fraction will come when 65 is multiplied with 3.

So, the missing number is: 34

Question 12.

Answer: The missing number is: 87

Explanation:

In the given figure, the partial fractions are given.

The 1st partial fraction represents the multiplication with the unit digit and the 2nd partial fraction represents the multiplication with the tens digit.

The first partial fraction will come when 93 is multiplied with 7 and the 2nd partial fraction will come when 93 is multiplied with 8.

So, the missing number is: 87

Question 13.

**Writing**

Explain why you start multiplying with the one’s place when using regrouping to multiply.

Answer: When using ” Regrouping” to multiply, we start multiplying from the rightmost position i.e.., one’s position because the place value of that position is 1.

Question 14.

**DIG DEEPER!**

Find the missing digit so that both products are the same.

Answer: The missing digit so that both products are the same is: 3

Explanation:

The product of 26 × 15 is:

26 × 15 = 26 × ( 10 + 5)

= ( 26 × 10 ) + ( 26 × 5)

= ( 20 + 6 ) × 10 + ( 20 + 6 ) × 5

= ( 20 × 10 ) + ( 6 × 10 ) + ( 20 × 5 ) + ( 6 × 5)

= 200 + 60 + 100 + 30

= 390

So, **26 × 15 = 390**

To get the same result in the next product, we have to find the missing number.

So, **390 / 30 = 13**

Hence, the missing digit so that both products are the same is: 3

**Think and Grow: Modeling Real Life**

**Example**

A swinging ship ride runs 50 times each afternoon. The ship has 10 rows of benches with 4 seats in each bench. If the ship is full each time it runs, how many people will ride the swinging ship in 1 afternoon?

Multiply to find how many people will ride the swinging ship ride each time.

10 × 4 = 40

So,

40 people will ride the swinging ship ride each time.

Multiply to find how many people will ride the swinging ship in 1 afternoon.

40 × 50 = 40 × (5 × 10) (Rewrite 50 as 5 × 10)

= (40 × 5) × 10 ( By using Associative Property of Multiplication)

= 200 × 10

= 2,000

Hence,

2,000 people will ride the swinging ship in 1 afternoon.

**Show and Grow**

Question 15.

A teacher orders 25 rock classification kits. Each kit has 4 rows with 9 rocks in each row. How many rocks are there in all?

Answer: 900 rocks

Explanation:

Given that a teacher orders 25 rock classification kits and each kit has 4 rows with 9 rocks in each row.

So,

The total number of rows present in 25 rock classification kits = 25 × 4 = 100 rows

We have to find the number of rocks in 100 rows by multiplying 100 × 9.

Now, 100 × 9 = 900 rocks.

From the above,

We can conclude that there are 900 total rocks.

Question 16.

A hotel has 12 floors with 34 rooms on each floor. 239 rooms are in use. How many rooms are not in use?

Answer: The total number of rooms that are not in use: 169

Explanation:

Given that a hotel has 12 floors with 34 rooms on each floor.

So, the total number of rooms in a hotel = 34 × 12

By using the Distributive method,

34 × 12 = 34 ( 10 + 2 )

= ( 34 × 10 ) + ( 34 × 2 )

= ( 30 + 4 ) × 10 + ( 30 + 4 ) × 2

= ( 30 × 10 ) + ( 4 × 10 ) + ( 30 × 2 ) + ( 4 × 2)

= 300 + 40 + 60 + 8

= 408

But, it is also given that 239 rooms are in use.

So, **the number of rooms that are not in use = 408 – 239 = 169 rooms**

Question 17.

A child ticket for a natural history museum costs $13. An adult ticket costs twice as much as a child ticket. How much does it cost for 21 children and 14 adults to go to the museum?

Answer: $637

Explanation:

Given that a child ticket for a natural history museum costs $13 and an adult ticket costs twice as much as a child ticket.

So, the cost of an adult ticket = 2 × $13 = $26

So, to find the total cost for 21 children and 14 adults in a museum, we have to find

21 × $13 and 14 × $26

Now,

21 × 13 = 21 ( 10 + 3 )

= ( 21 × 10 ) + ( 21 × 3 )

= ( 20 + 1 ) × 10 + ( 20 +1 ) × 3

= ( 20 × 10 ) + ( 1 × 10 ) + ( 20 × 3 ) + ( 1 × 3)

= 200 + 10 + 60 + 3

= 273

14 × 26 = 14 ( 20 + 6 )

= ( 14 × 20 ) + ( 14 × 6 )

= ( 10 + 4 ) × 20 + ( 10 +4 ) × 6

= ( 10 × 20 ) + ( 4 × 20 ) + ( 10 × 6 ) + ( 4 × 6)

= 200 + 80 + 60 + 24

= 364

Hence,

**The total cost for children and adults in a museum = 273 + 364 = $637**

### Practice Multiplication Strategies Homework & Practice 4.7

**Find the product.**

Question 1.

16 × 13 = _____

Answer: 208

Explanation: By using the Distributive method,

16 × 13 = 16 ( 10 + 3 )

= ( 16 × 10 ) + ( 16 × 3 )

= ( 10 + 6 ) × 10 + ( 10 + 6 ) × 3

= ( 10 × 10 ) + ( 6 × 10 ) + ( 10 × 3 ) + ( 6 × 3)

= 100 + 30 + 60 + 18

= 208

Question 2.

29 × 50 = _____

Answer: 1,450

Explanation: By using the Associative Property of Multiplication,

29 × 50 = 29 × ( 5 × 10 )

= ( 29 × 5 ) × 10

= 145 × 10

= 1,450

Question 3.

78 × 45 = _____

Answer: 3,510

Explanation: By using the Distributive method,

78 × 45 = 78 ( 40 + 5 )

= ( 78 × 40 ) + ( 78 × 5 )

= ( 70 + 8 ) × 40 + ( 70 + 8 ) × 5

= ( 70 × 40 ) + ( 8 × 40 ) + ( 70 × 5 ) + ( 8 × 5)

= 2,800 + 320 + 350 + 40

= 3,510

Question 4.

30 × 71 = ______

Answer: 2,130

Explanation: By using the Associative Property of Multiplication,

30 × 71 = 71 × ( 3 × 10 )

= ( 71 × 3 ) × 10

= 213 × 10

= 2,130

Question 5.

