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## Big Ideas 5th Grade Chapter 4 Multiply Whole NumbersMath Book Answer Key

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**Lesson: 1 Multiplication Patterns**

**Lesson: 2 Estimate Products**

**Lesson: 3 Multiply by One-Digit Numbers**

**Lesson: 4 Multiply by Two-Digit Numbers**

**Lesson: 5 Multiply by Multi-Digit Whole Numbers**

- Lesson 4.5 Multiply by Multi-Digit Whole Numbers
- Multiply by Multi-Digit Whole Numbers Homework & Practice 4.5

**Performance Task**

- Multiply Whole Numbers Performance Task
- Multiply Whole Numbers Activity
- Multiply Whole Numbers Chapter Practice

### Lesson 4.1 Multiplication Patterns

**Explore and Grow**

Complete the table. Find the value of each expression.

What patterns do you notice?

Answer:

Power | Expression | Value |

8 x 10^{1} |
8 x 10 | 80 |

8 x 10^{2} |
8 x 100 | 800 |

8 x 10^{3} |
8 x 1,000 | 8,000 |

8 x 10^{4} |
8 x 10,000 | 80,000 |

Explanation:

In each product, the number of zeros after 8 is the same as the exponent.

**Patterns**

Explain how to multiply any number by a power of 10.

Answer:

By multiplying the given number with the 10 as many times as to its the given power value.

Explanation :

ExampleÂ 4 x 10^{2}Â weÂ take asÂ 4 x 10 x 10 means 10 is multiplied twice

means as the power of 10 is 2 so weÂ multiply the number 4 with 10 twice,

if it 4 x 10^{3}Â we take it as 4 x 10 x 10 x 10 means we take 10 by 3 times as power is 3^{
}

**Think and Grow: Use Patterns to Find Products**

**Example**

Find 46 Ã— 10^{3}.

One Way:

Use powers and look for a pattern

46,000

Another Way:

Use place value.

46 Ã— 10^{3} = 46 Ã— 1,000

= 46 thousands

= ___46,000___

So, 46 Ã— 10^{3}.

Notice the pattern: In each product, the number of zeros after 46 is the same as the exponent.

**Example**

Find 40 Ã— 600.

Use a multiplication fact and look for a pattern.

So, 40 Ã— 600 = __24,000____.

Notice the pattern: In each product, the number of zeros after 24 is equal to the number of zeros in the factors.

**Show and Grow**

**Find the product.**

Question 1.

78 Ã— 10^{4}

Answer:

The product of 78 Ã— 10^{4Â }= 78 x 10,000 = 780,000

Explanation: As 78 is multiplied by 10^{4Â Â }we get the result as 780,000

Question 2.

20 Ã— 400 = ______

Answer:

The product of 20 x 400 = 2x 10 x 4 x 100 = 2 x 4 x 10 x 100 = 8,000

Explanation:

As 20 X 400 has 3 zeros we have 20 x 400 as 8,000

**Apply and Grow: Practice**

**Find the product**

Question 3.

11 Ã— 10^{3} = _______

Answer:

The product of 11 Ã— 10^{3} = 11 x 1,000=11,000

Explanation :

The result ofÂ 11 Ã— 10^{3}Â is 11,000

Question 4.

40 Ã— 70 = _______

Answer:

The product of 40 x 70 = 4 x 10 x 7 x 10 =4 x 7 x 10 x 10 = 2,800

Explanation :

When 40 is multiplied byÂ 70 the result is 2,800

Question 5.

300 Ã— 90 = ________

Answer:

The product of 300 x 90 = 3 x 100 x 9 x 10 = 3 x 9 x 100 x 10 = 27,000

Explanation :

When 300 is multiplied byÂ 90 the result is 27,000

Question 6.

10^{4} Ã— 60 = _______

Answer:

The product of 10^{4} Ã— 60 = 10 x 10 x 10 x 10 x 60 = 6,00,000

Explanation :

When 10^{4}Â is multiplied by 60 the result is 6,00,000

Question 7.

206 Ã— 10^{2} = _______

Answer:

The product of 206 Ã— 10^{2} = 206 x 10 x 10 = 20,600

Explanation :

When 206 is multiplied by 10^{2} the result is 20,600

Question 8.

15 Ã— 200 = _________

Answer:

The product of 15 x 200 = 15 x 2 x 10 x 10 = 3,000

Explanation :

When 15 is multiplied by 200 the result is 3,000

**Find the missing factor.**

Question 9.

30 Ã— ______ = 15,000

Answer:

30 x ____= 15,000,15,000/30 = 500

Explanation:

So when 15,000 is divided by 30 we get 500 the missing factor is 500

Question 10.

_____ Ã— 10^{3} = 54,000

Answer:

_____ Ã— 10^{3} = 54,000

the missing factor is 54

Explanation :

When 54,000 is divided by 10^{3Â }or 1000

we get 54,000 x 1/ 1000= 54

Question 11.

500 Ã— ______ =40,000

Answer:

500 Ã— ______ =40,000

the missing factor is 8,000

Explanation:

so when 40,000 is dived by 500 its is equal to

40,000 x 1/500=8,000

Question 12.

A heart pumps about 2,000 gallons of blood each day. How many gallons of blood does the heart pump in 7 days?

Answer:

Given that heart pumps about 2,000 gallons of blood each day and for 7 days it is

2,000 x 7 = 14,000 gallons

Explanation :

So we multiply 2000 by 7 for 7 days and the result is 14,000 gallons

Question 13.

**Number Sense**

Which expressions are equal to 24,000?

Answer:

240 x 100= 24 x 10 x 10 x 10Â = 24,000 so it is equal

30 x 800 = 3 x 10 x 8 x 10 x 10 = 24,000 so this is also equal

400 x 600= 4 x 10 x 10 x 6 x 10 x 10 =24,000 so this also equal

and 24 x 1,000 = 24 x 10 x 10 x 10 = 24,000 which is also equal

so all the given expressions are equal to 24,000

Explanation :

When

these numbers are multiplied all results are equal to 24,000

Question 14.

**Logic**

When you multiply any whole number by 100, what do you know about the digits in the product?

Answer:

When we multiply any whole number by 100, it becomes the digit with two zeros in the right , number x 100= number x 10^{2} =number,00

or we get the whole number with additional 2 zeros in the right

Explanation:

For example if the number is 5 it becomes as 5 x 100 = 5 x 10^{2}= 500, 2 zeros after 5

Question 15.

**DIG DEEPER!**

Show how to find 20 Ã— 10^{3} using the Associative Property of Multiplication.

Answer:

The Associative Property of Multiplication of 20 Ã— 10^{3Â Â }is

(20 x 10) x 10 x 10 = 20 x ( 10 x 10 ) x 10

(200) x 10 x 10 = 20 x (100) x 10

20,000 = 20,000

Explanation:

Both sides are equal by using the Associative Property of Multiplication Law.

**Think and Grow: Modeling Real Life**

**Example**

A black bear consumes 12,000 calories each day for 30 days. A grizzly bear consumes 400,000 calories in 30 days. Which bear consumes more calories in 30 days?

Multiply 12,000 and 30 to find the number of calories the black bear consumes in 30 days. Use a multiplication fact and a pattern.

12 Ã— 3 = ____36____ Multiplication fact

The multiplication fact is 12 Ã— 3 = 36. The factors 12,000 and 30 have a total of _____4_ zeros. So, the product has __4___ zeros after 36.

12,000 Ã— 30 = ___3,60,000______ calories

The black bear consumes 3,60,000 calories in 30 days. Compare the numbers of calories the bears consume in 30 days.

A grizzly bear consumes 4,00,000 x 30 = 120,00,000

SoÂ grizzly bear consumes more calories than black bear

The ___grizzly ___ bear consumes more calories in 30 days.

**Show and Grow**

Question 16.

The attendance at a theme park is about 300,000 guests each month. The attendance at a water park is 2,280,000 guests in 1 year. Which park has a greater attendance in 1 year?

Answer:

The theme park has a greater attendance in 1 year.

Explanation:

The attendance at theme park is about 3,00,000 guests in one month so in a year it is 3,00,000 x 12 = 36,00,000 guests.

and given water park has 22,80,000 guests= 228 x 10^{4} Â in 1 year

so as compared between the two parks 36,00,000 guests = 360 x10^{4} Â is greater than 22,80,000 guests= 228 x 10^{4Â } means the theme park has a greater attendance in 1 year.

Question 17.

Your heart beats 120,000 times each day. In 1 week, a professional athleteâ€™s heart beats 607,000 times. How many more times does your heart beat in 1 week compared to the athlete?

Answer:

Our heart beats 233,000 times more compared to the athlete in 1 week

Explanation :

Each day our heart beats 120,000 times each day

so in 1 week it is 120,000 x 7 = 840,000 times our heart beats Â in 1 week givenÂ athlete’s heart beats in 1 week is 607,000 times so compared to both it is

840,000 – 607,000 = 233,000 times

So our heart beats 233,000 times more compared to the athlete in 1 week

Question 18.

A whaleâ€™s brain weighs 10^{3} times as much as a platypusâ€™s brain. The whaleâ€™s brain weighs 9,000 grams. How many grams does the platypusâ€™s brain weigh?

Answer:

platypusâ€™s brain weighs 9 grams

Explanation:

Given whale’ brain weighs 10^{3} timesÂ as much as a platypusâ€™s brain and also given that whaleâ€™s brain weighs 9,000 grams

so platypusâ€™s brain weighs 9,000 x 1/ 10^{3} times = 9,000x 1/1000 = 9 grams.

### Multiplication Patterns Homework & Practice 4.1

**Find the product**

Question 1.

37 Ã— 10^{4}

Answer:

37 Ã— 10^{4Â }= 370,000

Explanation:

The product of 37 Ã— 10^{4Â }= 37 x 10 x 10 x 10 x 10= 370,000

Question 2.

400 Ã— 90 = ______

Answer:

400 Ã— 90 = 36,000

Explanation:

The product of 400 Ã— 90 = 4 x 10 x 10 x 9 x 10 = 4 x 9 x 10^{3} = 36,000

Question 3.

100 Ã— 900 = _____

Answer:

100 x 900 = 90,000

Explanation:

The product of 100 x 900 = 10 x 10 x 9 x 10 x 10 = 9 x 10^{4Â }= 90,000

Question 4.

800 Ã— 700 = _____

Answer:

800 x 700 = 560,000

Explanation:

The product of 800 x 700 = 8 x 10 x 10 x 7 x 10 x 10 = 8 x 7 x 10^{4Â }=560,000

Question 5.

867 Ã— 10^{3} = ______

Answer:

867 Ã— 10^{3} =867,000

Explanation:

The product of 867 Ã— 10^{3} = 867 x 10 x 10 x 10 = 867,000

Question 6.

12 Ã— 6,000 = _______

Answer:

12 x 6,000 = 72,000

Explanation:

The product of 12 x 6,000 = 12 x 6 x 10 x 10 x 10= 12 x 6 x 10^{3} = 72,000

**Find the missing factor.**

Question 7.

____ Ã— 10^{2} = 3,000

Answer:

30 x 10^{2} = 3,000

Explanation:

The missing factor ofÂ ____ Ã— 10^{2} = 3,000 is 3,000 x 1/100= 3 x 10^{3} / 10^{2Â }=30

Question 8.

______ Ã— 500 = 450,000

Answer:

900 x 500 = 450,000

Explanation:

The missing factor of ______ Ã— 500 = 450,000 is 450,000 x 1/500= 450,000/500=

45 x 10^{4Â Â }/ 5 x 10^{2Â }= 9 x 10^{2Â }= 900

Question 9.

80 Ã— _____ = 640,000

Answer:

80 x 8000 = 640,000

Explanation:

The missing factor of 80 Ã— _____ = 640,000 is 640,000 x 1/80 = 64 x 10^{4Â Â }/ 8 x 10=

8 x 10^{3Â }=8,000

Question 10.

**Reasoning**

Do 50 Ã— 8,000 and 50 Ã— 9,000 have the same number of zeros in their products? Explain.

Answer:

Yes, 50 Ã— 8,000 and 50 Ã— 9,000 have the same number of zeros in their products

Explanation:

Why because 50 x 8,000 = 5 x 10 x 8 x 10 x 10 x 10 = 5 x 8 x 10^{4
}and 50 x 9,000 = 5 x 10 x 9 x 10 x 10 x 10 = 5 x 9 x 10^{4
}so when compared between 5 x 8 x 10^{4Â Â }and 5 x 9 x 10^{4Â }we have 4 zeros in both the products.

Question 11.

**DIG DEEPER!**

The product of a number and twice that number is 180,000. Write the multiplication equation.

Answer:

2 n^{2 }= 18 x 10^{4
}Explanation:

let the number be n and its twice is 2 n is 180,000

n x 2n = 18 x 10 x 10 x 10 x 10

2 n^{2 }= 18 x (10 x 10) x (10 x 10)

so the multiplication equation is 2 n^{2 }= 18 x 10^{4Â }

Question 12.

**Modeling Real Life**

A hummingbird flutters its wings 80 times in 1 second. A bumblebee flutters its wings 7,800 times in 1 minute. Which animal flutters its wings more times in 1 minute?

Answer:

bumblebee flutters more

Explanation:

Given humming bird flutters its wings 80 times in 1 second equals to 8 x 10,

bumblebee flutters its wings 7,800 times in 1 second equals to 78 x 10^{2
}as 78 x 10^{2Â }> 8 x 10 means bumblebee flutters its wings more than humming bird in 1 minute.

Question 13.

**DIG DEEPER!**

In 1 day, the blood in your body travels a total of 12,000 miles. This is about 4 times the distance across the United States from coast to coast. About how many miles is the distance across the United States?

Answer:

The distance across the United States is 3,000 miles.

Explanation:

Given in 1 day the blood in our body travels a total of 12,000 miles which is equal to 4 times the distance across the United States from coast to coast.

so the number of miles in the distance across the United States is

12,000 miles / 4=3,000 miles.

**Review & Refresh**

**Classify the triangle by its sides.**

Question 14.

Answer:

Equilateral Triangle

Explanation:

In theÂ given figure it is showing all the 3 sides are equal so we callÂ the triangle as Equilateral Triangle.

Question 15.

Answer:

Isosceles Triangle

Explanation:

In the above figure it is showing only 2 sides are equal so we call the given triangle as Isosceles Triangle.

Question 16.

Answer:

Scalene Triangle

Explanation:

In the above figure it is showing no side is equal so we call the given triangle as

Scalene Triangle.