62 × 14 = _____

Answer: 868

Explanation: By using the Distributive method,

62 × 14 = 62 ( 10 + 4 )

= ( 62 × 10 ) + ( 62 × 4 )

= ( 60 + 2 ) × 10 + ( 60 + 2 ) × 4

= ( 60 × 10 ) + ( 2 × 10 ) + ( 60 × 4 ) + ( 2 × 4)

= 600 + 20 + 240 + 8

= 868

Question 6.

80 × 90 = _____

Answer: 7,200

Explanation: By using the Associative Property of Multiplication,

80 × 90 = 80 × ( 9 × 10 )

= ( 80 × 9 ) × 10

= 720 × 10

= 7,200

**Find the product.**

Question 7.

70 × 18 = _____

Answer: 1,260

Explanation: By using the Associative Property of Multiplication,

70 × 18 = 18 × ( 7 × 10 )

= ( 18 × 7 ) × 10

= 126 × 10

= 1,260

Question 8.

32 × 59 = _____

Answer: 1,888

Explanation: By using the Distributive method,

32 × 59 = 59 ( 30 + 2 )

= ( 59 × 30 ) + ( 59 × 2 )

= (50 + 9 ) × 30 + ( 50 + 9 ) × 2

= ( 50 × 30 ) + ( 9 × 30 ) + ( 50 × 2 ) + ( 2 × 9)

= 1,500 + 270 + 100 + 18

= 1,888

Question 9.

67 × 20 = ____

Answer: 1,340

Explanation: By using the Associative Property of Multiplication,

67 × 20 = 67 × ( 2 × 10 )

= ( 67 × 2 ) × 10

= 134 × 10

= 1,340

Question 10.

51 × 84 = _____

Answer: 4,284

Explanation: By using the Distributive method,

51 × 84 = 51 ( 80 + 4 )

= ( 51 × 80 ) + ( 51 × 4 )

= (50 + 1 ) × 80 + ( 50 + 1 ) × 4

= ( 50 × 80 ) + ( 1 × 80 ) + ( 50 × 4 ) + ( 1 × 4)

= 4,000 + 80 + 200 + 4

= 4,284

Question 11.

40 × 40 = _____

Answer: 1,600

Explanation: By using the Associative Property of Multiplication,

40 × 40 = 40 × ( 4 × 10 )

= ( 40 × 4 ) × 10

= 160 × 10

= 1,600

Question 12.

23 × 97 = ______

Answer: 2,231

Explanation: By using the Distributive method,

23 × 97 = 97 ( 20 + 3 )

= ( 97 × 20 ) + ( 97 × 3 )

= (90 + 7 ) × 20 + ( 90 + 7 ) × 3

= ( 90 × 20 ) + ( 7 × 20 ) + ( 90 × 3 ) + ( 7 × 3)

= 1,800 + 140 + 270 + 21

= 2,231

Question 13.

**Writing**

Which strategy do you prefer to use when multiplying two-digit numbers? Explain.

Answer: The strategy you have to prepare when multiplying 2-digit numbers must depend on the numbers.

some strategies to multiply 2-digit numbers are:

A) The place-value method B) The Associative Property of Multiplication C) Distributive Property D) Partial Products method E) Regrouping method

Question 14.

**Patterns**

What number can you multiply the number of tires by to find the total weight? Use this pattern to complete the table.

Answer: The number you can multiply the number of tires by to find the total weight is: 20

Explanation:

From the above table,

to find the multiple of total weight, divide the number of tires by the total weight. ( Take any 2 values)

So, 80 /4 = **20 ( Multiple of total weight)**

From the above,

We can conclude that the number you can multiply the number of tires by to find the total weight is: 20

Question 15.

**Modeling Real Life**

Each bag of popcorn makes 13 cups. A school has a movie day, and the principal brings 15 boxes of popcorn. Each box has 3 bags of popcorn. How many cups of popcorn does the principal bring?

Answer: 585 cups of popcorn

Explanation:

Given that each bag of popcorn makes 13 cups and the principal brings 15 boxes of popcorn. It is also given that each box has 3 bags of popcorn.

So, to find the total number of cups of popcorn the principal bring = 13 × 15 × 3

Now,

By using the Distributive method,

13 × 45 = 45 ( 10 + 3 )

= (45 × 10 ) + ( 45 × 3 )

= (40 +5 ) × 10 + ( 40 + 5 ) × 3

= ( 40 × 10 ) + ( 5 × 10 ) + ( 40 × 3 ) + ( 5 × 3)

= 400 + 50 + 120 + 15

= 585

From the above,

we can conclude that the number of cups the principal bring is: 585 cups of popcorn

**Review & Refresh**

**Find the product.**

Question 16.

8 × 200 = _____

Answer: 1,600

Explanation: By using the Associative Property of Multiplication,

8 × 200 = 8 × (20 × 10)

= (8 × 20) × 10

= (8× 5 × 4) × 10

= 160 × 10

= 1,600

Question 17.

7 × 300 = _____

Answer: 2,100

Explanation: By using the Associative Property of Multiplication,

7 × 300 = 7 × (30 × 10)

= (7 × 30) × 10

= (7× 5 × 6) × 10

= 210 × 10

= 2,100

Question 18.

6,000 × 5 = _____

Answer: 30,000

Explanation: By using the Associative Property of Multiplication,

5 × 6,000 = 5 × (600 × 10)

= (5 × 600) × 10

= (6× 5 × 100) × 10

= 300 × 10

= 3,000

Question 19.

9 × 90 = ____

Answer: 810

Explanation: By using the Associative Property of Multiplication,

9 × 90 = 9 × (9 × 10)

= (9 × 9) × 10

= 81 × 10

= 810

Question 20.

3,000 × 6 = _____

Answer: 18,000

Explanation: By using the Associative Property of Multiplication,

6 × 3,000 = 6 × (300 × 10)

= (6 × 300) × 10

= (6× 3 × 100) × 10

= 1800 × 10

= 18,000

Question 21.

5 × 500 = _____

Answer: 2,500

Explanation: By using the Associative Property of Multiplication,

5 × 500 = 5 × (50 × 10)

= (5 × 50) × 10

= (5× 5 × 10) × 10

= 250 × 10

= 2,500

### Lesson 4.8 Problem Solving: Multiplication with Two-Digit Numbers

**Explore & Grow**

Explain, in your own words, what the problem below is asking. Then explain how you can use multiplication to solve the problem.

A ferry can transport 64 cars each time it leaves a port. The ferry leaves a port 22 times in 1 day. How many cars can the ferry transport in 1 day?

Answer: 1,408 cars can ferry transport in 1 day

Explanation:

Given that a ferry can transport 64 cars each time it leaves a port and the ferry leaves a port 22 times in 1 day.

From this, the total number of cars that can ferry transport in 1 day is: 64 × 22

By using the Distributive method,

64 × 22 = 64 ( 20 + 2 )

= (64 × 20 ) + ( 64 × 2 )

= (60 + 4 ) × 20 + ( 60 + 4 ) × 2

= ( 60 × 20 ) + ( 4 × 20 ) + ( 60 × 2 ) + ( 4 × 2)

= 1,200 + 80 + 120 + 8

= 1,408

From the above,

we can conclude that the total number of cars that ferry transport in 1 day is 1,408 cars.

Construct Arguments

Make a plan to find how many cars the ferry can transport in 1 week.

Answer: 9,856 cars

Explanation:

From the above problem, we know that the total number of cars a ferry can transport in 1 day is: 1,408 cars

We know that,

1 week = 7 days

First, we have to find the total number of cars the ferry can transport in 1 day using the Product 64 × 22.

By using the Distributive method,

64 × 22 = 64 ( 20 + 2 )

= (64 × 20 ) + ( 64 × 2 )

= (60 + 4 ) × 20 + ( 60 + 4 ) × 2

= ( 60 × 20 ) + ( 4 × 20 ) + ( 60 × 2 ) + ( 4 × 2)

= 1,200 + 80 + 120 + 8

= 1,408

Now,

**the total number of cars a ferry can transport in 1 week = 1,408 × 7 = 9,856 cars**

**Think and Grow: Problem Solving: Multiplication with Two-Digit Numbers**

**Example**

A pet store receives a shipment of 8 boxes of dog treats. Each box is 2 feet high and has 18 bags of dog treats. How many ounces of dog treats does the pet store receive in the shipment?

**Understand the Problem**

What do you know?

• The store receives 8 boxes.

• Each box is 2 feet high.

• Each box has 18 bags of dog treats.

• Each bag weighs 32 ounces.

What do you need to find?

• You need to find how many ounces of dog treats the pet store receives in the shipment.

**Make a Plan**

How will you solve it?

• Multiply 32 by 18 to find how many ounces of dog treats are in each box.

• Then multiply the product by 8 to find how many ounces of dog treats the pet store receives in the shipment.

• The height of each box is unnecessary information.

**Solve**

Answer: 4,608 ounces

Explanation:

Given that the store receives 8 boxes and Each box has 18 bags of dog treats. It is also given that each bag weighs 32 ounces.

The number of ounces of dog treats the pet store receives in the shipment = 18 × 8 × 32

It is also given that each box is 2 feet high. But it is not necessary for the calculation of a total number of ounces.

First, we will find the weight of 1 box = 18 × 32

By using the Distributive method,

18 × 32 = 18 ( 30 + 2 )

= (18 × 30 ) + ( 18 × 2 )

= (10 + 8 ) × 30 + ( 10 + 8 ) × 2

= ( 10 ×30 ) + ( 8 × 30 ) + ( 10 × 2 ) + ( 8 × 2)

= 300 + 240 + 20 + 16

= 576

So,

The total weight of dog treats the pet store receives in the shipment = 576 × 8 = 4,608 ounces

Hence,

The pet store receives 4,608 ounces of dog treats.

**Show and Grow**

Question 1.

Show how to solve the problem above using one equation.

Answer: 18 × 32 × 8

**Apply and Grow: Practice**

**Understand the problem. What do you know? What do you need to find? Explain.**

Question 2.

Thirteen students create a petition for longer recess. They need 5,000 signatures in all. So far, each student has 99 signatures. How many more signatures do they need?

Answer: 3,713 signatures

Explanation:

Given that there are 13 students that create a petition for longer recess and they need 5,000 signatures in all.

It is also given that each student has 99 signatures.

So, the total number of signatures that 13 students have are: 13 × 99

By using the Distributive method,

13 × 99 = 13 ( 90 + 9 )

= (13 × 90 ) + ( 13 × 9 )

= (10 +3 ) × 90 + ( 10 + 3 ) × 9

= ( 90 × 10 ) + ( 3 × 90 ) + ( 10 × 9 ) + ( 9 × 3)

= 900 + 270 + 90 + 27

= 1,287

But, the students required 5000 signatures in total.

So,

*The remainin number of signatures required by students = 5,000 – 1,287 = 3,713 signatures*

Question 3.

An activity book has 35 pages and costs $7. Each page has 4 puzzles. You have completed all of the puzzles on 16 of the pages. How many puzzles do you have left to complete?

Answer: 76 puzzles

Explanation:

Given that an activity book has 35 pages and each page has 4 puzzles.

So,

The total number of puzzles = 35 × 4 = 140 puzzles

But, it is also given that the puzzles completed in all of the 16 pages and we know that each page has 4 puzzles.

So,

The number of puzzles in 16 pages = 16 × 4 = 64 puzzles

Now,

The remaining number of puzzles in the remaining pages = 140 – 64 = 76 puzzles

Understand the problem. Then make a plan. How will you solve it? Explain.

Question 4.

Twelve classes provide items for a time capsule. There are 23 students in each class. Each student puts 2 small items in the time capsule. How many items are in the time capsule?

Answer: 552 items

Explanation:

Given that there are 12 classes that provide items for a time capsule and there are 23 students in each class and each student puts 2 small items in the time capsule.

First, we have to find the total number of students by the product 23 × 12

By using the Distributive method,

12 × 23 = 23( 10 + 2 )

= (23 × 10 ) + ( 23 × 2 )

= (20 +3 ) × 10 + ( 20 + 3 ) × 3

= ( 20 × 10 ) + ( 3 × 10 ) + ( 20 × 3 ) + ( 3 × 3)

= 200 + 30 + 60 + 9

= 296 students

Now,

The total number of small items put by the total number of students = 296 × 2 = 552 small items

Question 5.

A craftsman cuts letters and numbers from license plates to make signs. He has 15 Florida plates and 25 Georgia plates. Each plate has a total of 7 letters and numbers. How many letters and numbers does the craftsman cut in all?

Answer: 280 letters and numbers

Explanation;

Given that a craftsman has 15 Florida plates and 25 Georgia plates and each plate has a total of 7 letters and numbers.

Hence,

The total number of plates that a craftsman have = 25 + 15 = 40 plates

The total number of letters and numbers each plate has = 40 × 7 = 280 letters and numbers

Question 6.