### 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 partnerâ€™s. Did you choose the same expressions?

Answer:

29 x 26

30 x 25

Explanation:

so for 29 x 26 i am choosing the expression 30 x 25 as 29 is near to 30 and 26 is near to 26 i have selected the expression 30 x 25

21 x 24

20 x 25

Explanation :

for 21 x 24 i am choosing the expression 20 x 25 as 21 is near to 20 and 24 is near to 25 i have selected the expression 20 x 25

32 x 26

30 x 25

Explanation :

for 32 x 26 i am choosing the expression 30 x 25 as in the given expressions only 32 is near to 30 and 26 is near to 25 i have selected the expression 30 x 25

28 x 24

30 x 25

Explanation :

for 28 x 24 also i am choosing the expression 30 x 25 why because 28 is near to 30 and 24 is near to 25 so i am selecting the expressionÂ 30 x 25

Yes i have selected the same expression 30 x 25Â for all the three products 29 x 26, 32 x 26,28 x 24 because for all the given three products the nearest expression we are getting is 30 x 25

**Construct Arguments**

You estimate the product of 23 and 26 using the expression 25 Ã— 30. Without multiplying, determine whether the estimate is greater than or less than the actual product. Explain.

Answer:

Given the product 23 x 26 as 25 x 30

So the result of given estimate is greater than the actual value

Explanation:

Because as 25 is greater than 23 and 30 is greater than 26 so obviously the expression 25 x 30 has greater value than that of the product of 23 X 26

**Think and Grow: Estimate Products**

An overestimate is greater than the actual value, and an underestimate is less than the actual value. When you estimate a product, your answer will be an overestimate when both numbers are greater than the original factors. Your answer will be an underestimate when both numbers are less than the original factors.

**Example**

Use rounding to estimate 204 Ã— 61. Explain whether your estimate is an overestimate or an underestimate.

12 x 1,000 = 12,000

So, 204 Ã— 61 is about __12,444___. This is an __underestimate______ because about both rounded numbers are ___200___, __60____ the original factors.

**Example**

Use compatible numbers to estimate 23 Ã— 194. Explain whether your estimate is an overestimate or an underestimate.

Choose compatible numbers. Then multiply.

50 x100 = 5,000

So, 23 Ã— 194 is about __4,462____. This is an __overestimate_____ because both compatible numbers are __25____ __200____ the original factors.

**Show and Grow**

**Estimate the product. Explain whether your estimate is an overestimate or an underestimate.**

Question 1.

387 Ã— 29

Answer:

387 x 29 =11,223

400Â X 30 = 12,000 is overestimate

Explanation :

As our estimate afterÂ rounding each factor becomes 387 as 400 nearest hundredÂ and 29 as 30 to nearest ten so it is 400 x 30 = 12 x 1,000=12,000 as 387 x 29 < 400 x 30 as the estimate result is greater than the given product results our estimate is an overestimate

Question 2.

52 Ã— 913

Answer:

52 x 913 = 47,476

50 x 900 = 45,000 is underestimate

Explanation:

As our estimate after rounding each factor becomes 52 as 50 to nearest ten and 913 as 900 nearest hundred so it is 50 X 900 = 45,000

as 52 x 913 > 50 x 900 as the estimate result is less than the given product results

our estimate is an underestimate.

**Apply and Grow: Practice**

**Estimate the product. Explain whether your estimate is an overestimate or an underestimate.**

Question 3.

45 Ã— 98

Answer:

45 x 98 = 4,410

50 x 100 = 5,000 is overestimate

Explanation:

As our estimate after rounding each factor becomes 45 as 50 to nearest ten and 98 as 100 to nearest hundred so it is 50 X 100 = 5,000

as 45 x 98 < 50 x 100 as the estimate result is greater than the given product results our estimate is an overestimate

Question 4.

21 Ã— 404

Answer:

21 x 404 = 8,484

20 x 400 = 8,000 is underestimate

Explanation:

As our estimate after rounding each factor becomes 21 as 20 nearest ten and 404 as 400 to nearest hundred so it is 20 X 400 = 8,000

as 21 x 404 > 20 x 400 as the estimate result is less than the given product results our estimate is an underestimate.

Question 5.

394 Ã— 285

Answer:

394 x 285 = 112,290

400 x 300 = 120,000 is overestimate

Explanation:

our estimate after rounding each factor becomes 394Â as 400 to nearest hundred and 285 as 300 to nearest hundred so it is 400 X 300 = 120,000

as 394 x 285 < 400 x 300 as the estimate result is greater than the given product results our estimate is an overestimate

Question 6.

596 Ã— 488

Answer:

596 x 488 = 290,848

600 x 500 = 300,000 is overestimate

Explanation:

As our estimate after rounding each factor becomes 596Â as 600 to nearest hundred and 488 as 500 to nearest hundred so it is 600 X 500 = 300,000

as 596 x 488 < 600 x 500 as the estimate result is greater than the given product results our estimate is an overestimate

Question 7.

194 Ã— 46

Answer:

194 x 46=8,924

200 x 50 = 10,000 overestimate

Explanation:

As our estimate after rounding each factor becomes 194Â as 200 to nearest hundred and 46 as 50 to nearest ten so it is 200 X 50 = 10,000

as 194 x 46 < 600 x 500 as the estimate result is greater than the given product results our estimate is an overestimate

Question 8.

22 Ã— 221

Answer:

22 x 221 =4,862

20 x 200 = 4,000 underestimate

Explanation :

As our estimate after rounding each factor becomes 22Â as 20 to nearest ten and 221 as 200 to nearest hundred so it is 20 X 200 = 4,000

as 22 x 221 > 20 x 200 as the estimate result is less than the given product results our estimate is an underestimate.

Question 9.

**Number Sense**

You estimate 27 Ã— 408 by rounding each number to the nearest ten. Your friend estimates the product using the compatible numbers 25 and 400. Without multiplying, determine which answer is an overestimate and which answer is an underestimate. Explain.

Answer:

27 x 408

30 x 410 Mine is overestimate and

27 x 408

25 x 400 Friend is underestimate

Explanation:

Given my estimate as 27 x 408 by rounding the number to the nearest ten it becomes 27 as 30 and 408 as 410 as 27 is less than 30 and 408 is also less than 410 so the product 27 x 408 is less than 30 x 410

27 x 408

30 x 410

as 27 x 408 < 30 x 410 mine is overestimate.

Now 27 x 408

asÂ Â Â 25 x 400

my friend estimates the product using the compatible numbers 25 and 400 as 25 is less than 27 and 400 is less than 408 obviously the product results 25 X 400 <27 x 408 so my friend results are underestimate.

therefore mine is overestimate and friends is underestimate

Question 10.

**Writing**

Explain two different methods to estimate 49 Ã— 305. Which do you prefer?

Answer:

I prefer 50 x 300

Explanation:

49 x 305 by rounding each number to the nearest ten it is 50 x 310 ,

49 x 305

50 x 310

49 x 305=14,945 and 50 x 310 = 15,500

49 as 50 and 305 as 310 product so 49 is less than 50 and 305 is also less than 310 so the product 49 x 305 is less than 50 x 310

49 x 305 <Â 50 x 310 which is overestimate

now 49 x 305

50 x 300

49 x 305 compatible numbers are 50 and 300 the results 49 x 305 = 14,945 and 50 x 300 = 15,000 means 49 x 305 < 50 x 300 which is also overestimate,

as both the results are overestimate but i prefer 50,300Â compatible numbers only as these number results are very near to the given product 49 x 305 as compared to the rounding the numbers to nearest ten.

so i prefer 50 x 300

Question 11.

**DIG DEEPER!**

You estimate 9 Ã— 26 using the compatible numbers 10 and 25. Is your estimate an overestimate or an underestimate? Explain.

Answer:

My estimate is underestimate.

Explanation:

My estimate is given as 9 x 26 = 234

and compatible numbers result isÂ 10 x 25 = 250,

as 9 x26 < 10 x 25 as my estimate results is less than the compatible numbers result so my estimate is underestimate

**Think and Grow: Modeling Real Life**

**Example**

Earth travels about 1,118 miles in 1 minute. About how far does Earth travel in 1 hour?

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

There are 60 minutes in 1 hour, so multiply the distance by 60.

60 Ã— 1,118 = ?

Use rounding to estimate the product.

So, Earth travels about _60,000_____ miles in 1 hour.

**Show and Grow**

Question 12.

Old Faithful erupts about 19 times in 1 day. Each eruption sprays about 6,050 gallons of water. About how many gallons of water does Old Faithful spray in 1 day?

Answer:

Old faithful spray in 1 day19 x 6,000= 114,000 gallons of water

Explanation :

Given Old Faithful erupts about 19 times in 1 day and each eruption sprays about 6,050 gallons of water, so Old faithful sprays about 19 x 6,050=114,950 gallons of water in 1 day.

Now using rounding to estimate the product it becomes 19 as 20 and 6,050 as 6,000

so Old faithful sprays about 19 x 6,000=114,000 gallons of water in 1 day.

Question 13.

Workers place a foam finger on every seat in a stadium for an upcoming football game. There are 29 sections in the stadium and about 245 seats in each section. About how many foam fingers are needed? Is it better to have an overestimate or an underestimate? Explain.

Answer:

Needed are 7,105 number of foam fingers and It is better to have overestimate

Explanation:

Given there are total 29 sections in the stadium

and 245 seats in each section.

The number of foam fingers needed would be 29 x 245 = 7,105 foam fingers

So we need 7,105 number of foam fingers

So now by using rounding 29 becomes 30 and 245 as 250 so it becomes

30 x 250=7,500 foam fingers.

Now on comparing 29 x 245 < 30 x 350 so the results is overestimate.

So it is better to have overestimate only

Question 14.

**DIG DEEPER!**

One acre of land is equal to the area of a rectangular piece of land that is 22 yards wide and 220 yards long. Central Park in New York City is 843 acres. What is the approximate area of Central Park in square yards?

Answer:

Central Park in New York City has 22 x 220 x 843 square yards

Explanation:

Given one acre of land is equal to 22 yards wide and 220 yards long

means one acre is 22 x 220 square yards

So Central Park in New York City has 22 x 220 x 843 square yards.

### Estimate Products Homework & Practice 4.2

**Use rounding to estimate the product. Explain whether your estimate is an overestimate or an underestimate.**

Question 1.

85 Ã— 96

Answer:

After rounding 90x 100= 9,000, overestimate

Explanation:

85 x 96=8,160Â after rounding it becomes 90 x 100 =9,000

as 85 is less than 90 and 96 is less than 100 so it is overestimate

Question 2.

41 Ã— 21

Answer:

After rounding 40 x 20=800, underestimate

Explanation:

41 x 21 = 861 after rounding it becomes 40 x 20 = 800

as 41 is greater than 40 and 21 is also greater than 20 so it becomes underestimate

**Use compatible numbers to estimate the product. Explain whether your estimate is an overestimate or an underestimate.**

Question 3.

56 Ã— 106

Answer:

56 x 106 = 5,936 and 55 x 100 = 5,500

as 5,936 > 5,500 ,So my estimate is overestimate

Explanation:

For 56 x 106 compatible numbers are 55 and 100 and its product is 5,500,

56 is greater than 55 and 106 is greater than 100,so the product of given numbers is greater than the product of compatible numbers, so my estimate is overestimate

Question 4.

23 Ã— 597

Answer:

23 x 597 = 13,731 and 25 x 600 = 15,000

as 13,731 < 15,000, So my estimate is underestimate

Explanation:

For 23 x 597 compatible numbers are 25 and 600

56 is greater than 55 and 106 is greater than 100,so the product of given numbers is lesser than the products of compatible numbers, so my estimate is underestimate

**Estimate the product**

Question 5.

203 Ã— 85

Answer:

203 x 85 = 17,255 and 200 x 90 = 18,000

as 17,255 < 18,000 So my estimate is underestimate

Explanation:

For 203 x 85 compatible numbers are 200 and 90

203 is greater than 200 and 85 is lesser than 90,But the product of given numbers is lesser than the product of compatible numbers so my estimate is underestimate

Question 6.

67 Ã— 405

Answer:

67 x 405 = 27,135 and 70 x 400 = 28,000

as 27,135 < 28,000 So my estimate is underestimate

Explanation:

For 67 x 405 compatible numbers are 70 and 400

As 67 is less than 70 and 405 is greater than 400,but the product of given numbers is lesser than the product of compatible numbers, so my estimate is underestimate

Question 7.

**Number Sense**

Estimate 426 Ã— 2,045. Is your answer an overestimate or an underestimate? Explain.

Answer:

426 x 2,045=871,170 and 430 x 2,000= 860,000

as 871,170 > 860,000 so mine is overestimate

Explanation:

For 426 x 2,045 compatible numbers are 430 and 2000

As 426 is less thanÂ and 430 and 2,045 is greater than 2,000 but the product of given numbers is greater than the product of compatible numbers, so my estimate is overestimate

Question 8.

**Open-Ended**

Write 2 three-digit numbers. Then estimate their product by rounding so that the answer is an underestimate.

Answer:

188 x 478 = 89,864

200 x 500 = 100,000

as 89,864 < 100,000 , so 188 x 478 is underestimate

Explanation:

To make the product as an underestimate let us take the 2 three-digit numbers as 188 and 478 and their compatible numbers 200 and 500,

As 188 is lesser than 200 and 478 is also less than 500 obviously the product becomes lesser than the product of compatible numbers and their product becomes underestimate.

Question 9.

**Reasoning**

Without multiplying, determine which estimate is closer to the actual product. Explain.

Answer:

The closer product to 21 x 372Â is 20 x 400

Explanation :

If we compare 21 x 372 with 20 x 400 we see 20 is less than 21 which is very close and 372 is near to 400 and the result is much closer than when compared to the result of product of 25 x 400 as 25 is greater than to 21 and even 400 is greater than 372, so obviously the product is much far, So the closer product is 20 x 400

Question 10.

**Modeling Real Life**

Your cousin sells jars of jam at a farmersâ€™ market. He sells 48 jars in 1 day for $12 each. About how much money does he earn in sales in 1 day?

Answer:

48 x $12 = $ 576 in 1 day

Explanation:

Given that cousin sells 48 jars in 1 day, each jar cost $12 , so the total cost per 1 day is product of number of jars X cost of 1 jar =48 x $12 = $ 576 in 1 day

So my cousin sells $ 576 in 1 day

Question 11.

**DIG DEEPER!**

SupersaurusA weighed 45 tons. About how many more pounds did an Argentinosaurus weigh than a Supersaurus?