**DIG DEEPER!**

In 1 month, the solar panel and the wind turbine can produce the kilowatt-hours of electricity shown. How much electricity can 28 solar panels and1 small wind turbine produce each month?

Answer: 1,673 kilowatt-hours of electricity

Explanation;

Given that each solar panel produces 30 kilowatt-hours and a wind turbine produces 833 kilowatt-hours.

Now, the electricity produced by 28 solar panels = 28 × 30

By using the Associative Property of Multiplication,

28 × 30 = 28 × (3 × 10)

= (28 × 3) × 10

= (7× 4 × 3) × 10

= 84 × 10

= 840 kilowatt-hours

Hence,

The total electricity produced by 28 solar panels and 1 wind turbine = 840 + 833 = 1,673 kilowatt-hours

**Think and Grow: Modeling Real Life**

**Example**

An adult ticket for a zip line course costs $48.A child ticket costs $19 less than an adult ticket. In 1 day, 86 adults and 42 children ride the zipline. How much more money was earned from adult tickets than from child tickets?

Think: What do you know? What do you need to find? How will you solve?

Step 1: How much money was earned from adult tickets?

$48 × 86 = ‘a’

‘a’ is an unknown product.

So,

a = 4,128

Step 2: How much money was earned from child tickets?

A child ticket costs $48 – $19 = $29.

$29 × 42 = c

c is the unknown product.

So,

c = 1,218

Step 3: Use m to represent how much more money was earned from adult tickets.

So, $ 2910 more was earned from adult tickets.

**Show and Grow**

Question 7.

A theater has 45 rows of 72 seats on the floor level and 22 rows of 36 seats in the balcony. How many seats are there in all?

How many more seats are on the floor level than on the balcony?

Answer: 4,032 seats

Explanation;

Given that a theater has 45 rows of 72 seats on the floor level and 22 rows of 36 seats in the balcony.

So,

The total number of seats on the floor level = 45 × 72

The total number of seats on the balcony = 22 × 36

By using the Distributive method,

72 × 45 = 45 ( 70 + 2 )

= (45 × 70 ) + ( 45 × 2 )

= (40 +5 ) × 70 + ( 40 + 5 ) × 2

= ( 40 × 70 ) + ( 5 × 70 ) + ( 40 × 2 ) + ( 5 × 2)

= 2,800 + 350 + 80 + 6

= 3,240

By using the Distributive method,

22 × 36 = 36 ( 20 + 2 )

= (36 × 20 ) + ( 36× 2 )

= (30 +6 ) × 20 + ( 30 + 6) × 2

= ( 30 × 20 ) + ( 6 × 20 ) + ( 30 × 2 ) + ( 6 × 2)

= 600 + 120 + 60 + 12

= 792

So,

The total number of seats ( Floor level and balcony) = 3,240 + 792 = 4,032 seats

### Problem Solving: Multiplication with Two-Digit Numbers Homework & Practice 4.8

**Understand the problem. Then make a plan. How will you solve it? Explain.**

Question 1.

Seventy-two mushers compete in a sled-dog race. Each musher has 16 dogs. How many dogs compete in the race than mushers?

Answer: 1,152 dogs

Explanation:

Given that there are 72 mushers compete in a sled-dog race and each musher has 16 dogs.

So,

The total number of dogs that compete in the race = 16 × 72

By using the Distributive method,

16 × 72 = 72 ( 10 + 6 )

= (72 × 10 ) + ( 72× 6 )

= (70 +2 ) × 10 + ( 70 + 2) × 6

= ( 70 × 10 ) + ( 2 × 10 ) + ( 70 × 6 ) + ( 6 × 2)

= 700 + 20 + 420 + 12

= 1,152

Hence,

The total number of dogs that compete in the race are: 1,152 dogs

Question 2.

A photographer buys 3 USB drives that each cost $5. She puts 16 folders on each drive. Each folder has 75 photographs. How many photographs does the photographer put on the USB drives in all?

Answer: 3,600 photographs

Explanation;

Given that a photographer has 3 USB drives and there are 16 folders and 75 photographers on each drive.

So,

The total number of photographs on all the USB drives = 16 × 3 × 75 = 48 × 75

By using the Distributive method,

48 × 75 = 75 (40 + 8 )

= (75 × 40 ) + ( 75 × 8 )

= (70 +5 ) × 40 + ( 70 + 5) × 8

= ( 70 × 40 ) + ( 5 × 40 ) + ( 70 × 8 ) + ( 5 × 8)

= 2,800 + 200 + 560 + 40

= 3,600 photographs

Hence,

The total number of photographs on all the USB drives are: 3,600 photographs

Question 3.

A teacher has 68 students take 25

Question test. The teacher checks the answers for 9 of the tests. How many answers does the teacher have left to check?

Answer: 1,475 answers

Explanation:

Given that a teacher has 68 students take 25

Question test.

So,

The total number of answers the teacher have to check = 68 × 25

By using the Distributive method,

68 × 25 = 68 ( 20 + 5 )

= (68 × 20 ) + ( 68× 5 )

= (60 +8 ) × 20 + ( 60 + 8) × 5

= ( 60 × 20 ) + ( 8 × 20 ) + ( 60 × 5 ) + ( 8 × 5)

= 1,200 + 160 + 300 + 40

= 1,700

It is also given that the teacher checked 9 papers only.

So.

The number of answers checked = 9 × 25 = 225

Hence,

The number of answers remained unchecked = 1,700 – 225 = 1,475 answers

Question 4.

Each day, a cyclist bikes uphill for 17 miles and downhill for 18 miles. She drinks 32 fluid ounces of water after each bike ride. How many miles does the cyclist bike in 2 weeks?

Answer: 490 miles

Explanation;

Given that a cyclist bikes uphill for 17 miles and downhill for 18 miles.

SO,

The total distance that cyclist bikes each day = 17 + 18 = 35 miles

We know that,

1 week = 7 days

S0, 2 weeks = 2 × 7 = 14 days.

So, the distance traveled by a cyclist in 2 weeks = 35 × 14

By using the Distributive method,

35 × 14 = 35 ( 10 + 4 )

= (35 × 10 ) + ( 35× 4 )

= (30 +5 ) × 10 + ( 30 + 5) × 4

= ( 30 × 10 ) + ( 5 × 10 ) + ( 30 × 4 ) + ( 5 × 4)

= 300 + 50 + 120 + 20

= 490 miles

Hence,

The distance traveled by a cyclist in 2 weeks is: 490 miles

Question 5.