Answer:

Argentinosaurus weighs 72,000 pounds more than a Supersaurus

Explanation:

As we know 1 ton = 2000 pounds, given Supersaurus weighed 45 tons = 45 x 2000=90,000 pounds and Argentinosaurus weighs 81 tons = 81 x 2000= 162,000 pounds, So 162,000 – 90,000= 72,000 means Argentinosaurus weigh 72,000 more than a Supersaurus

**Review & Refresh**

**Use the figure.**

Question 12.

Name a pair of lines that appear to be parallel.

Answer:

( A,G ) and ( C,J) appear as parallel

Explanation:

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet so ( A,G ) and ( C,J) appear as parallel

Question 13.

Name two lines that are perpendicular.

Answer:

( D, F ) and ( B, H ) are perpendicular

Explanation:

In geometry,

Two distinct lines intersecting each other at 90Â° or a right angle are called perpendicular lines

Question 14.

Name two intersecting lines.

Answer:

(D,F) and (C,J) are two intersecting lines

Explanation:

As the line DF are CJ are intersecting at point F so DF,CJ are called as intersecting lines

### Lesson 4.3 Multiply by One-Digit Numbers

**Explore and Grow**

Use the area model and partial products to find 1,985 Ã— 4.

Answer:

1,985 x 4 = 7,940

Reasonable 7,940Â is close to 8,000

Explanation :

Step 1: Multiply the ones. Regroup

4 x 5 ones = 20 ones, RegroupÂ 20 ones as 2 tens and 0Â ones

2

1985

__xÂ Â 4
__Â Â Â 0

Step 2 : Multiply the tens. Regroup

4 x 8 tensÂ = 32 tens,Â 32 tens + 2 tens = 34 tens, Regroup 34 tens as

3 hundreds and 4 tens

3

1985

__xÂ Â 4Â__

40

Step 3 : Multiply the hundreds. Regroup hundreds

4 x 9 hundreds = 36 hundreds, 36 hundreds + 3 hundreds = 39 hundreds

Regroup 39 hundreds as 3 thousands and 9 hundred

3

1985

__xÂ Â 4Â__

940

Step 4 : Multiply the thousands. Add the regrouped thousands

4 x 1 thousands = 4 thousands,4 thousands +3 thousands=7Â thousands

3

1985

__xÂ Â 4__

7,940

1,985 x 4 = 7,940Â Â Â Â Â Reasonable 7,940Â is close to 8,000

**Structure**

Explain how you can use an area model and partial products to find 2,083 Ã— 3.

Answer:

2,083 x 3 = 6,249

Reasonable 6,249Â is close to 6,000 or 6,300

Explanation:

Step 1: Multiply the ones.

3 x 3 ones = 9 ones,

2083

__xÂ Â 3
__Â Â Â 9

Step 2 : Multiply the tens. Regroup

3 x 8 tensÂ = 24 tens, Regroup 24 tens as 2Â hundreds and 4 tens

2

2083

__xÂ Â 3__

Â Â 49

Step 3 : Multiply the hundreds.

3 x 0 hundreds = 0 hundred, 0 hundred + 2 hundreds = 2 hundreds

2083

__xÂ Â 3__

Â 249

Step 4 : Multiply the thousands.

3 x 2Â thousands = 6 thousands

2083

__xÂ Â 3__

6,249

2,083 x 3 = 6,249Â Â Â Â Â Reasonable 6,249Â is close to 6,000 or 6,300

**Think and Grow: Multiply by One-Digit a Number**

**Example**

Find 8,902 Ã— 4. Estimate ___35,608___

So 8,902 x 4 = 35,608.Â Â Â Â Â Â Â Â Â Reasonable 35,608 is close to 35,600

**Show and Grow**

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

Question 1.

Answer:

1. 7,346 x 2= 14,692Â Â Â Â Â Â Â Â Reasonable 14,692 andÂ is close to 15,000

2. 12,053 x 3 = 36,159Â Â Â Â Â Â Reasonable 36,159 andÂ is close to 36,000

Explanation:

1.7,346 x 2=14,692

Step 1: Multiply the ones. Regroup

2 x 6 ones = 12 ones, Regroup 12 ones as 1 tens and 2 ones

1

7,346

__xÂ Â 2
__Â Â Â 2

Step 2 : Multiply the tens.

2 x 4 tensÂ = 8 tens,Â 8 tens + 1 tens = 9 tens

7,346

__xÂ Â 2__

Â Â 92

Step 3 : Multiply the hundreds.

2 x 3 hundreds = 6 hundreds

7,346

__xÂ Â Â 2__

Â Â 692

Step 4 : Multiply the thousands.

2 x 7 thousands = 14 thousands

7,346

__xÂ Â Â 2__

14,692

So 7,346 x 2 = 14,692Â Â Â Â Reasonable 14,692 andÂ is close to 15,000

2. 12,053 x 3 =36,159

Step 1: Multiply the ones.

3 x 3 ones = 9 ones

12,053

__xÂ Â Â 3
__Â Â Â Â 9

Step 2 : Multiply the tens. Regroup

3 x 5 tensÂ = 15 tens, Regroup 15 tens as 1 hundred and 5 tens

1

12,053

__xÂ Â Â Â 3__

Â Â Â Â 59

Step 3 : Multiply the hundreds. Regroup

3 x 0 hundreds = 0 hundreds, Regroup 0 hundred +1 hundred = 1 hundred

12,053

__xÂ Â Â 3__

159

Step 4 : Multiply the thousands.

3 x 2 thousands = 6 thousands

12,053

__xÂ Â Â 3__

Â 6,159

Step 5Â : Multiply the ten thousands.

3 x 1 ten thousands = 3 ten thousands

12,053

__xÂ Â Â 3__

36,159

12,053 x 3 = 36,159Â Â Â Â Â Â Â Reasonable 36,159 is close to 36,000

**Apply and Grow: Practice**

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

Question 3.

Answer:

503 x 5 = 2,515Â Â Â Â Â Â Reasonable as 2,515 is close to 2,500

Explanation:

Step 1: Multiply the ones.

5 x 3 ones = 15 ones, Regroup 15 ones as 1 tens and 5 ones

1

503

__xÂ 5
__Â Â 5

Step 2 : Multiply the tens. Regroup

5 x 0 tensÂ = 0 tens,Â 0 tens + 1 tens = 1 tens

503

__xÂ 5__

Â 15

Step 3 : Multiply the hundreds.

5 x 5 hundreds = 25 hundreds

503

__xÂ 5__

2,515

503 x 5 = 2,515Â Â Â Â Reasonable 2,515 is close to 2,500

Question 4.

Answer:

5,295 x 9 = 47,655Â Â Â Â Â Â Â Reasonable 47,655 is close to 48,000

Explanation:

Step 1: Multiply the ones. Regroup

9 x 5 ones = 45 ones, Regroup 45 ones as 4 tens and 5 ones

4

5,295

__xÂ Â Â 9
__Â Â Â 5

Step 2 : Multiply the tens. Regroup

9 x 9 tensÂ = 81 tens, Regroup 81 tens+ 4 tens = 85 tens as 8 hundred and 5 tens

8

5,295

__xÂ Â Â 9__

55

Step 3 : Multiply the hundreds. Regroup

9 x 2 hundreds = 18 hundreds, Regroup 18 hundred +8 hundred =

26 hundreds as 2 thousand and 6 hundreds

2

5,295

__xÂ Â Â 9__

655

Step 4 : Multiply the thousands.

9 x 5 thousands = 45 thousands, Regroup 45 thousands+2 thousand=47 thousand

2

5,295

__xÂ Â Â 9Â__

47,655

5,295 x 9Â =47,655Â Â Â Â Â Reasonable 47,655 is close to 48,000

Question 5.

Answer:

87,294 x 3 = 2,61,882Â Â Â Â Reasonable 2,61,888 is close to 2,60,000

Explanation:

Step 1: Multiply the ones. Regroup

3 x 4 ones = 12 ones, Regroup 12 ones as 1 ten and 2 ones

1

87,294

__xÂ Â Â 3
__Â Â Â Â 2

Step 2 : Multiply the tens. Regroup

3 x 9 tensÂ = 27 tens, RegroupÂ 27 tens + 1 ten = 28 tens as 2 hundred and 8 tens

2

87,294

__xÂ Â Â Â 3__

82

Step 3 : Multiply the hundreds. Regroup

3 x 2 hundreds = 6 hundreds, Regroup 6 hundred +2 hundred = 8 hundreds

87,294

__xÂ Â Â 3__

882

Step 4 : Multiply the thousands. Regroup

3 x 7 thousands = 21 thousands, Regroup as 2 ten thousands and 1 thousand

2

87,294

__xÂ Â Â 3__

1882

Step 5Â : Multiply the ten thousands.

3 x 8 ten thousands = 24 ten thousands,24 ten thousands+ 2 ten thousands

=26 ten thousands, regroup as 2 hundred thousand and 6 ten thousand

2

87,294

__xÂ Â Â 3__

2,61,882

87,294 x 3 =2,61,882Â Â Â Â Reasonable 2,61,888 is close to 2,60,000

Question 6.

399 Ã— 2 = _____

Answer:

399 x 2 = 798Â Â Â Â Reasonable 798 is close to 800

Explanation:

Step 1: Multiply the ones.

2 x 9 ones = 18 ones, Regroup 1 ones as 1 tens and 8 ones

1

399

__xÂ Â 2
__Â Â Â 8

Step 2 : Multiply the tens. Regroup

2 x 9 tensÂ = 18 tens,Â 18 tens + 1 tens = 19 tens, Regroup 19 tens as 1 hundredÂ and 9 tens

1

399

__xÂ Â 2__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

__Â Â 98__

Step 3 : Multiply the hundreds.

2 x 3 hundreds = 6 hundreds, Regroup 6 hundreds+1 hundreds=Â 7 hundreds

399

__xÂ Â 2Â__

798

So 399 x 2 = 798Â Â Â Â Reasonable 798 is close to 800

Question 7.

33,184 Ã— 2 = _____

Answer:

33,184 x 2 =66,368Â Reasonable 66,368 is close to 66,000

Explanation:

Step 1: Multiply the ones.

2 x 4 ones =8 ones

33,184

__xÂ Â Â 2
__Â Â Â Â 8

Step 2 : Multiply the tens. Regroup

2 x 8 tensÂ = 16 tens, Regroup 16 tens as 1 hundredÂ and 6 tens

1

33,184

__xÂ Â Â 2__

68

Step 3 : Multiply the hundreds. Regroup

2 x 1 hundreds = 2 hundreds, Regroup 2 hundreds +1 hundred = Â 3 hundreds

33,184

__xÂ Â Â 2__

368

Step 4 : Multiply the thousands.

2 x 3 thousands = 6 thousands

33,184

__xÂ Â Â 2__

Â 6368

Step 5Â : Multiply the ten thousands.

2 x 3 ten thousands = 6 ten thousands

33184

__xÂ Â Â 2__

66,368

66,368Â x 2 = 66,368Â Â Â Â Reasonable 66,368 is close to 66,000

Question 8.

60,759 Ã— 4 = _______

Answer:

60,759 x 4 = 2,43,036Â Â Â Â Reasonable 2,43,036 is close to 2,40,000

Explanation:

Step 1: Multiply the ones.

4 x 9 ones =36 ones, Regroup 36 ones as 3 tens and 6 ones

3

60759

__xÂ Â Â 4
__Â Â Â Â 6

Step 2 : Multiply the tens. Regroup

4 x 5 tensÂ = 20 tens, Regroup 20 tens + 3 tens = 23 tens as 2 hundred and 3 tens

2

60759

__xÂ Â Â 4__

36

Step 3 : Multiply the hundreds. Regroup

4 x 7 hundreds = 28 hundreds, Regroup 28 hundred +2 hundred =30 hundreds as 3 thousand and 0 hundreds

3

60759

__xÂ Â Â 4__

036

Step 4 : Multiply the thousands.

4 x 0 thousands = 0 thousands , Regroup 0 thousands + 3 thousands=3Â thousands

60759

__xÂ Â Â 4__

3036

Step 5Â : Multiply the ten thousands.

4 x 6 ten thousands =24 ten thousands

60759

__xÂ Â Â 4__

243068

60,759 x 4 = 2,43,036Â Â Â Â Reasonable 2,43,036 is close to 2,40,000

Question 9.

A multiplex has 9 different movie theaters. Each theater has 455 seats. How many seats are in the multiplex?

Answer:

9 x 455 = 4,095 seats

Explanation:

Given a multiplex has 9 different movie theaters, and each theater has 455 seats , so total number of seats in the multiplex is 9 x 455=4,095

there are total 4,095 seats available.

Question 10.

An interstellar object travels 85,700 miles in 1 hour. How far does the object travel in 5 hours?

Answer:

85,770 x 5 = 428,850 miles

Explanation:

Given interstellar object travels 85,700 miles in 1 hour, in 5 hours the interstellar object will travel 85,770 x 5 = 428,850 miles

Question 11.

Without multiplying, determine how much greater 4,395 Ã— 7 is than 4,395 Ã— 6. Explain.

Answer:

it is more by 4,395

Explanation:

Comparing the values both the sides 4,395 is same and as 7 is one time more than 6 we multiply the value by one more time,

so the value of 4,395 x 7 to 4,395 x 6 is one time greater by 4,395

Question 12.

**DIG DEEPER!**

Find the missing digits.

Answer:

40,716 Ã· 3 = 13572 , Missing digits are 1 , 5, 2

Explanation:

To get the missing digits we divide 40,716 by 3

3)40716(13572

3Â Â Â Â Â Â Â 3x 1=3

4-3 =1 , we take next digit 0 so it becomes10

——

10Â Â Â Â Â 3 x 3=9

09Â Â Â Â Â 10- 9=1 , we take next digit 7 becomes 17

——

17Â Â Â Â Â Â 3x 5 = 15

15Â Â Â Â Â Â 17-15=2, we take next digit 1 becomes 21

——

21Â Â Â Â Â Â 3 x 7 = 21

21Â Â Â Â Â Â 21-21 = 0,then we take next digit becomes 6

——–

06Â Â Â Â Â 3 x 2 =6

6Â Â Â Â Â Â 6-6=0 and we ends as nextÂ no number

——

0

If 40,716 is dividedÂ by 3 we will get results as 13572Â and missing digits are 1 , 5, 2

**Think and Grow: Modeling Real Life**

**Example**

A Cuvierâ€™s beaked whale can dive 1,324 feet deeper than 4 times the depth a beluga whale can dive. How deep can a Cuvierâ€™s beaked whale dive?

Write and solve an equation to find the depth.

Let d represent the diving depth of a Cuvierâ€™s beaked whale.

d = (4 Ã— 2,123) + 1,324

= __8,492___ + 1,324

= __9,816___

A Cuvierâ€™s beaked whale can diveÂ Â 9,816 feet.

**Show and Grow**

Question 13.

The height of Chicagoâ€™s Willis Tower is 469 feet more than 2 times the height of the Gateway Arch. How tall is Willis Tower?

Answer:

The height of Chicago’s Willis Tower is 1,729 feet

Explanation:

Willis Tower = ( 2 X height of the Gateway Arch) +469 feet

Given the height of the Gateway Arch inÂ St.Louis as 630 feet

Willis Tower = ( 2 X 630 feet ) + 469 feet

Willis Tower = 1,260 + 469 = 1,729 feet

Question 14.

**DIG DEEPER!**

The Amazon River is 350 miles shorter than 3 times the length of the Colorado River. How much longer is the Amazon River than the Mississippi River?

Answer:

Amazon River is 1,660 miles longer than the Mississippi River

Explanation:

Given Amazon River is = ( 3 x Colorado River )- 350 miles

Amazon River = (3 x 1,450)-350 miles

Amazon River = 4,350 – 350 = 4,000 miles

Now comparing Amazon River with Mississippi River = Mississippi River – Amazon River = 4,000-2,340=1,660 miles

So Amazon River is 1,660 miles longer than the Mississippi River

### Multiply by One-Digit Numbers Homework & Practice 4.3

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

Question 1.

Answer:

814 x 2=1,628Â Â Reasonable 1,624 is close to 1,600 or 2,000

Explanation:

Step 1: Multiply the ones.

2 x 4 ones = 8 ones.

814

__xÂ Â 2
__Â Â Â 8

Step 2 : Multiply the tens.

2 x 1 tensÂ = 2 tens,

814

__xÂ Â 2__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

__Â 28__

Step 3 : Multiply the hundreds.

2 x 8 hundreds = 16 hundreds

814

__xÂ 2__

1,628

814 x 2=1,628Â Â Â Reasonable 1,624 is close to 2,000 or 1,600

Question 2.

Answer:

206 x 4 = 824Â Â Â Â Â Â Â Reasonable 824 is close to 1,000

Step 1: Multiply the ones.

4 x 6 ones = 24 ones. Regroup 24 ones as 2 tens and 4 ones

2

206

__xÂ Â 4
__Â Â Â 4

Step 2 : Multiply the tens. Regroup

4 x 0 tensÂ = 0 tens, Regroup 0 tens + 2 tens = 2 tens

206

__xÂ Â 4__Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

__Â Â 24__

Step 3 : Multiply the hundreds.

4 x 2 hundreds = 8 hundreds

206

__xÂ 4__

824

206 x 4=824Â Â Â Reasonable 824 is close to 1,000

Question 3.

Answer:

2,425 x 6 = 14,550Â Â Â Â Â Â Â Reasonable 14,550 is close to 14,500

Explanation:

Step 1: Multiply the ones. Regroup

6 x 5 ones = 30 ones, Regroup 30 ones as 3 tens and 0 ones

3

2,425

__xÂ Â Â 6
__Â Â Â 0

Step 2 : Multiply the tens. Regroup

6 x 2 tensÂ = 12 tens, Regroup 12 tens+ 3 tens = 15 tens as 1 hundredÂ and 5 tens

1

2425

__xÂ Â 6__

50

Step 3 : Multiply the hundreds. Regroup

6 x 4 hundreds = 24 hundreds, Regroup 24 hundred +1 hundred =Â 25 hundreds as 2 thousand and 5 hundreds

2

2425

__xÂ Â 6__

550

Step 4 : Multiply the thousands.

6 x 2 thousands = 12 thousands, Regroup 12 thousands+2 thousands as

14 thousand

2425

__xÂ Â Â 6__

14,550

2,425 x 6 = 14,550 Â Â Â Â Reasonable 14,550 is close to 14,500

Question 4.

Answer:

5,149 x 9 = 46,341Â Â Â Reasonable 46,341 is close to 46,000

Explanation:

Step 1: Multiply the ones. Regroup

9 x 9 ones = 81 ones, Regroup 81 ones as 8 tens and 1 ones

8

5149

__xÂ Â Â 9
__Â Â Â 1

Step 2 : Multiply the tens. Regroup

9 x 4 tensÂ = 36 tens, Regroup 36 tens+ 8 tens =44 tens as 4 hundredÂ and 4 tens

4

5149

__xÂ Â 9__

41

Step 3 : Multiply the hundreds. Regroup

9 x 1 hundreds = 9 hundreds, Regroup 9 hundred +4 hundred =13 hundreds as

1 thousand and 3 hundreds

1

5149

__xÂ Â 9__

341

Step 4 : Multiply the thousands.

9 x 5 thousands = 45 thousands, Regroup 45 thousands+1 thousand as 46 thousand

5149

__xÂ Â 9__

46,341

5,149 x 9 = 46,341Â Â Â Reasonable 46,341 is close to 46,000

Question 5.

Answer:

17,823 x 3 = 53,469Â Â Â Â Reasonable 53,469 is close to 50,000 or 53,000

Explanation:

Step 1: Multiply the ones.

3 x 3 ones = 9 ones

17,823

__xÂ Â Â 3
__Â Â Â Â 9

Step 2 : Multiply the tens.

3 x 2 tensÂ = 6 tens

17,823

__xÂ Â Â Â 3__

69

Step 3 : Multiply the hundreds. Regroup

3 x 8 hundreds = 24 hundreds, Regroup as 2 thousands and 4Â hundreds

2

17823

__xÂ Â Â 3__

Â Â 469

Step 4 : Multiply the thousands. Regroup

3 x 7 thousands = 21 thousands, Regroup 21 thousands+ 2 thousands= 23 thousands as 2 ten thousands and 3 thousands

2

17823

__xÂ Â Â 3__

3,469

Step 5Â : Multiply the ten thousands.

3 x 1 ten thousands = 3 ten thousands ,Regroup 3 ten thousands + 2 ten thousands = 5 ten thousands

17823

__xÂ Â Â 3__

53,469

17823 x 3 = 53,469Â Â Â Reasonable 53,469 is close to 50,000 or 53,000

Question 6.

Answer:

61,837 x 8 = 494,696Â Â Â Â Reasonable 494,696 is close to 500,000

Explanation:

Step 1: Multiply the ones.

8 x 7 ones =56 ones, Regroup 56 ones as 5 tens and 6 ones

5

61,837

__xÂ Â Â 8
__Â Â Â Â 6

Step 2 : Multiply the tens. Regroup

8 x 3 tensÂ = 24 tens, Regroup 24 tens + 5 tens = 29 tens as 2 hundred and 9 tens

2

61,837

__xÂ Â Â 8__

96

Step 3 : Multiply the hundreds. Regroup

8 x 8 hundreds = 64 hundreds, Regroup 64 hundred +2 hundred =66Â hundreds as 6 thousand and 6 hundreds

6

61837

__xÂ Â Â 8__

696

Step 4 : Multiply the thousands. Regroup

8 x 1 thousands = 8 thousands , Regroup 8 thousands + 6 thousands=

14 thousands as 1 ten thousand and 4 thousands

1

61837

__xÂ Â Â 8__

4,696

Step 5Â : Multiply the ten thousands. Regroup

8 x 6 ten thousands =48 ten thousands, Regroup 48 ten thousands +1 ten thousand = 49 ten thousands

61837

__xÂ Â Â 8__

494,696

61,837 x 8 = 494,696Â Â Â Â Reasonable 494,696 is close to 500,000

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

Question 7.

4,257 Ã— 5 = _______

Answer:

4,257 x 5 = 21,285Â Â Â Â Â Â Â Â Reasonable 21,285 is close to 20,000

Explanation:

Step 1: Multiply the ones. Regroup

5 x 7 ones = 35 ones, RegroupÂ 35 ones as 3 tens and 5 ones

3

4257

__xÂ Â 5
__Â Â Â 5

Step 2 : Multiply the tens. Regroup

5 x 5 tensÂ = 25 tens, Regroup 25 tens+ 3 tens =28 tens as 2 hundreds and 8 tens

2

4257

__xÂ Â 5__

85

Step 3 : Multiply the hundreds. Regroup

5 x 2 hundreds = 10 hundreds, Regroup 10 hundreds + 2 hundreds =Â 12 hundreds as 1 thousand and 2 hundreds

1

4257

__xÂ Â 5__

285

Step 4 : Multiply the thousands.

5 x 4 thousands = 20 thousands, Regroup 20 thousands + 1 thousand =21 thousands

4257

__xÂ Â 5__

21,285

4,257 x 5 = 21,285Â Â Â Â Â Â Â Â Reasonable 21,285 is close to 20,000

Question 8.

6,702 Ã— 6 = _____

Answer:

6,702 x 6 = 40,212Â Â Â Â Â Â Â Â Â Â Reasonable 40,212 is close to 40,000

Explanation:

Step 1: Multiply the ones. Regroup

6 x 2 ones = 12 ones, RegroupÂ 12 ones as 1 ten and 2 ones

1

6702

__xÂ Â 6
__Â Â Â 2

Step 2 : Multiply the tens. Regroup

6 x 0 tensÂ = 0 tens, RegroupÂ 0 tens+ 1 tens =1 tens

6702

__xÂ Â 6__

12

Step 3 : Multiply the hundreds. Regroup

6 x 7 hundreds = 42 hundreds, Regroup 42 hundreds as 4 thousands and 2 hundreds

4

6702

__xÂ Â 6__

212

Step 4 : Multiply the thousands.

6 x 6 thousands = 36 thousands, Regroup 36 thousands+ 4 thousand = 40 thousands

6702

__xÂ Â 6__

40,212

6,702 x 6 = 40,212Â Â Â Â Â Â Â Â Reasonable 40,212 is close to 40,000

Question 9.

28,956 Ã— 7 = ______

Answer:

28,956 x 7 = 2,02,692Â Â Â Â Â Â Â Â Â Reasonable 2,02,692 is close to 2,00,000

Explanation:

Step 1: Multiply the ones.

7 x 6 ones =42 ones, Regroup 42 ones as 4 tens and 2 ones

4

28,956

__xÂ Â Â Â 7__

Â Â Â Â 2

Step 2 : Multiply the tens. Regroup

7 x 5 tensÂ = 35 tens, Regroup 35 tens + 4 tens = 39 tens as 3 hundreds and 9 tens

3

28956

__xÂ Â Â 7__

92

Step 3 : Multiply the hundreds. Regroup

7 x 9 hundreds = 63 hundreds, Regroup 63 hundreds +3 hundred =

66Â hundreds as 6 thousand and 6 hundreds

6

28956

__xÂ Â Â 7__

692

Step 4 : Multiply the thousands. Regroup

7 x 8 thousands = 56 thousands , Regroup 56 thousands + 6 thousands=

62 thousands as 6 ten thousand and 2 thousands

6

28956

__xÂ Â Â 7__

2692

Step 5Â : Multiply the ten thousands. Regroup

7 x 2 ten thousands = 14Â ten thousands, Regroup 14 ten thousands +

6 ten thousands = 20 ten thousands

28956

__xÂ Â Â 7__

20,2692

28,956 x 7 = 2,02,692Â Â Â Â Â Â Â Â Â Reasonable 2,02,692 is close to 2,00,000

Question 10.

A parking garage has 8 levels. There are 194 parking spots on each level. How many parking spots does the garage have?

Answer:

194 x 8 =1,552 parking spots

Explanation:

Given a parking garage has 8 levels and each level has 194 parking spots so total number of parking spots are 194 is multiplied by 8 ,194 x 8 =1,552 , there are total

1,552 parking spots available in the garage.

Question 11.

**YOU BE THE TEACHER**

Newton finds 16,041 Ã— 8. Is Newton correct? Explain.

Answer:

Yes, Newton is correct

Explanation:

Step 1: Multiply the ones.

8 x 1 ones = 8 ones

16,041

xÂ Â Â Â 8

Â Â Â Â 8

Step 2 : Multiply the tens. Regroup

8 x 4 tensÂ = 32 tens, Regroup 3 hundreds and 2 tens

3

16,041

__xÂ Â Â 8__

28

Step 3 : Multiply the hundreds. Regroup

8 x 0 hundreds = 0 hundreds, Regroup 0 hundreds +3 hundreds = 3Â hundreds

16,041

__xÂ Â Â 8__

328

Step 4 : Multiply the thousands. Regroup

8 x 6 thousands = 48 thousands , Regroup 48 thousands as 4 ten thousand and 8 thousands

4

16,041

__xÂ Â Â 8Â __

8328

Step 5Â : Multiply the ten thousands. Regroup

8 x 1 ten thousands = 8 ten thousands, Regroup 8 ten thousands + 4 ten thousands = 12 ten thousands

16,041

__xÂ Â Â 8__

128,328

As the value of 16,041 x 8 = 128,328, Yes Newton is correct

Question 12.

**DIG DEEPER!**

Write a different multiplication problem that has the same product as 726 Ã— 5.

Answer:

726 x 5 =3,630

605 x 6 =3,630

Explanation:

we divide the product 3630 by 6

we get Quotient as 605 meansÂ when we multiply 605 x 6 we get theÂ same product result 3,630 similarly when 726 x 5 is multiplied,

So 726 x 5 = 605 x 6

Question 13.

**Modeling Real Life**

The land area of Florida is 8,056 square miles more than 5 times the land area of Vermont. What is the land area of Florida?

Answer:

The land area of Florida is 49,496 square miles

Explanation:

Given land area of Florida is 8,056 square miles more than 5 times the land area of Vermont and land area of Vermont is 9,216 square miles

land area of Florida = ( 5 x land area of Vermont ) + 9,216 square miles

land area of Florida = ( 5 x 8056 ) + 9,216 square miles

land area of Florida =40280+9,216 = 49,496 square miles

So the land area of Florida is 49,496 square miles.

Question 14.

**DIG DEEPER!**

A solar farm has 6 rectangular arrays of solar panels. Each array has 105 rows with 8 panels in each row. How many solar panels are on the solar farm?