**Precision**

Which expressions can be used to solve the problem?

Twelve friends play a game that has 308 cards. Each player receives 16 cards. How many cards are left?

(308 – 12) × 16

308 – (16 × 12)

308 – (12 × 16)

(308 – 16) – 12

Answer: Let the Expressions be named as A), B), C) and D)

Either B) or C) can be used to solve the problem.

Explanation:

The given Expressions are;

A) (308 – 12) × 16

B) 308 – (16 × 12)

C) 308 – (12 × 16)

D) (308 – 16) – 12

It is given that there are 12 friends that have 16 cards each and there are 308 cards in total.

So,

The number of cards that have left = 308 – ( 16 × 12 ) (or) 308 – ( 12 × 16 )

Hence,

From the above,

we can conclude that either B) or C) can be used to solve the problem.

Question 6.

**Modeling Real Life**

A child ticket costs $14 less than an adult ticket. What is the total ticket cost for 18 adults and 37 children?

Answer: The total ticket cost is: $2,617

Explanation:

The given cost of an Adult ticket = $57

It is also given that a child ticket costs $14 less than an adult ticket.

So,

The given cost of a child ticket = 57 – 14 = $43

Now,

The cost for 18 adults = 18 × 57

The cost for 37 children = 37 × 43

By using the Distributive method,

18 × 57 = 57 ( 10 + 8 )

= (57 × 10 ) + ( 57× 8 )

= (50 + 7 ) × 10 + ( 50 + 7) × 8

= ( 50 × 10 ) + ( 7 × 10 ) + ( 50 × 8 ) + ( 7 × 8)

= 500 + 70 + 400 + 56

= 1,026

By using the Distributive method,

37 × 43 = 37 ( 40 + 3 )

= (37 × 40 ) + ( 37× 3 )

= (30 +7 ) × 40 + ( 30 + 7) × 3

= ( 30 × 40 ) + ( 7 × 40 ) + ( 30 × 3 ) + ( 7 × 3)

= 1,200 + 280 + 90 + 21

= 1,591

Hence,

The total cost of tickets = 1,591 + 1,026 = $2,617

Question 7.

**Modeling Real Life**

An artist creates a pattern by alternating square and rectangular tiles. The pattern has 14 square tiles and 13 rectangular tiles. How long is the pattern?

Answer: 1,680 cm

Explanation:

Given that an artist creates a pattern by alternating square and rectangular tiles and the pattern 14 square tiles and 13 rectangular tiles.

From the given fig.,

Area of Square = 8 × 8 = 64 square cm

Area of Rectangle = 8 × 14 = 112 square cm

So,

Area of 14 squares = 14 × 64

Area of 13 rectangles = 112 × 13

By using the Distributive method,

14 × 64 = 64 ( 10 + 4 )

= (64 × 10 ) + ( 64× 4 )

= (60 +4 ) × 10 + ( 60 + 4) × 4

= ( 60 × 10 ) + ( 4 × 10 ) + ( 60 × 4 ) + ( 4 × 4)

= 600 + 40 + 240 + 16

= 896

By using the Distributive method,

112 × 13 = 13 ( 100 + 12 )

= (13 × 100 ) + ( 13× 12 )

= (10 +3 ) × 100 + ( 10 + 3) × 12

= ( 10 × 100 ) + ( 3× 100 ) + ( 10 × 12 ) + ( 12 × 3)

= 1,000 + 300 + 120 + 36

= 1,456

Hence,

The total length of the Pattern = 896 + 1,456 = 2,352 square cm

Question 8.

**Modeling Real Life**

A cargo ship has go ship has 34 rows of crates. Each row has 16 stacks of crates. There are 5 crates in each stack. The ship workers unload 862 crates. How many crates are still on the ship?

Answer: 1,858 crates are still on the ship.

Explanation:

Given that a cargo ship has a go ship has 34 rows of crates and each row has 16 stacks of crates. It is also given that there are 5 crates in each stack.

So,

The total number of crates = 34 × 16 × 5 = 34 × 80

By using the Associative Property of Multiplication,

34 × 80 = 34 × (8 × 10)

= (34 × 8) × 10

= (17× 2 × 8) × 10

= 272 × 10

= 2,720

It is also given that the ship workers unload 862 crates.

Hence,

The number of crates that the ship had = 2,720 – 862 = 1,858 crates

Review & Refresh

Estimate the product.

Question 1.

4 × 85

Answer: 340

Explanation:

By using the partial products method,

4 × 85 = ( 80 + 5 ) × ( 2 + 2 )

= ( 80 × 2 ) + (80 × 2 ) + ( 5 × 2 ) + ( 5 × 2 )

= 160 + 160 + 10 + 10

= 340

Question 2.

6 × 705

Answer: 4,230

Explanation:

By using the partial products method,

6 × 705 = ( 700 + 5 ) × ( 2 + 4 )

= ( 700 × 2 ) + (700 × 4 ) + ( 5 × 2 ) + ( 5 × 4 )

= 1,400 + 2,800 + 10 + 20

= 4,230

Question 3.

8 × 7,923

Answer: 63,384

### Multiply by Two-Digit Numbers Performance Task

Wind turbines convert wind to energy. Most wind or turbines have 3 blades. The blades rotate slower or faster depending on the speed of the wind. More energy is generated when the blades spin faster.

Question 1.

A wind turbine rotates between 15 and 40 times in 1 minute.

a.What is the least number of times the turbine rotates in 1 hour?

b.What is the greatest number of times the turbine rotates in 1 hour?

Answer:

a) 900 times

b) 2,400 times

Explanation:

Given that a wind turbine rotates between 15 and 40 times in 1 minute.

We know that,

1 hour = 60 minutes

The wind turbine rotates minimum 15 times and maximum 40 times in a minute.

So,

The minimum number of times a wind turbine rotate in 1 hour = 15 × 60

The maximum number of times a wind turbine rotate in 1 hour = 40 × 60

Using the Associative Property of Multiplication,

15 × 60 = 15 ( 6 × 10)

= ( 15 × 6) × 10

= 90 × 10

= 900

Using the Associative Property of Multiplication,

40 × 60 = 40 ( 6 × 10)

= ( 40 × 6) × 10

= 240 × 10

= 2,400

Hence,

The minimum number of times a wind turbine rotate in 1 hour = 900 times

The maximum number of times a wind turbine rotate in 1 hour = 2,400 times

Question 2.