Answer:

6 x 105 x 8 = 5,040 panels

Explanation:

Given a solar farm has 6 rectangular arrays of solar panels and each array has 105 rows with 8 panels in each row so there are 105 x 8 = 840 panels and we have total 6 rectangular arrays

So total number of solar panels available are 6 x 840 =5,040 panels

**Review & Refresh**

**Multiply.**

Question 15.

2 Ã— \(\frac{1}{4}\)

Answer:

2 x 1/4=1/2 or 1 by 2

Explanation:

When 2 is multiplied by fraction of 1,4 we get 2 x 1/4 as 1/2 or 1 by 2

Question 16.

3 Ã— \(\frac{2}{6}\)

Answer:

3 x 2/6 = 6/6 =1

Explanation:

When 3 is multiplied by fraction of 2,6 we get 3 x 2/6 as 6/6 equals to 1

Question 17.

1 Ã— \(\frac{7}{10}\)

Answer:

1 x 7/10 = 7/10 or 0.7

Explanation:

When 1 is multiplied by fraction of 7,10 we get 1 x 7/10 as 7/10 or 0.7

### Lesson 4.4 Multiply by Two-Digit Numbers

**Explore and Grow**

Use the area model and partial products to find 28 Ã— 13.

Answer:

28 x 13 = 364Â Â Â Â Â Â Reasonable 364 is close to 400

Explanation:

Step 1: Multiply 28 by 3 ones. Regroup

3 ones x 28 = 84 ones

2

28

x 13

Â 84

Step 2: Multiply 28 by 1 tens or 10, Regroup

1 tens x 28 =28 tens =280 ones

28

x 13

Â 84

280

Step 3 : Add the partial products.

28

xÂ Â 13

Â Â 84

+280

364

28 x 13 =364Â Â Â Â Â Â Reasonable 364 is close to 400

**Repeated Reasoning**

Explain how you can use an area model and partial products to find 128 Ã— 13.

Answer:

128 x 13 =1,664Â Â Â Â Â Â Reasonable 1,664 is close to 1,600

Explanation:

Step 1: Multiply 128 by 3 ones. Regroup

3 ones x 128 = 384 ones

2

128

xÂ 13

Â 384

Step 2: Multiply 128 by 1 tens or 10, Regroup

1 tens x 128 =128 tens =1280 ones

128

Â Â x 13

Â Â 384

1280

Step 3 : Add the partial products.

128

xÂ Â Â 13

Â Â Â 384

+ 1280

1664

128 x 13 =1,664Â Â Â Â Â Â Reasonable 1,664 is close to 1,600

**Think and Grow: Multiply by a Two-Digit Number**

**Example**

Find 312 Ã— 82. Estimate _______

So 312 x 82= 25,584Â Â Â Â Â Â Â Â Â Reasonable 25,584 is close to 25,500

Show and Grow

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

Question 1.

Answer:

184 x 23 = 4,232Â Â Â Â Â Â Â Â Â Â Â Reasonable 4,232 is close to 4,000

Explanation:

Step 1: Multiply 184 by 3 ones. Regroup

3 ones x 184 = 552 ones

21

184

x 23

552

Step 2: Multiply 184 by 2 tens or 20, Regroup

2 tens x 184 =368 tens =3680 ones

1

184

Â x 23

Â 552

3680

Step 3 : Add the partial products.

184

xÂ Â 23

Â Â Â 552

+3680

4232

184 x 23 =4,232Â Â Â Â Â Â Reasonable 4,232 is close to 4,000

Question 2.

Answer:

817 x 49 = 40,033Â Â Â Â Â Â Reasonable 40,033 is close to 40,000

Explanation:

Step 1: Multiply 817 by 9 ones. Regroup

9 ones x 817 = 7353 ones

1 6

817

x 49

7353

Step 2: Multiply 817 by 4 tens or 40, Regroup

4 tens x 817 =3,268 tens =32680 ones

2

817

Â x 49

Â 7353

32680

Step 3 : Add the partial products.

817

xÂ Â 49

Â Â Â 7353

+32680

40033

817 x 49 =40,033Â Â Â Â Â Â Reasonable 40,033 is close to 40,000

Question 3.

Answer:

5046 x 91 = 4,59,186Â Â Â Â Â Reasonable 4,59,186 is close to 4,60,000

Explanation:

Step 1: Multiply 5046 by 1 ones. Regroup

1 ones xÂ = 5046 ones

5046

xÂ 91

5046

Step 2: Multiply 5046 by 9 tens or 90, Regroup

9 tens x 5046 =45,414 tens =45,4140 ones

45

5046

Â xÂ Â 91

Â Â 5046

454140

Step 3 : Add the partial products.

5046

xÂ Â Â 91

Â Â Â Â 5046

+ 454140

4,59,186

5046 x 91 = 4,59,186Â Â Â Â Reasonable 4,59,186 is close to 4,60,000

**Apply and Grow: Practice**

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

Question 4.

Answer:

96 x 24 = 2,304Â Â Â Â Â Â Â Â Reasonable 2,304 is close to 2,300

Explanation:

Step 1: Multiply 96 by 4 ones. Regroup

4 ones x 96 =Â ones

2

96

x 24

384

Step 2: Multiply 96 by 2 tens or 20, Regroup

2 tens x 96 =192 tens =1920 ones

1

96

Â x 24

Â 384

1920

Step 3 : Add the partial products.

96

xÂ Â 24

Â Â Â 384

+1920

2,304

96 x 24 = 2,304Â Â Â Â Reasonable 2,304 is close to 2,300

Question 5.

Answer:

108 x 19 = 2,052Â Â Â Â Â Â Â Reasonable 2,052 is close to 2,000

Explanation:

Step 1: Multiply 108 by 9 ones. Regroup

9 ones x 108 = 972 ones

7

108

x 19

972

Step 2: Multiply 108 by 1 tens or 10, Regroup

1 tens x 108 =108 tens =1080 ones

108

Â x 19

Â 972

1080

Step 3 : Add the partial products.

108

xÂ 19

Â Â Â 972

+1080

2,052

108 x 19 = 2,052Â Â Â Â Â Â Â Reasonable 2,052 is close to 2,000

Question 6.

Answer:

6420 x 75 = 4,81,500Â Â Â Â Â Â Reasonable 4,81,500 is close to 5,00,000

Explanation:

Step 1: Multiply 6420 by 5 ones. Regroup

5 ones x 6420 = 32100 ones

21

6420

xÂ 75

32,100

Step 2: Multiply 6420 by 7 tens or 70, Regroup

7 tens x 6420 =44,940 tens =449400 ones

6420

Â x 75

Â 32100

449400

Step 3 : Add the partial products.

6420

xÂ Â 75

Â Â Â 32100

+449400

481500

6420 x 75 = 4,81,500Â Â Â Â Â Â Reasonable 4,81,500 is close to 5,00,000

Question 7.

802 Ã— 41 = ______

Answer:

802 x 41 = 32,882Â Â Â Â Â Â Â Â Â Reasonable 32,882 is close to 33,000

Explanation:

Step 1: Multiply 802 by 1 ones. Regroup

1 ones x 802 = 802 ones

802

x 41

802

Step 2: Multiply 802 by 4 tens or 40, Regroup

4 tens x 802 =3208 tens =32080 ones

802

Â x 41

Â 802

32080

Step 3 : Add the partial products.

802

xÂ Â Â Â 41

Â Â Â Â 802

+32080

32,882

802 x 41 = 32,882Â Â Â Â Â Reasonable 32,882 is close to 33,000

Question 8.

577 Ã— 86 = _____

Answer:

577 x 86 = 49,622Â Â Â Â Â Â Â Â Â Reasonable 49,622 is close to 50,000

Explanation:

Step 1: Multiply 577 by 6 ones. Regroup

6 ones x 577 =3,462 ones

4 4

577

x 86

3462

Step 2: Multiply 577 by 8 tens or 80, Regroup

8 tens x 577 =4616 tens =46160 ones

577

Â x 86

Â 3462

46160

Step 3 : Add the partial products.

577

xÂ Â Â 86

Â Â 3462

+46160

49622

577 x 86 = 49,622Â Â Â Â Â Â Â Â Â Reasonable 49,622 is close to 50,000

Question 9.

9,513 Ã— 67 = _____

Answer:

9513 x 67 = 6,37,371Â Â Â Â Â Â Â ReasonableÂ 6,37,371Â Â is close to 6,50,000

Explanation:

Step 1: Multiply 9513 by 7 ones. Regroup

7 ones x 9513 =66,591 ones

2

9513

x 67

66,591

Step 2: Multiply 9513 by 6 tens or 60, Regroup

6 tens x 9513 =57078 tens = 570780 ones

9513

Â x 67

Â 66591

570780

Step 3 : Add the partial products.

9513

xÂ Â Â 67

Â Â 66591

+570780

637371

9513 x 67 = 6,37,371Â Â Â Â Â Â Â ReasonableÂ 6,37,371Â Â is close to 6,50,000

Question 10.

Is 6,364 a reasonable product for 706 Ã— 45? Explain your reasoning.

Answer:

No 6,344 is not a reasonable product for 706 x 45 as 706 x 45 = 31,770

Explanation:

When we multiply 706 x 45 we get result as 31,770

as 6,364Â is not at all close to 31,770, So 6,344 is not reasonable product for 706 x 45

Question 11.

**DIG DEEPER!**

Which two-digit number when multiplied by itself has a product of 625?

Answer:

25, because 25 x 25 = 625

Explanation:

Given that a two-digit number when multiplied by itself has a product of 625

lets take the two digit number as X and X x X = 625

X^{2}=625 so X = square root of 625 = âˆš625= âˆš25 x 25, X = 25

So 25 when multiplied by itself we get 625

**Think and Grow: Modeling Real Life**

**Example**

A blood bank receives 58 donors in 1 day. Each person donates 1 pint, or about 473 milliliters of blood. About how many milliliters of blood are donated that day?

Multiply the number of people by the amount of blood each person donates to find the total amount of blood donated.

Multiply 473 and 58.

So, about _27,434_ milliliters of blood are donated that day.

**Show and Grow**

Question 12.

A store sells 15 drones. How much money does the store collect?

Answer:

248 x 15 = $3,720

Explanation:

Given the cost of drone as $248 and the store sells 15 drones, total money collected in the store is $248 x 15=$3,720

Step 1: Multiply 248 by 5 ones. Regroup

5 ones x 248 = 1240 ones

4

248

x15

1240

Step 2: Multiply 248 by 1 tens or 10, Regroup

1 tens x 248 =248 tens = 2480 ones

248

Â x 15

Â 1240

2480

Step 3 : Add the partial products.

248

xÂ 15

Â 1240

+2480

3720

The store collected total amount is $3,720

Question 13.

What is the area of the soccer field?

Answer:

The area of the soccer field is 120 x 80 =9,600 square yards

Explanation:

Step 1: Multiply 120 by 0 ones.

0 ones x 120 =120 ones

120

x 80

000

Step 2: Multiply 120 by 8 tens or 80, Regroup

8 tens x 120 =960 tens =Â 9600 ones

120

x 80

Â 000

9600

Step 3 : Add the partial products.

120

x 80

Â Â 000

+9600

9600

The total area of the soccer field is 120 x 80 =9,600 square yards

Question 14.

The Cassini spacecraft orbited Saturn for 13 years and 77 days. Three of those years were leap years. For how many days did the Cassini spacecraft orbit Saturn? Justify your answer.

Answer:

Cassini spacecraft orbited Saturn for total 4,825 days

Explanation:

Given the Cassini spacecraft orbited Saturn for 13 years and 77 days and three of those years were leap, First we need to convert years to days and add to 77 days, we knowÂ each year has 365 days so first we multiply 365 with 13= 365 x 13 = 4,745 days,

365

x 13

4,745

And we know leap year has 366 days and in 13 years we have 3 leap years so we will add 3 more days to 4,745+3=4,748 days or

adding 3 days as it is saying in 13 years leap years 3 years are leap to 4,745 days=4,745+3=4,748 days

3 days as 3 are leap years

4745

+Â Â 3

4,748

Now adding 4,748 and 77 days

4,748

+Â Â 77

4,825

Cassini spacecraft orbited Saturn for total 4,825 days

### Multiply by Two-Digit Numbers Homework & Practice 4.4

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

Question 1.

Answer:

107 x 11 =1,177Â Â Â reasonable 1,177 is close to 1,000 or 12,00

Explanation:

Step 1: Multiply 107 by 1 ones.

1 ones x 107 =107 ones

107

x 11

107

Step 2: Multiply 107 by 1 tens or 10, Regroup

1 tens x 107 =107 tens =Â 1070 ones

107

x 11

Â 107

1070

Step 3 : Add the partial products.

107

x 11

Â Â 107

+1070

1,177

107 x 11 =1,177Â Â Â reasonable 1,177 is close to 1,000 or 12,00

Question 2.

Answer:

72 x 13 = 936Â Â Â Â reasonable 936 is close to 1,000

Explanation:

Step 1: Multiply 72 by 3 ones.

3 ones x 72 =216 ones

72

x 13

216

Step 2: Multiply 72 by 1 tens or 10, Regroup

1 tens x 72 =72 tens =Â 720 ones

72

x 13

Â 216

Â 720

Step 3 : Add the partial products.

72

x 13

Â Â 216

+720

936

72 x 13 =936Â Â Â Â reasonable 936 is close to 1,000

Question 3.

Answer:

466 x 27 = 12,582Â Â Â Â reasonableÂ 12,582 is close to 13000 or 12,600

Explanation:

Step 1: Multiply 466 by 7 ones.

7 ones x 466 = 3262 ones

44

466

x 27

3262

Step 2: Multiply 466 by 2 tens or 20, Regroup

2 tens x 466 =932 tens = 9320 ones

466

x 27

Â 3262

Â 9320

Step 3 : Add the partial products.

466

x 27

Â 3262

+9320

12,582

466 x 27 = 12,582Â Â reasonableÂ Â 12,582 is close to 13000 or 12,600

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

Question 4.

Answer:

83 x 57 = 4,731Â Â Â Â Â Â Â reasonable 4731 is close to 5,000

Explanation:

Step 1: Multiply 83 by 7 ones.

7 ones x 83 = 581 ones

2

83

x 57

__581__

Step 2: Multiply 83 by 5 tens or 50, Regroup

5 tens x 83 =415 tens =Â 4150 ones

83

x 57

Â 518

4150

Step 3 : Add the partial products.

83

x 57

Â Â Â 581

+4150

4731

83 x 57 = 4,731Â Â Â Â Â reasonable 4731 is close to 5,000

Question 5.