The tips of the turbine blades spin 5 times faster than the speed of the wind. The speed of the wind is 22 miles per hour. How fast do the blade tips spin?

Answer: 110 miles per hour

Explanation;

Given that the tips of the turbine blades spin 5 times faster than the speed of the wind. It is also given that the speed of the wind is 22 miles per hour.

So,

The speed of the blade tips = 22 × 5 = 110 miles per hour

Question 3.

A turbine farm has 7 large wind turbines. Each wind turbine can generate enough energy to power 1,485 houses. How many houses can the turbine farm power in all?

Answer: 10,395 houses

Explanation:

Given that a turbine farm has 7 large wind turbines and each wind turbine can generate enough energy to power 1,485 houses.

So,

The total number of houses that a turbine farm generates enough energy = 1,485 × 7 = 10,395 houses

Question 4.

Use the chart.

a. How many times more houses are powered when the length of each blade is doubled?

b. A wind turbine has blades that are each 60 meters long. How many houses can the wind turbine power?

Answer:

a) 2 times

b) 33,000 houses

Explanation;

a) The given original length of each blade is 15 meters and 30 meters. It is also given that some houses are powered.

Now,

It is also given that the length of each blade is doubled.

So, 15 meters becomes 30 meters and 30 meters becomes 60 meters.

From this, we have to observe that the change in length also changes the energy powered in a directly proportional way.

From this, we can conclude that

The number of times more houses are powered when the length of each blade is doubled is: 2 times

b) Given that the length f each wind turbine is 60 meters long.

So, the number of houses that can be powered up = 60 × 550

Using the Associative Property of Multiplication,

550 × 60 = 550 × ( 10 × 6)

= ( 550 × 6 ) × 10

= 3300 × 10

= 33,000

Hence,

The number of houses can the wind turbine power is: 33,000 houses

### Multiply by Two-Digit Numbers Activity

**Multiplication Boss**

**Directions:**

1. Each player flips 4 Number Cards and uses them in any order to create a multiplication problem with two-digit factors.

2. Each player finds the product of the two factors.

3. Players compare products. The player with the greater product takes all 8 cards.

4. If the products are equal, each player flips 4 more cards and plays again. The player with the greater product takes all 16 cards.

5. The player with the most cards at the end of the round wins

### Multiply by Two-Digit Numbers Chapter Practice

#### 4.1 Multiply by Tens

Find the product.

Question 1.

50 × 20 = _____

Answer: 1,000

Explanation:

By using the Place-value method,

50 × 20 = 50 × 2 tens

= 5 tens × 2 tens

= 10 × 10 × 10

= 1,000

So, 50 × 20 = 1,000

Question 2.

30 × 60 = _____

Answer: 1,800

Explanation:

By using the Place-value method,

30 × 60 = 30 × 6 tens

= 3 tens × 6 tens

= 18 × 10 × 10

= 1,800

So, 30 × 60 = 1,800

Question 3.

80 × 10 = _____

Answer: 800

Explanation:

By using the Place-value method,

80 × 10 = 10 × 8 tens

= 1 ten × 8 tens

= 8 × 10 × 10

= 800

So, 80 × 10 = 800

Question 4.

40 × 70 = _____

Answer: 2,800

Explanation:

By using the Place-value method,

70 × 40 = 70 × 4 tens

= 7 tens × 4 tens

= 28 × 10 × 10

= 2,800

So, 70 × 40 = 2,800

Question 5.

60 × 50 = _____

Answer: 3,000

Explanation:

By using the Place-value method,

50 × 60 = 50 × 6 tens

= 5 tens × 6 tens

= 30 × 10 × 10

= 3,000

So, 50 × 60 = 3,000

Question 6.

90 × 90 = _____

Answer: 8,100

Explanation:

By using the Place-value method,

90 × 90 = 90 × 9 tens

= 9 tens × 9 tens

= 81 × 10 × 10

= 8,100

So, 90 × 90 = 8,100

Question 7.

70 × 11 = _____

Answer: 770

Explanation:

By using the Place-value method,

70 × 11 = 11 × 7 tens

= 77 tens

= 77 × 10

= 770

So, 70 × 11 = 770

Question 8.

18 × 30 = _____

Answer: 540

Explanation:

By using the Place-value method,

30 × 18 = 18 × 3 tens

= 54 tens

= 54 × 10

= 540

So, 30 × 18 = 540

Question 9.

20 × 75 = _____

Answer: 1,500

Explanation:

By using the Place-value method,

20 × 75 = 75 × 2 tens

= 150 tens

= 150 × 10

= 1,500

So, 20 × 75 = 1,500

Find the missing factor.

Question 10.

40 × ____ = 3,200

Answer: The missing number is: 80

Explanation;

Let the missing number be X

So, 40 × X = 3,200

X = 3,200 /40 = 80

Hence, the value of X is: 80

Question 11.

_____ × 20 = 1,200

Answer:

The missing number is: 60

Explanation;

Let the missing number be X

So, 20 × X = 1,200

X = 1,200 /20 = 60

Hence, the value of X is: 60

Question 12.

30 × ____ = 2,100

Answer:

The missing number is: 70

Explanation;

Let the missing number be X

So, 30 × X = 2,100

X = 2,100 /30 = 70

Hence, the value of X is: 70

#### 4.2 Estimate Products

Estimate the product.

Question 13.

25 × 74

Answer: 1,850

Explanation:

Let 74 be rounded to 75

By using the Partial Fraction method,

25 × 75 = ( 20 + 5) × ( 70 + 5)

= ( 20 × 70) + ( 20 × 5) + ( 5 × 70) + ( 5 × 5)

= 1,400 + 100 + 350 + 25

= 1,875

So,

25 × 74 = 1,875

Question 14.

16 × 28

Answer: 448

Explanation:

Let 16 be rounded to 15

Let 28 be rounded to 30

By using the Partial Fraction method,

15 × 30 = ( 10 + 5) × ( 25 + 5)

= ( 10 × 25) + ( 10 × 5) + ( 5 × 25) + ( 5 × 5)

= 200 + 50 + 125 + 25

= 400

So,

16 × 28 = 400

Question 15.

42 × 81

Answer: 3,402

Explanation:

Let 42 be rounded to 40

Let 81 be rounded to 80

By using the tens method,

40 × 80 = 40 × 8 tens

= 4 tens × 8 tens

= 32 × 1 ten × 1 ten

= 32 × 10 × 10

= 3,200

So,

42 × 81 = 3,200

Open-Ended

Write two possible factors that can be estimated as shown.