Answer:

893 x 44 = 39,292Â Â reasonable 39,292 is close to 40,000

Explanation:

Step 1: Multiply 893 by 4 ones.

4 ones x 893 = 3,572 ones

3 1

893

x 44

3572

Step 2: Multiply 893 by 4 tens or 40, Regroup

4 tens x 893 =3572 tens = 35720 ones

893

x 44

Â 3572

35720

Step 3 : Add the partial products.

893

x 44

Â Â Â 3572

+35720

39292

893 x 44 = 39,292Â Â reasonable 39,292 is close to 40,000

Question 6.

Answer:

2079 x 82 = 170,478Â Â reasonable 170,478 is close to 170,000

Explanation:

Step 1: Multiply 2079 by 2 ones.

2 ones x 2079 = 4,158 ones

11

2079

xÂ 82

4158

Step 2: Multiply 2079 by 8 tens or 80, Regroup

8 tens x 2079 = 16,632 tens = 16,6320 ones

2079

x 82

Â Â 4158

16,6320

Step 3 : Add the partial products.

2079

xÂ Â Â 82

Â Â Â Â 4158

+16,6320

170478

2079 x 82 = 170,478Â Â reasonable 170,478 is close to 170,000

Question 7.

6,082 Ã— 25 = ______

Answer:

6,082 x 25 = 152,050Â Â reasonable 152,050 is close to 150,000

Explanation:

Step 1: MultiplyÂ by 5 ones.

5 ones x 6082 = 30,410 ones

41

6082

xÂ Â 25

30410

Step 2: Multiply 6082 by 2 tens or 20, Regroup

2 tens x 6082 = 12164 tens = 121640 ones

6082

xÂ 25

Â 30410

12,1640

Step 3 : Add the partial products.

6082

xÂ Â Â 25

Â Â Â 30410

+121640

15,2050

6,082 x 25 = 152,050Â Â reasonable 152,050 is close to 150,000

Question 8.

158 Ã— 96 = ______

Answer:

158 x 96 = 15,168Â Â Â Â Â reasonable 15168 is close to 15,000

Explanation:

Step 1: Multiply 158 by 96 ones.

6 ones x 158 = 948 ones

34

158

x 96

948

Step 2: Multiply 158 by 9 tens or 90, Regroup

9 tens x 158 =1422 tens = 14220 ones

57

158

x 96

Â Â 948

14220

Step 3 : Add the partial products.

158

x 96

Â Â Â 948

+14220

15,168

158 x 96 = 15,168Â Â Â Â Â reasonable 15168 is close to 15,000

Question 9.

98 Ã— 74 = ______

Answer:

98 x 74 = 7252Â Â Â Â Â Â Â reasonable 7252 is close to 7000

Explanation:

Step 1: Multiply 98 by 4 ones.

4 ones x 98 = 392 ones

3

98

x74

__392__

Step 2: Multiply 98 by 7 tens or 70, Regroup

7 tens x 98Â = 686 tens = 6860 ones

98

x74

392

6860

Step 3 : Add the partial products.

98

x 74

Â Â Â 392

+6860

7252

98 x 74 = 7252Â Â Â Â Â Â Â Reasonable 7252 is close to 7000

Question 10.

**Writing**

Why is one partial product always greater than the other partial product when multiplying by a two-digit number?

Answer:

The first partial product cannot have a multiplicand greater than 9.

The second partial product cannot have a multiplicand less than 10.

So one partial product is always greater than the other partial product when multiplying by a two-digit number

Explanation:

Lets multiply 315 with 26 a two digit number(26)

The multiplicand 26 can be decomposed to (20 + 6). The first partial product is the product of 315 x 6= 1890. The second partial product is the product of 315 x 20 = 6300.

Here the first partial product cannot have a multiplicand greater than 9Â which is 6 and the second partial product cannot have a multiplicand less than 10 which is 20,thereforeÂ one partial product always greater than the other partial product when multiplying by a two-digit number.

Question 11.

**DIG DEEPER!**

Use the numbers 2, 4, 6, and 8 once to form the greatest product.

Answer:

The greatest product is 806 x 42 = 33,852

Explanation:

Given numbers are 2,4,6,8 , first greatest number among given numbers areÂ 8 and next is 6 then 4 and then 2 we have the patternÂ given as 3 digit number multiplied byÂ 2 digit number, so first 3 great digits numbers are 8,6,0 in these the biggest is 8 then 6 but the middle digit is already given as 0 so the first three digits are 806,

Now the left two digits are 2,4 now to make the greatest 2 digit number we take from the combination of 2 and 4 ,in these the greatest number is 4 first then 2 making it as 42 as second greatest two digit number,

therefore the product is 806 X 42 =33,852 making it as the greatest product.

806

xÂ Â 42

33,852

Question 12.

**Modeling Real Life**

A store sells 79 virtual reality headsets. How much money does the store collect?

Answer:

$125 X 79 = $9,875

Explanation:

Given that the virtual reality headset cost as $ 79 and the store sells 79 virtual reality headsets, Total money collected by the store is $125 x 79=$9,875

125

x 79

9,875

Question 13.

**Modeling Real Life**

Your friend needs a trumpet for 12 months. She can rent a trumpet for $42 each month and pay a yearly fee of $25, or she can buy a trumpet for $550. Should she buy or rent the trumpet? Explain.

Answer:

Friend should take the trumpet for rent because it is costing less than buying it.

Rent for 12 months is $529

Buying costs to $550.

Explanation:

Friend needs a trumpet for 12 months and rent of trumpet is $42 for each month, so for 12 months it costs as $42 x 12=Â $504 and also has to payÂ a yearly fee of $25 means total cost for entire 12 months is $504+$25= $529.

Given that if she buys its cost to $550, now comparing between rent and buy as $529<$550 ,as rent is less than buying she has to take it for rent so that she can save $21

**Review & Refresh**

**Use a place value chart to answer the question.**

Question 14.

4,000 is 10 times as great as what number?

Answer:

4,000 is 10 times as great as 400

Explanation:

Lets us take the number as X,

Given 4,000 is 10 times as great as X means XÂ x 10= 4,000

the value of X equals to 4000 x 1/10= 4000/10=400

X=400 therefore 4,000 is 10 times as great as 400

Question 15.

50 is \(\frac{1}{10}\) of what number?

Answer:

50 is \(\frac{1}{10}\) of 500

Explanation:

Let the number be X and given 50 = 1/10 x X, so X = 50 x 10 = 500

### Lesson 4.5 Multiply by Multi-Digit Whole Numbers

**Explore and Grow**

Use any strategy to find each product.

Answer:

425 x 2 = 850Â , 425 x 12 =5,100Â , 425 x 112 = 47,600

Explanation:

1) 425 x 2 =850, multiply 425 by 2 ones or 2

1

425

xÂ 2

850

2) 425 x 12 = 51,00

Explanation:

Step 1 : Multiply 425 by 2 ones or 2

1

425

x 12

850

Step 2 : Multiply 425 by 1 tens or 10.

425

x 12

Â 850

4250

Step 3: Add the partial products.

425

x 12

Â Â 850

+4250

Â 5100

3) 425 x 112 = 47,600

Explanation:

Step 1 : Multiply 425 by 2 ones or 2

1

425

x112

850

Step 2 :Multiply 425 by 1 tens or 10.

425

x 112

Â 850

4250

Step 3 : Multiply 425 by 1 hundred or 100. Regroup

425

x 112

Â Â 850

4250

42500

Step 4: Add the partial products.

425

x 112

Â Â Â Â 850

4250

+ 42500

47,600Â

**Structure**

How can you use the first product to find the second product? How can you use the second product to find the third product?

Answer:

Yes we can use the first product to find the second product and use the second product to find the third product.

Explanation:

For example let the numbers be 324 x 125 = 40,500

First product result will be product of 324 is first multiplied by last digit 5 at ones place as 324 x 5=1620

Second product result will be the first product results in addition to multiple of 324 with the second digit which is at tens place as 324 x 20 and add to first product results, so here we have used the first product result to find the second product results

324

x25

1620

6480

8100

Third product result will be the second product results and we add it to the multiple of product of third digit which is at hundreds place as Â 324 x 100 and add to second product results, so here we have used the second product result to find the third product results

324

x125

Â 8100

32400

40,500

**Think and Grow: Multiply Multi-Digit Whole Numbers**

**Example**

Find 2,043 Ã— 132. Estimate __2,69,676_____

2,043 x 132 = 2,69,676Â Â reasonable 2,69,676 is close to 2,70,000

**Show and Grow**

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

Question 1.

Answer:

318 x 523 =166,314Â Â Â Â Â Â reasonable 1,66,314 is close to 1,70,000

Explanation:

Step 1 : Multiply 318 by 3 ones or 3

2

318

x 523

Â 954

Step 2 :Multiply 318 by 2 tens or 20.

1

318

x 523

Â 954

6360

Step 3 : Multiply 318 by 5 hundred or 500. Regroup

318

x 523

Â Â Â 954

6360

159000

Step 4: Add the partial products.

318

xÂ Â Â 523

Â Â Â Â 954

6360

+159000

166314

So 318 x 523 =166,314Â Â Â Â Â Â reasonable 1,66,314 is close to 1,70,000

Question 2.

Answer:

7291 x 308 = 2,245,628Â reasonable 2,245,628 is close to 2,300,000

Explanation:

Step 1 : Multiply 7291 by 8 ones or 8

27

7291

x 308

58328

Step 2 :Multiply 7219 by 0 tens .

7291

x 308

58328

00000

Step 3 : Multiply 7219 by 3 hundred or 300. Regroup

2

7291

x 308

Â Â 58328

00000

2187300

Step 4: Add the partial products.

7291

x 308__

Â Â Â 58328

00000

+2187300

2245628

7291 x 308 = 2,245,628Â Â Â Reasonable 2,245,628 is close to 2,300,000

**Apply and Grow: Practice**

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

Question 3.

Answer:

521 x 317 = 1,65,157Â Â Reasonable 165,157Â is close to 1,700,00

Explanation:

Step 1 : Multiply 521 by 7 ones or 7

1

521

x 317

3647

Step 2 :Multiply 521 by 1 tens or 10 .

521

x 317

3647

5210

Step 3 : MultiplyÂ 521 by 3 hundred or 300. Regroup

521

x 317

Â Â 3647

5210

156300

Step 4: Add the partial products.

Â 521

x 317

Â Â Â Â 3647

5210

+156300

165157

521 x 317 = 1,65,157Â Â Reasonable 165,157Â is close to 1,700,00

Question 4.

Answer:

631 x 574 = 3,62,194Â Reasonable 3,62,194 is close to 3,60,000

Explanation:

Step 1 : Multiply 631 by 4 ones or 4

631

x 574

2524

Step 2 :Multiply 631 by 7 tens or 70 .

631

x 574

Â 2524

44170

Step 3 : Multiply 631 by 5 hundred or 500. Regroup

631

x 574

Â Â 2524

44170

315500

Step 4: Add the partial products.

631

x 574

Â Â Â 2524

44170

+315500

362194Â Â Â Â Â

631 x 574 = 3,62,194Â Â Â Â Â Reasonable 3,62,194 is close to 3,60,000Â Â

Question 5.

Answer:

2496 x 358 =8,93,568Â Â Â Â Reasonable 8,93,568 is close to 9,00,000

Explanation:

Step 1 : Multiply 2496 by 8 ones or 8

374

2496

x 358

19,968

Step 2 :Multiply 2496 by 5 tens or 50 .

243

2496

x 358

Â 19968

124800

Step 3 : Multiply 2496 by 3 hundred or 300. Regroup

2496

x 358

Â 19968

124800

748800

Step 4: Add the partial products.

2496

x 358

Â 19968

124800

748800Â Â

893568

2496 x 358 =8,93,568Â Â Â Reasonable 8,93,568 is close to 9,00,000

Question 6.

155 Ã— 956 = ______

Answer:

155 x 956 = 1,48,180Â Â Â Reasonable 1,48,180 is close to 1,50,000

Explanation:

Step 1 : Multiply 155 by 6 ones or 6

33

155

x 956

Â 930

Step 2 :Multiply 155 by 5 tens or 50 .

22

155

x 956

Â 930

7750

Step 3 : Multiply 155 by 9 hundred or 900. Regroup

155

x 956

Â Â Â 930

7750

139500

Step 4: Add the partial products.

155

x 956

Â Â Â 930

7750

139500

148180

155 x 956 = 1,48,180Â Â Â Reasonable 1,48,180 is close to 1,50,000

Question 7.

748 Ã— 239 = ______

Answer:

748 x 239 = 1,78,772Â Â Â ReasonableÂ 1,78,772 is close to or 1,80,000 orÂ 2,00,000

Explanation:

Step 1 : Multiply 748 by 9 ones or 9

47

748

x239

Â 6732

Step 2 :Multiply 748 by 3 tens or 30 .

12

748

x 239

Â 6732

22440

Step 3 : Multiply 748 by 2 hundred or 200. Regroup

1

748

x 239

Â Â 6732

22440

149600

Step 4: Add the partial products.

748

x 239___

Â Â Â Â 6732

22440

+149600

178772

748 x 239 = 1,78,772Â Â Â ReasonableÂ 1,78,772 is close to or 1,80,000 orÂ 2,00,000

Question 8.

1,907 Ã— 218 = ______

Answer:

1907 x 218 = 415,726Â Reasonable 4,15,726 is close to 4,20,000

Explanation:

Step 1 : Multiply 1907 by 8 ones or 8

7 5

1907

x 218

15256

Step 2 :Multiply 1907 by 1 tens or 10 .

1907

x 218

Â 15256

19070

Step 3 : MultiplyÂ 1907 by 2 hundred or 200. Regroup

1Â 1

1907

x 218

Â 15256

19070

381400

Step 4 :Add the partial products.

1907

x 218

Â Â Â 15256

19070

+381400

415726

1907 x 218 = 415,726Â Reasonable 4,15,726 is close to 4,20,000

Question 9.

The delta of the Nile River is about 150 miles wide. How many feet wide is the delta?

Answer:

5280 x 150 = 7,92,000 feet

Explanation:

Given the delta of the Nile River is about 150 miles wide and 1 mile is equal to 5,280 feet so total feet of Nile River is product of 5280 and 150 , 5280 x 150 = 7,92,000 feet

Question 10.

**Reasoning**

When you multiply a three-digit number by a four-digit number, what is the greatest number of digits the product can have? Explain.

Answer:

999 x 9999 = 9,989,001 the product will have 7 greatest number of digits.