Question 16.

8,100

Answer:

Explanation:

The Products of 81 are:

9 × 9 = 81

From the above two products, we can conclude that the two possible numbers that can give the product 6,400 are: 90,90

Question 17.

400

Answer:

Explanation:

The Products of 64 are:

2 × 2 = 4

4 × 1 =4

From the above two products, we can conclude that the two possible numbers that can give the product 400 are: 20,20 and. 10,40

#### 4.3 Use Area Models to Multiply Two-Digit Numbers

**Draw an area model to find the product.**

Question 18.

13 × 19 = _____

Answer: 247

Explanation:

By using the Partial Products method,

13 × 19 = ( 10 + 3) × ( 10 + 9)

10 × 10 + 10× 9 + 10 × 3 + 3 × 9

= 100 + 90 + 30 + 27

= 247

So,

19 × 13 = 247

Question 19.

21 × 36 = _____

Answer: 756

Explanation:

By using the Partial Products method,

21 × 36 = ( 20 + 1) × ( 30 + 6)

= 20 × 30 + 20× 6 + 30 × 1 + 1 × 6

= 600 + 120 + 30 + 6

= 756

So,

21 × 36 = 756

Question 20.

**YOU BE THE TEACHER**

Your friend finds 28 × 24. Is your friend correct? Explain.

Answer: Your friend is not correct.

Explanation;

By using the partial Products method,

400 + 160 +80 + 32 = 672

From the above,

we can conclude that in place of 16, 160 must be placed.

#### 4.4 Use Distributive Property to Multiply Two-Digit Numbers

**Use Distributive Property to find a product.**

Question 21.

27 × 34 = 27 × (30 + 4)

= (27 × 30) + (27 × 4)

= (20 + 7) × 30 + (20 + 7) × 4

= (20 ×30) + (7 × 30) + (20 ×4) + (7 × 4)

= 600 + 210 + 80 + 28

= 918

So, 27 × 34 = 918.

Question 22.

43 × 18 = _____

Answer: 774

Explanation: Using the Partial Products method,

43 × 18 = 43× (10 + 8)

= (43 × 10) + (43 × 8)

= (40 + 3) × 10 + (40 + 3) × 8

= (40 ×10) + (3 × 10) + (40 ×8) + (3 × 8)

= 400 + 30 + 320 + 24

= 774

So, 43 × 18 = 774

Question 23.

35 × 57 = _____

Answer: 1,995

Explanation: Using the Partial products method,

35 × 57 = 35 × (50 + 7)

= (35 × 50) + (35 × 7)

= (30 + 5) × 50 + (30 + 5) × 7

= (50 ×30) + (5 × 50) + (30 ×7) + (7 × 5)

= 1,500 + 250 + 210 + 35

= 1,995

So, 35 × 57 = 1,995

Question 24.

81 × 76 = _____

Answer: 6,156

81 × 76 = 81 × (70 + 6)

= (81 × 70) + (81 × 6)

= (80 + 1) × 70 + (80 + 1) × 6

= (80 ×70) + (70 × 1) + (80 ×6) + (1 × 6)

= 5,600 + 70 + 480 + 6

= 6,156

So, 81 × 76 = 6,156

#### 4.5 Use Partial Products to Multiply Two-Digit Numbers

**Find the product. Check whether your answer is reasonable.**

Question 25.

Answer: 396

Explanation: Using the Partial Products method,

18 × 22 = 22 × (10 + 8)

= (22 × 10) + (22 × 8)

= (20 + 2) × 10 + (20 + 2) × 8

= (20 ×10) + (2 × 10) + (20 ×8) + (2 × 8)

= 200 + 20 + 160 + 16

= 396

So, 18 × 22 = 396

Question 26.

Answer: 3,358

Explanation: Using the Partial Products method,

73 × 46 = 73 × (40 + 6)

= (73 × 40) + (73 × 6)

= (70 + 3) × 40 + (70 + 3) × 6

= (70 ×40) + (3 × 40) + (70 ×6) + (3 × 6)

= 2,800 + 120 + 420 + 18

= 3,358

So, 73 × 46 = 3,358.

Question 27.

Answer: 3,276

Explanation: By using the Partial Products method,

39 × 84 = 39 × (80 + 4)

= (39 × 80) + (39 × 4)

= (30 + 9) × 80 + (30 + 9) × 4

= (80 ×30) + (9 × 80) + (30 ×4) + (9 × 4)

= 2,400 + 720 + 120 + 36

= 3,276

So, 39 × 84 = 3,276

Question 28.

57 × 19 = _____

Answer: 1,083

Explanation: By using the Partial Products method,

57 × 19 = 57 × (10 + 9)

= (57 × 10) + (57 × 9)

= (50 + 7) × 10 + (50 + 7) × 9

= (50 ×10) + (7 × 10) + (50 ×9) + (7 × 9)

= 500 + 70 + 450 + 63

= 1,083

So, 57 × 19 = 1,083

Question 29.

38 × 65 = _____

Answer: 2,470

Explanation: By using the Partial Products method,

38 × 65 = 65 × (30 + 8)

= (65 × 30) + (65 × 8)

= (60 + 5) × 30 + (60 + 5) × 8

= (60 ×30) + (5 × 30) + (60 ×8) + (5 × 8)

= 1,800 + 150 + 480 + 40

= 2,470

So, 38 × 65 = 2,470

Question 30.

94 × 26 = _____

Answer: 2,444

Explanation: By using the Partial Products method,

94 ×26 = 94 × (20 + 6)

= (94 × 20) + (94 × 6)

= (90 + 4) × 20 + (90 + 4) × 6

= (90 ×20) + (4 × 20) + (90 ×6) + (4 × 6)

= 1,800 + 80 + 540 + 24

= 2,444

So, 94 × 26 = 2,444

Reasoning

Find the missing digits. Then find the product.

Question 31.

Answer:

Question 32.

Answer:

#### 4.6 Multiply Two-Digit Numbers

**Find the product. Check whether your answer is reasonable.**

Question 33.

Estimate: _____

Answer: 2,108

Explanation:

Using the Partial Products method,

34 × 62 = ( 60 + 2) × ( 30 + 4)

= 30 × 60 + 4 × 60 + 30 × 2 + 2 × 4

= 1,800 + 240 + 60 + 8

= 2,108

Estimate:

*Let 62 be Rounded to 60.*

*Let 34 be Rounded to 35.*

So, 60 × 35 = 2,100

As the Estimate and the actual answer are near, the answer is reasonable.