Explanation:

We know 9 is the greatest digit, so the greatest three-digit number is 999 and the greatest four-digit number is 9999 when 999 x 9999 we get the results as 999 x 9999 = 9,989,001 which consists of total 7 digits in it, therefore when we multiply a three-digit number by a four-digit number, we get 7 greatest number of digits in the results.

Question 11.

**DIG DEEPER!**

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

Answer:

The missing digit is 0, as 850 x 150= 1,27,500 and 375 x 340 = 1,27,500 are same

Explanation:

To find the missing digit first we multiply 850 X 150 we get 1,27,500 andÂ it is mentioned that the products are same means

850 x 150= 1,27,500 = 375 x 34___. So to find the missing digit from 34___, we divide 1,27,500 by 375 and the result is 340. So obviously the missingÂ digit is 0.

**Think and Grow: Modeling Real Life**

**Example**

The employees at a baseball bat factory need to make 350,000 bats in 6 months. They make 2,750 bats each day and work 127 days in the 6 months. Do the employees make enough bats?

Multiply the number of bats produced each day by the number of days.

Compare the number of bats produced to the number of bats needed.

2750 x 127 = 3,49,250 bats as 3,49,250 < 3,50,000

The employees does not___ make enough bats.

Explanation:

Each day the employees make 2750 bats and has worked 127 days in 6 months , so in 6 months the employees have made

2750 x 127 =3,49,250 bats, given that the employees at a baseball bat factory need to make 350,000 bats in 6 months, now comparingÂ we are getting difference as the employees made to the required number of bats.

We are getting employees made is less when compared to the needed number of bats as 3,49,250 < 3,50,000. Both are not matching so employees have not made enough bats.

**Show and Grow**

Question 12.

The drivers at a warehouse need to deliver 40,000 packages each day. The warehouse has 128 trucks. Each truck has 350 packages. The drivers deliver all of the packages on the trucks. Do the warehouse drivers deliver enough packages?

Answer:

350 x 128= 44,800 and required is 40,000 as compared it is less,

Yes, the warehouse drivers can deliver enough packages each day.

Explanation:

Each truck has 350 packages and the ware house has 128 trucks, so the total number of packages in a day are 350 x 128 = 44,800 packages. Now comparing the drivers need only 40,000 packages each day asÂ 44,800 is greater than 40,000, 44,800>40,000.Easily the drivers can deliver the packages each day.

Question 13.

A school buys 5 tablets and 5 laptops. Each tablet costs $379. Each laptop costs $449. How much more does the school pay for laptops than it pays for tablets?

Answer:

Tablets costs = $379 x 5=Â $1,895

Laptop costs = $449 x 5 = $2,245, Laptop to Tablets = $ 2,245-$1,895=$350, School pays $350 more.

Explanation:

School buys 5 tablets and 5 laptops and each tablet costs $379 and laptop costs $449,the total amount for tablets costs = $379 x 5=Â $1,895 and for laptop costs = $449 x 5 = $2,245,Now comparing the costs of laptops to tablets $2,245 to $1895 we are getting a difference ofÂ $350 among them. So the school pays $379

Question 14.

**DIG DEEPER!**

A koala sleeps 18 hours each day. How many minutes does the koala sleep in 1 year?

Answer:

The koala sleeps 3,94,200 minutes in 1 year.

Explanation:

We know that in 1 hour equals to 60 minutes and in 1 year we have total 365 days a koala sleep 18 hours each day means

18 x 60 =1,080 minutes in each day, so in 1 year koala sleeps 1080 minutes x 365= 3,94,200 minutes in 1 year.

### Multiply by Multi-Digit Whole Numbers Homework & Practice 4.5

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

Question 1.

Answer:

102 x 104 =10,608Â Â Â Reasonable 10,608Â is close to 10,000

Explanation:

Step 1 : Multiply 102 by 4 ones or 4

102

x 104

Â 408

Step 2 : Multiply 102 by 0 tens .

102

x 104

408

000

Step 3 : Multiply 102 by 1 hundred or 100. Regroup

102

x 104

Â Â 408

000

10200

Step 4 : Add the partial products.

102

x 104

Â Â Â Â 408

000

+ 10200

10608

102 x 104 =10,608Â Â Â Reasonable 10,608 is close to 10,000

Question 2.

Answer:

185 x 123 = 22,755Â Reasonable 22,755 is close to 20,000

Explanation:

Step 1 : Multiply 18 by 3 ones or 3

21

185

x 123

Â 555

Step 2 : Multiply 185 by 2 tens or 20

11

185

x 123

Â 555

3700

Step 3 : Multiply 185 by 1 hundred or 100. Regroup

185

x 123

Â 555

3700

18500

Step 4 : Add the partial products.

185

x 123

Â Â Â Â 555

3700

+ 18500

22755

185 x 123 = 22,755Â Reasonable 22,755 is close to 20,000

Question 3.

Answer:

3410 x 251 = 855,910Â Â Reasonable 855,910 is close to 8,60,000

Explanation:

Step 1 : Multiply 3410 by 1 ones or 1

3410

x 251

3410

Step 2 : Multiply 3410 by 5 tens or 50

2

3410

x 251

Â Â 3410

170500

Step 3 : Multiply 3410 by 2 hundred or 200. Regroup

3410

x 251

Â Â 3410

170500

682000

Step 4 : Add the partial products.

3410

x 251

3410

170500

+682000

855910

3410 x 251 = 855,910Â Â Reasonable 855,910 is close to 8,60,000

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

Question 4.

Answer:

954 x 176 = 1,67,904Â Â Â Reasonable 1,67,904 is close to 1,68,000 or 1,70,000

Explanation:

Step 1 : Multiply 954 by 6 ones or 6

32

954

x 176

5724

Step 2 : Multiply 954 by 7 tens or 70

32

954

x 176

Â Â 5724

66780

Step 3 : Multiply 954 by 1 hundred or 100. Regroup

954

x 176

Â Â 5724

66780

95400

Step 4 : Add the partial products.

954

x 176

Â Â 5724

66780

+95400

167904

954 x 176 = 1,67,904Â Â Â Reasonable 1,67,904 is close to 1,68,000 or 1,70,000

Question 5.

Answer:

818 x 524 = 428,632Â Â Reasonable 4,28,632 is close to 4,30,000 or 4,00,000

Explanation:

Step 1 : Multiply 818 by 4 ones or 4

3

818

x 524

3272

Step 2 : Multiply 818 by 2 tens or 20

1

818

xÂ 524

Â Â 3272

16360

Step 3 : Multiply 818 byÂ 5 hundred or 500. Regroup

4

818

xÂ 524

Â Â 3272

16360

409000

Step 4 : Add the partial products.

818

xÂ 524

Â Â Â Â 3272

16360

+ 409000

428632

818 x 524 = 428,632Â Â Reasonable 4,28,632 is close to 4,30,000 or 4,00,000

Question 6.

Answer:

6301 x 472 =2,974,072Â Â Reasonable 2,974,072 is close to 3,000,000

Explanation:

Step 1 : Multiply 6301 by 2 ones or 2

6301

x 472

12602

Step 2 :Â Multiply 6301 by 7 tens or 70

2

6301

x 472

Â Â 12602

441070

Step 3 : Multiply 6301 byÂ 4 hundred or 400. Regroup

6301

x 472

Â Â Â 12602

441070

2520400

Step 4 : Add the partial products.

6301

x 472

Â Â Â 12602

441070

+2520400

2974072

6301 x 472 =2,974,072Â Â Reasonable 2,974,072 is close to 3,000,000

Question 7.

999 Ã— 186 = ______

Answer:

999 x 186 = 185,814Â Â Â Reasonable 185,814 is close to 2,00,000

Explanation:

Step 1 : Multiply 999 by 6 ones or 6

55

999

x 186

5994

Step 2 :Â Multiply 999 by 8 tens or 80

77

999

x 186

Â 5994

79920

Step 3 : Multiply 999 byÂ 1 hundred or 100. Regroup

999

x 186

Â Â 5994

79920

99900

Step 4 : Add the partial products.

999

x 186

Â Â 5994

79920

+99900

185814

999 x 186 = 185,814Â Â Â Reasonable 185,814 is close to 2,00,000

Question 8.

2,445 Ã— 356 = ______

Answer:

2445 x 356 = 870420Â Â Â Reasonable 870420 is close to 8,70,000

Explanation:

Step 1 : Multiply 2445 by 6 ones or 6

223

2445

x 356

14670

Step 2 :Â Multiply 2445 by 5 tens or 50

222

2445

xÂ 356

Â 14670

122250

Step 3 : Multiply 2445 byÂ 3 hundred or 300. Regroup

111

2445

x 356

Â 14670

122250

733500

Step 4 : Add the partial products.

2445

x 356

Â Â Â 14670

122250

+733500

Â 870420

2445 x 356 = 870420Â Â Â Reasonable 870420 is close to 8,70,000

Question 9.

1,564 Ã— 389 = ______

Answer:

1564 x 389 = 608396Â Â Â Reasonable 6,08,396 is close to 6,00,000

Step 1 : Multiply 1564 by 9 ones or 9

553

1564

x 389

14076

Step 2 :Â Multiply 1564 by 8 tens or 80

453

1564

x 389

Â 14076

125120

Step 3 : Multiply 1564 byÂ 3 hundred or 300. Regroup

111

1564

x 389

Â 14076

125120

469200

Step 4 : Add the partial products.

1564

x 389

Â Â 14076

125120

+469200

608396Â

1564 x 389 = 608396Â Â Â Reasonable 6,08,396 is close to 6,00,000

Question 10.

**Reasoning**

Your friend says the product of 4,164 and 137 is 70,460. How will finding an estimate help your friend realize the answer is not reasonable?

Answer:

4164 X 137 = 570,468, 5,70,468 is not equal to 70,460.

Explanation:

Friend says product of 4,164 and 137 is 70,460 , Now finding the estimate the product of 4,164 x 137 = 5,70,468 but friend says it is 70,460. So after finding friend realize the answer is not reasonable and not even close.

Question 11.

**YOU BE THE TEACHER**

Your friend says that when multiplying 300 by 126, she can multiply 3 Ã— 126 and write two zeros after the product. Is your friend correct? Explain.

Answer:

Yes, Friend is correct

Explanation:

When first we multiply 300 x 126 we get the product as 37,800 and when we multiply 3 x 126 we get result as 378 and if we write two zeros after the product it becomes 37800 which is similar to the result of 300 x 126, so friend is correct.

We can write 300 x 126 as 3 x 10^{2 }x 126=Â Â (3 x 126 ) x 10^{2 , }We know that if any whole number is multiplied by 10 with powersÂ we get the product whole number with theÂ given number of power value additional number ofÂ zeros in the right.

as (3 x 126 ) x 10^{2Â Â }has 2 as power to 10 we write the result with 2 zeros after the product which is equal to 300 x 126,So friend is correct.

Question 12.

**Modeling Real Life**

Your friend starts a video channel and wants to have 50,000 subscribers by the end of 1 year. She gets 140 new subscribers each day for 365 days. Does she meet her goal?

Answer:

140 x 365 = 51,100 as 51,100 > 50,000, Yes friend meets her goal.

Explanation:

As friend starts a video channel and wants to have 50,000 subscribers by the end of 1 year, and each day friend gets 140 new subscribers for 365 days , So total number of subscribers for 365 days or 1 year is 140 x 365= 51,100.

As 51,100 is greater than 50,000 means friend can easily meets her goal.

**Review & Refresh**

**Evaluate the expression.**

Question 13.

(5 + 8) Ã— 4

Answer:

(5+8) x 4 = 13 x 4 = 52

Explanation:

Expressions inside parentheses are evaluated first from left to right, i.e (5+8) and then we proceed with multiplication.

So first we add the values inside the parentheses or values of bracket (5+8) x 4 ,5+8=13 and multiply by 4= 13 x 4 = 52,

(5 + 8) Ã— 4 = 52

Question 14.

16 + (9 Ã· 3)

Answer:

16 + (9 Ã· 3) = 16 + 3 = 19

Explanation:

First we take expressions inside parentheses (9 Ã· 3) and evaluate then we proceed with addition,

WhenÂ 9 Ã· 3 we getÂ 3 , Now we go with addition so 16 + 3 = 19.

16 + (9 Ã· 3) = 19

Question 15.

7 Ã— (4 + 6)

Answer:

7 x (4 +6) = 7 x 10 = 70

Explanation:

First we take expressions inside parentheses ( 4 + 6)=10 and proceed with multiplication, 7 x 10 = 70,

7 x (4 +6) = 70

### Multiply Whole Numbers Performance Task

The Grand Coulee Dam is located on the Columbia River in Washington. The dam is used to control ï¬‚ood waters, provide irrigation, and generate power.

Question 1.

The dam has 12 pumps that each transfer the same amount of water through pipes from Lake Roosevelt to Banks Lake. Together, the pumps can transfer about 12,000 gallons of water each second.

a. About how many gallons of water can each pump transfer in 1 second?

b. About how many gallons of water can each pump transfer in 1 hour? Explain.

Answer:

a. 12,000 Ã· 12 = 1,000 gallons of water can each pump transfer in 1 second.

b. 1000 x 3,600 seconds = 3,600,000 gallons of water can each pump transfer in 1 hour.

Explanation :

a. Given a dam has 12 pumps that each transfer the same amount of water through pipes from Lake Roosevelt to Banks Lake, and together, the pumps can transfer about 12,000 gallons of water each second.

12 pumps = 12,000 gallons of water each second, Each pump transfer in 1 second is equal to 12,000 divided by 12= 12,000 Ã· 12 =

1,000 gallons of water can each pump transfer in 1 second.

b. Now number of gallons of water can each pump transfer in 1 hour, we know in 1 hour we have 60 minutes and 1 minute has 60 seconds so making it as 3,600 seconds in an hour.1 hour equals to 3,600 seconds. If in 1 second each pump can transfer 1000 gallons of water then in hour it will transfer 1000 x 3,600= 3,600,000 gallons of water can each pump transfer in 1 hour.

Question 2.

The dam generates power Capacity of Power at the Grand Coulee Dam using 33 generators located in 4 different powerhouses.

a. What is the total Power for the Grand Coulee Dam?

b. Only about one-third of the capacity of power for each powerhouse is actually generated each year. About how many megawatts does the Third Powerhouse actually generate in 1 year?

c. There are 10^{6} watts in 1 megawatt. Without calculating, how can you find about how many watts the Third Powerhouse actually generates in 1 year?