Question 34.

Estimate: ____

Answer: 7,917

Explanation:

Using the Partial Products method,

87 × 91 = ( 80 + 7) × ( 90 + 1)

= 80 × 90 + 7 × 90 + 80 × 1 + 7 × 1

= 7,200 + 630 + 80 + 7

= 7,917

Estimate:

*Let 87 be Rounded to 85.*

*Let 91 be Rounded to 90.*

So, 90 × 85 = 7,650

As the Estimate and the actual answer are not near, the answer is not reasonable.

Question 35.

Estimate: _____

Answer: 3,285

Explanation:

Using the Partial Products method,

73 × 45 = ( 70 + 3) × ( 40 + 5)

= 70 × 40 + 3 × 40 + 70 × 5 + 5 × 3

= 2,800 + 120 + 350 + 15

= 3,285

Estimate:

*Let 73 be Rounded to 75.*

So, 45 × 75 = 3,375

As the Estimate and the actual answer are near, the answer is reasonable.

Question 36.

Estimate: ____

13 × 21 = ______

Answer: 273

Explanation:

Using the Partial Products method,

13 × 21 = ( 20 + 1) × ( 10 + 3)

= 20 × 10 + 20 × 3 + 10 × 1 + 1 × 3

= 200 + 60 + 10 + 3

= 273

Estimate:

*Let 13 be Rounded to 15.*

*Let 21 be Rounded to 20.*

So, 20 × 15 = 300

As the Estimate and the actual answer are near, the answer is reasonable.

Question 37.

Estimate: _____

42 × 53 = _____

Answer: 2,226

Explanation:

Using the Partial Products method,

42 × 53 = ( 40 + 2) × ( 50 + 3)

= 40 × 50 + 3 × 40 + 50 × 2 + 2 × 3

= 2,000 + 120 + 100 + 6

= 2,226

Estimate:

*Let 42 be Rounded to 40.*

*Let 53 be Rounded to 55.*

So, 40 × 55 = 2,200

As the Estimate and the actual answer are near, the answer is reasonable.

Question 38.

Estimate: _____

29 × 66 = _____

Answer: 1,914

Explanation:

Using the Partial Products method,

29 × 66 = ( 20 + 9) × ( 60 + 6)

= 20 × 60 + 9 × 60 + 20 × 6 + 9 × 6

= 1,200 + 540 + 120 + 54

= 1,914

Estimate:

*Let 29 be Rounded to 30.*

*Let 66 be Rounded to 65.*

So, 30 × 65 = 1,950

As the Estimate and the actual answer are near, the answer is reasonable.

#### 4.7 Practice Multiplication Strategies

Find the product.

Question 39.

80 × 30 = _____

Answer: 2,400

Explanation: Using the Place-value method,

80 × 30 = 80 × 3 tens

= 240 tens

= 2,400

So, 80 × 30 = 2,400

Question 40.

26 × 51 = _____

Answer: 1,326

Explanation: Using the Partial Products method,

26 × 51 = ( 20 + 6) × ( 50 + 1)

= ( 20 × 50) + ( 20 × 1) + ( 6 × 50) + (6 × 1)

= 1,000 + 20 + 300 + 6

= 1,326

Question 41.

94 × 70 = _____

Answer: 6,580

Explanation: Using the Place-value method,

94 × 70 = 94 × 7 tens

= 658 tens

= 6,580

So, 94 × 70 = 6,580

Question 42.

15 × 67 = _____

Answer: 1,005

Explanation: Using the Partial Products method,

15 × 67 = ( 10 + 5) × ( 60 + 7)

= ( 10 × 60) + ( 10 × 7) + ( 5 × 60) + ( 5 × 7)

= 600 + 70 + 300 + 35

=1,005

Question 43.

40 × 38 = _____

Answer: 1,520

Explanation: Using the Place-value method,

38 × 40 = 38 × 4 tens

= 152 tens

= 1,520

So, 38 × 40 = 1,520

Question 44.

29 × 92 = _____

Answer: 2,668

Explanation: Using the partial products method,

29 × 92 = ( 20 + 9) × ( 90 + 2)

= ( 20 × 90 ) + ( 20 × 2) + ( 9 × 90) + ( 9 × 2)

= 1,800 + 40 + 810 + 18

= 2,668

Question 45.

**Modeling Real Life**

A Ferris wheel runs 40 times each day. It has 16 cars with 4 seats in each car. If the Ferris wheel is full each time it runs, how many people will ride it in 1 day?

Answer: 2,560 people will ride the Ferris wheel in 1 day

Explanation:

Given that a Ferris wheel runs 40 times each day and it has 16 cars with 4 seats in each car.

So, the total number of people that can ride a Ferris wheel = 40 × 16 × 4 = 40 × 64

By using the place-value method,

64 × 40 = 64 × 4 tens

= 256 tens

= 2,560

From the above,

We can conclude that there are 2,560 people who will ride the Ferris wheel in 1 day

4.8 Problem Solving: Multiplication with Two-Digit Numbers

Question 46.

A music fan memorizes 59 songs for a concert. Her goal is to memorize all of the songs from 13 albums. There are 15 songs on each album. How many more songs does the music fan still need to memorize?

Answer: 136 songs

Explanation:

Given that a music fan has to memorize all of the songs from 13 albums and there are 15 songs on each album.

So, the total number of songs the music fan has to memorize = 13 × 15

By using the Partial Products method,

13 × 15 = ( 10 + 3) × ( 10 + 5)

= ( 10 × 10 ) + ( 10 × 5) + ( 3 × 10 ) + ( 3 × 5)

= 100 + 50 + 30 + 15

= 195

It is also given that the music fan memorized 59 songs for the Concert.

Hence,

The number of songs that has to memorize by the music fan = 195 – 59 = 136 songs

Question 47.

Find the area of the Jamaican flag.

Answer: 2,592 inches

Explanation;

The given Jamaican flag is in the shape of a rectangle.

We know that,

Area of the rectangle = length × breadth

So,

Area of the Jamaican flag = 36 × ( 36 + 36) = 36 × 72

Using the Partial Products method,

36 × 72 = ( 30 + 6) × ( 70 + 2)

= ( 30 × 70 ) + ( 30 × 2 ) + ( 6 × 70) + ( 6 × 2)

= 2,100 + 60 + 720 + 12

= 2,592 inches

From this,

We can conclude that the area of the Jamaican flag is: 2,592 inches

*Final Words:*

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