Answer:

a. The total Power for the Grand Coulee Dam is 6,701 megawatts.

b. The Third Powerhouse actually generates only 1/3 in 1 year is 1800 x 1/3 = 1800/3=1800 Ã· 1/3 = 600 megawatts

c. The number of watts the Third Powerhouse actually generates in 1 year =600 x 10^{6} watts.

Explanation:

a. First we calculate the total capacity of the power house in each power house with the capacity of power from each generator with the number of generators as per the powerhouse, Total Capacity of the power house = capacity of powerhouse from each generator multiply by number of generatorsÂ separately. Then adding all capacities we get the total Power for the Grand Coulee Dam as shown in the below table, SoÂ total Power for the Grand Coulee Dam is 6,701 megawatts.

b. We have Third Powerhouse has total capacity as 1,800 megawatts as calculated in that only about one-third of the capacity of power for each powerhouse is actually generated each year means total capacity in third powerhouse multiply by 1/3=Â 1800 x 1/3 = 1800/3=1800 Ã· 1/3 = 600 megawatts.

Third Powerhouse actually generates 600 megawatts in 1 year.

c. Given 1 mega watt equals to 10^{6} watts , We have Third Powerhouse generates 600 megawatts in 1 year, so to convert megawattsÂ into watts we multiply it by 10^{6} watts =600 x 10^{6} watts, Third Powerhouse actually generates 600 x 10^{6} wattsÂ in 1 year.

### Multiply Whole Numbers Activity

**Multiplication Adventure**

**Directions:**

1. Players take turns rolling a die. Players solve problems on their boards to race the explorers to their destinations.

2. On your turn, solve the next multiplication problem in the row of your roll.

3. The first player to get an explorer to a destination wins!

Answer:

### Multiply Whole Numbers Chapter Practice

**4.1 Multiplication Patterns**

**Find the product.**

Question 1.

72 Ã— 10^{3} = ______

Answer:

72 Ã— 10^{3} = 72,000

Explanation :

72 Ã— 10^{3} =Â 72 x 10 x 10 x 10 =72,000 , we multiply 72 with 10 three times as 10 power is 3.

Question 2.

30 Ã— 900 = ______

Answer:

30 Ã— 900 =27,000

Explanation:

When we multiply 30 by 900 we get 27,000 or 30 Ã— 900 = 3 x 10 x 9 x 10 x 10 = 3 x 9 x 10^{3}= 27 x 10^{3}= 27,000

Question 3.

40 Ã— 500 = ______

Answer:

40 Ã— 500 = 20,000

Explanation:

When we multiply 40 by 500 we get 20,000 or 40 Ã— 500 = 4 x 10 x 5 x 10 x 10 = 4 x 5 x 10^{3}= 20Â x 10^{3}=20,000

Question 4.

60 Ã— 800 = ______

Answer:

60 x 800 = 48,000

Explanation:

When we multiply 60 by 800 we get 48,000 or 60 Ã— 800 = 6 x 10 x 8 x 10 x 10 = 6 x 8 x 10^{3}= 48 x 10^{3}=48,000

Question 5.

20 Ã— 90 = ______

Answer:

20 x 90 = 1800

Explanation:

When we multiply 20 by 90 we get 1800 or 20 Ã— 90 = 2 x 10 x 9 x 10 = 2 x 9 x 10^{2}= 18 x 10^{2}=1800

Question 6.

10^{2} Ã— 41 = _____

Answer:

10^{2} Ã— 41 =4100

Explanation:

When we multiplyÂ 10^{2} Ã— 41 =10 x 10 x 41 = 100 x 41 = 41,00

**Find the missing factor.**

Question 7.

_____ Ã— 10^{3} = 26,000

Answer:

The missing factor is 26

Explanation:

To get the missing factor, let us take it as X ,SoÂ X x 10^{3} = 26,000, therefore X = 26,000 / 10^{3} =26,000/1000=26

Question 8.

600 Ã— ____ = 24,000

Answer:

The missing factor is 40

Explanation:

To get the missing factor, let us take it as X , So 600 x X = 24,000, therefore X = 24,000/600 = 40

Question 9.

5,000 Ã— _____ = 250,000

Answer:

The missing factor is 50

Explanation:

To get the missing factor, let us take it as X , So 5,000 x X = 250,000, therefore X = 250,000/5000 = 50

Question 10.

**Logic**

The product of a number and twice that number is 320,000. Write the multiplication equation.

Answer:

Let the number be X the multiplication equation is X x 2X =320,000

Explanation:

Let us take the number as X given the product of a number and twice that number equals to 320,000 so the equation becomes as x X x 2X = 320,000 means X multiplied by 2X result is 320,000.

**4.2 Estimate Products**

**Estimate the product. Explain whether your estimate is an overestimate or an underestimate.**

Question 11.

44 Ã— 81

Answer:

44 x 81 = 3,564

50 x 80 = 4,000 is overestimate

Explanation :

As our estimate after rounding each factor becomes as 44 as 50 to nearest ten and 81 as 80 to nearest ten as 44 x 81 < 50 x 80 as the estimate result is greater than the given product results our estimate is an overestimate

Question 12.

29 Ã— 67

Answer:

29 x 67 = 1,943

30 x 70 = 2,100 is overestimate

Explanation :

As our estimate after rounding each factor becomes 29 as 30Â to nearest ten and 67 as 70 to nearest ten as 29 x 67 < 30 x 70 as the estimate result is greater than the given product results our estimate is an overestimate.

Question 13.

504 Ã— 302

Answer:

504 x 302 = 152,208

500 x 300 = 150,000 is underestimate

Explanation :

As our estimate after rounding each factor becomes 504 as 500 to nearest hundred and 302 as 300 to nearest hundred as 504 x 302Â > 500 x 300 as the estimate result is lesser than the given product results our estimate is an underestimate.

Question 14.

797 Ã— 29

Answer:

792 x 29 = 22,968

800 x 30 = 24,000 is overestimate

Explanation :

As our estimate after rounding each factor becomes 792 as 800 to nearest hundred and 29 as 30 to nearest ten as 792 x 29 < 800 x 30 as the estimate result is greater than the given product results our estimate is an overestimate.

**4.3 Multiply by One-Digit Numbers**

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

Question 15.

Answer:

663 x 5 = 3,315Â Â Â Reasonable 3,315 is close to 3,300

Explanation:

Step 1: Multiply the ones. Regroup

5 x 3 ones = 15 ones, RegroupÂ 15 ones as 1 tens and 5 ones

1

663

__xÂ Â 5
__Â Â Â 5

Step 2 : Multiply the tens. Regroup

5 x 6 tensÂ = 30 tens,Â 30 tens + 1 tens = 31 tens, Regroup 31 tens as

3 hundreds and 1 tens

3

663

__xÂ Â 5Â__

15

Step 3 : Multiply the hundreds. Regroup hundreds

5 x 6 hundreds = 30 hundreds, 30 hundreds + 3 hundreds = 33 hundreds

Regroup 33 hundreds as 3 thousands and 3 hundred

663

__xÂ Â 5Â Â__

3315

663 x 5 = 3,315Â Â Â Reasonable 3,315 is close to 3,300

Question 16.

Answer:

1973 x 7 = 13,811Â Â Â Reasonable 13,811Â is close to 14,000

Explanation:

Step 1: Multiply the ones. Regroup

7 x 3 ones = 21 ones, RegroupÂ 21 ones as 2 tens and 1 ones

2

1973

__xÂ Â 7
__Â Â Â 1

Step 2 : Multiply the tens. Regroup

7 x 7 tensÂ = 49 tens,Â 49 tens + 2 tens = 51 tens, Regroup 51 tens as

5 hundreds and 1 tens

5

1973

__xÂ Â 7Â__

11

Step 3 : Multiply the hundreds. Regroup hundreds

7 x 9 hundreds = 63 hundreds, 63 hundreds + 5 hundreds = 68 hundreds

Regroup 68 hundreds as 6 thousands and 8 hundreds

6

1973

__xÂ Â 7Â Â__

811

Step 4 : Multiply the thousands. Add the regrouped thousands

7 x 1 thousands = 7 thousands,7 thousands +6 thousands=13 thousands

1973

__xÂ Â 7__

13811

1973 x 7 = 13,811Â Â Â Reasonable 13,811Â is close to 14,000

Question 17.

Answer:

75,028 x 6 = 450,168Â Â Â Â ReasonableÂ 4,50,168 is close to 4,50,000

Explanation:

Step 1: Multiply the ones. Regroup

6 x 8 ones = 48 ones, RegroupÂ 48 ones as 4 tens and 8 ones

4

75028

__xÂ Â Â 6
__Â Â Â Â 8

Step 2 : Multiply the tens. Regroup

6 x 2 tensÂ = 12 tens,Â 12 tens + 4 tens = 16 tens, Regroup 16 tens as

1 hundreds and 6 tens

1

75028

__xÂ Â Â 6Â__

68

Step 3 : Multiply the hundreds. Regroup hundreds

6 x 0 hundreds = 0 hundreds, 0 hundreds + 1 hundreds = 1 hundred

75028

__xÂ Â Â 6Â Â__

168

Step 4 : Multiply the thousands. Regroup

6 x 5 thousands = 30 thousands, Regroup 30 thousands as 3 ten thousands and 0 thousands

3

75028

__xÂ Â Â 6__

Â Â 0168

Step 5Â : Multiply the ten thousands.

6 x 7 ten thousands = 42 ten thousands,42 ten thousands+ 3 ten thousands

=45 ten thousands, regroup as 4 hundred thousand and 5 ten thousand

75028

__xÂ Â Â 6__

450168

75,028 x 6 = 4,50,168Â Â Â Reasonable 4,50,168 is close to 4,50,000

Question 18.

**Modeling Real Life**

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail. The Iditarod Trail is 1,025 miles long. How long is the Great Western Trail?

Answer:

The Great Western Trail = 355 + ( 4 x 1,025)= 355 + 4,100 = 4,455 miles

Explanation :

Given that The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail,

The Great Western Trail= 355 + ( 4 x the Iditarod Trail),

and the Iditarod Trail is 1,025 miles ,

The Great Western Trail = 355 + ( 4 x 1025) = 355 + 4100 = 4,455 miles, The Great Western Trail is 4,455 miles long.

**4.4 Multiply by Two-Digit Numbers**

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

Question 19.

Answer:

45 x 35 = 1575Â Â Â Â Â Â Reasonable 1575 is close to 1500

Explanation:

Step 1: Multiply 45 by 5 ones. Regroup

5 ones x 45 = 225 ones

2

45

x 35

225

Step 2: Multiply 45 by 3 tens or 30, Regroup

3 tens x 45 =135 tens =1350 ones

45

x 35

Â 225

1350

Step 3 : Add the partial products.

45

xÂ Â 35

Â Â Â 225

+1350

1575

45 x 35 = 1575Â Â Â Â Â Â Reasonable 1575 is close to 1500

Question 20.

Answer:

206 x 74 = 15,244Â Â Â Â Â Reasonable 15,244 is close to 15,000

Explanation:

Step 1: Multiply 206 by 4 ones. Regroup

4 ones x 206 = 824 ones

2

206

x 74

824

Step 2: Multiply 206 by 7 tens or by 70, Regroup

7 tens x 206 =1442 tens =14420 ones

206

x 74

Â Â 824

14420

Step 3 : Add the partial products.

206

xÂ Â Â Â 74

Â Â Â Â 824

+ 14420

Â Â 15244

206 x 74 = 15,244Â Â Â Â Â Reasonable 15,244 is close to 15,000

Question 21.

Answer:

5,082 x 69 =Â 350,658Â Â Â Â Â Â Â Â Reasonable 3,50,658 is close to 3,50,000

Explanation:

Step 1: Multiply 5082 by 9 ones. Regroup

9 ones x 5082 = 45,738 ones

71

5082

xÂ 69

45,738

Step 2: Multiply 5082 by 6 tens or 60, Regroup

6 tens x 5082 = 30492 tens =304920 ones

5082

xÂ 69

Â 45738

304920

Step 3 : Add the partial products.

5082

xÂ Â 69

Â Â 45738

+304920

350658

5,082 x 69 =Â 350,658Â Â Â Â Â Â Â Â Reasonable 3,50,658 is close to 3,50,000

**4.5 Multiply by Multi-Digit Whole Numbers**

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

Question 22.

Answer:

612 x 143 = 87,516Â Â Â Reasonable 87,516 is close to 90,000

Explanation:

Step 1 : Multiply 612 by 3 ones or 3

612

x 143

1836

Step 2 :Multiply 612 by 4 tens or 40.

612

x 143

Â 1836

24480

Step 3 : Multiply 612 by 1 hundred or 100. Regroup

612

x 143

Â 1836

24480

61200

Step 4: Add the partial products.

Â 612

x 143

Â Â Â 1836

Â Â 24480

+61200

87516

612 x 143 = 87,516Â Â Â Reasonable 87,516 is close to 90,000

Question 23.

Answer:

899 x 475 = 427,025Â Â Reasonable 4,27,025 is close to 4,30,000

Explanation:

Step 1 : Multiply 899 by 5 ones or 5

44

899

x 475

Â 4495

Step 2 :Multiply 899 by 7 tens or 70.

66

899

x 475

Â 4495

62930

Step 3 : Multiply 899 by 4 hundred or 400. Regroup

33

899

x 475

Â 4495

62930

359600

Step 4: Add the partial products.

899

x 475

Â Â Â 4495

62930

+359600

427025

899 x 475 = 427,025Â Â Reasonable 4,27,025 is close to 4,30,000

Question 24.

Answer:

6182 x 794 = 4,908,508Â Â Reasonable 4,908,508Â is close to 5,000,000

Explanation:

Step 1 : Multiply 6182 by 4 ones or 4

3

6182

x 794

24728

Step 2 :Multiply 6182 by 9 tens or 90.

71

6182

x 794

Â 24728

556380

Step 3 : Multiply 6182 by 7 hundred or 700. Regroup

51

6182

x 794

Â 24728

556380

4327400

Step 4: Add the partial products.

6182

x 794

Â Â 24728

556380

4327400

4908508

6182 x 794 = 4,908,508Â Â Reasonable 4,908,508Â is close to 5,000,000

*Conclusion:*

We wish the Big Ideas Math Grade 5 Answer Key Chapter 4 Multiply Whole Numbers is beneficial for you all. There are different methods to solve the problems in multiply whole numbers. Prepare the questions on your own and solve the problems. Students are notified to improve their math skills by referring to the Big Ideas Math Answers Grade 5 Chapter 4 Multiply Whole Numbers.