# Big Ideas Math Answers Grade 2 Chapter 10 Subtract Numbers within 1,000

Big Ideas Math Book Grade 2 Chapter 10 Subtract Numbers within 1,000 Answers are provided in a comprehensive manner for better understanding. Interested students have to solve as many questions as possible using the Big Ideas Math Answers Grade 2 Ch 10 and become pro at solving subtraction problems below 1,000. So that you can understand the concept and answer any kind of questions framed on the Subtraction of Numbers within 1,000.

## Big Ideas Math 2nd Grade Answer Key Chapter 10 Subtract Numbers within 1,000

BIM 2nd Grade Chapter 10 Subtract Numbers within 1,000 Answer Key is useful for the students who are willing to be perfect in Math skills and also parents for guiding their kid to have the best score in the written exam. This chapter includes questions on vocabulary, Subtract 10 and 100, Use a Number Line to Subtract Hundreds and Tens, Use a Number Line to Subtract Three-Digit Numbers, Use Compensation to Subtract Three-Digit Numbers, Use Models to Subtract Three-Digit Numbers, Subtract Three-Digit Numbers, Subtract from Numbers That Contain Zeros, Use Addition to Subtract and Explain Subtraction Strategies.

Learn the different ways of finding the difference of two numbers within 1,000. By solving the questions on Big Ideas Math Grade 2 Chapter 10 Subtract Numbers within 1,000 Textbook, you can be able to find subtraction of any two numbers and explain how to use different subtraction strategies. Hence Download Big Ideas Math Answers Grade 2 Chapter 10 Subtract Numbers within 1,000 pdf and learn the fundamentals in an easy manner.

Lesson 1 Subtract 10 and 100

Lesson 2 Use a Number Line to Subtract Hundreds and Tens

Lesson 3 Use a Number Line to Subtract Three-Digit Numbers

Lesson 4 Use Compensation to Subtract Three-Digit Numbers

Lesson 5 Use Models to Subtract Three-Digit Numbers

Lesson 6 Subtract Three-Digit Numbers

Lesson 7 Subtract from Numbers That Contain Zeros

Lesson 8 Use Addition to Subtract

Lesson 9 Explain Subtraction Strategies

## Big Ideas Math Book 2nd Grade Answer Key Chapter 10 Subtract Numbers within 1,000

### Subtract Numbers within 1,000 Vocabulary

Organize It
Use the review words to complete the graphic organizer

8 is the sum and 5 is the difference.

Explanation:
By adding 5+3 we will get the sum of those two digits which is 8 and, by subtracting 8-3 we will get the difference of those two digits which is 5.

Define It
Match.

Explanation:

Regrouping in subtraction is a method of interchanging one ten into ten ones. This regrouping of subtraction is used to work out the different subtraction problems.
Compensation is a strategy used to make a ten to help add and subtract numbers.

### Lesson 10.1 Subtract 10 and 100

Explore and Grow

Model 251. Make a quick sketch of your model.

251
To model 251 which is 100+100+50+1.

Explanation:
To model 251 which is 100+100+50+1, we will take a table of 10×10 by which we can build 100 blocks. So for 251, we will take two 10×10 blocks and one 10×5 blocks for which we can build 50 blocks and a single block.

Model 10 less than 251. Make a quick sketch of your model.
251 − 10 = _____

251-10= 241

Explanation:
To model 10 less than 251, we will subtract 251 – 10 which is 241. So to model 241, we will expand that 241 as
100 + 100 + 40 + 1 so we will take two 10×10 blocks for which we and one 10×4 block and a single block.

Model 100 less than 251. Make a quick sketch of your model.
251 – 100 = ______
251 – 100= 151.

Explanation:
To model 100 less than 251, we will subtract 251 – 100 which is 251. So to model 151, we will expand that 151 as
100 + 50 + 1 so we will take one 10×10 block for which we and one 10×5 block and a single block.

Show and Grow

Question 1.
278 − 10 = _____
278 − 100 = _____
The difference of 278 − 10 is 268.
The difference of 278 − 100 is 178.

Explanation:
To find the difference of 278-10, we will pick the tens digit number in 278 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
7 – 1= 6
therefore 278 – 10= 268.
And to find the difference of 278-100, we will pick the hundred’s digit number in 278 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
2-1= 1
therefore 278-100= 178.

Question 2.
451 − 10 = ______
451 − 100 = _____
The difference of 451 − 10 is 441.
The difference of 451 − 100 is 351.

Explanation:
To find the difference of 451-10, we will pick the tens digit number in 451 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
5 – 1= 4
therefore 451 – 10= 441.
And to find the difference of 451-100, we will pick the hundred’s digit number in 451 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
4-1= 3
therefore 451-100= 351.

Question 3.
623 − 10 = ______
623 − 100 = _____
The difference of 623 − 10 is 623.
The difference of 623 − 100 is 523.

Explanation:
To find the difference of 623-10, we will pick the ten’s digit number in 623 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
2 – 1= 3
therefore 623 – 10= 613.
And to find the difference of 623-100, we will pick the hundred’s digit number in 623 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
6-1= 5
therefore 623-100= 523.

Question 4.
116 − 10 = _____
116 − 100 = ______
The difference of 116 − 10 is 106.
The difference of 116 − 100 is 16.

Explanation:
To find the difference of 116-10, we will pick the ten’s digit number in 116 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
1 – 1= 0
therefore 116 – 10= 106.
And to find the difference of 116-100, we will pick the hundred’s digit number in 116 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
1-1= 0
therefore 116-100= 016.

Apply and Grow: Practice

Question 5.
100 – 10 = ______
The difference of 100 – 10 is 90.

Explanation:
To find the difference of 100-10, we will pick the hundred’s digit number in 100 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
10 – 1= 9
therefore 100 – 10= 90.

Question 6.
599 – 100 = ______
The difference of 599-100 is 499.

Explanation:
To find the difference of 599 -100, we will pick the hundred’s digit number in 599 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
5-1= 4
therefore 599-100= 499.

Question 7.
614 − 10 = _____
The difference of 614 -10 is 604.

Explanation:
To find the difference of 614 -10, we will pick the hundred’s digit number in 614 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
1-1= 0
therefore 614 -10= 604.

Question 8.
890 – 10 = ______
The difference of 890 -10 is 880.

Explanation:
To find the difference of 890 -10, we will pick the ten’s digit number in 890 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
9-1= 8
therefore 890 -10= 880.

Question 9.
768 − 100 = _____
The difference of 768 -100 is 668.

Explanation:
To find the difference of 768 -100, we will pick the hundred’s digit number in 768 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
7-1= 0
therefore 768 -100= 668.

Question 10.
523 – 10 = _____
The difference of 523 -10 is 513.

Explanation:
To find the difference of 523 -10, we will pick the ten’s digit number in 523 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
2-1= 1
therefore 523 -10= 513.

Question 11.
362 − 100 = _____
The difference of 362 -100 is 262.

Explanation:
To find the difference of 362 -100, we will pick the hundred’s digit number in 362 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
3 -1= 2
therefore 362 -100= 262 .

Question 12.
396 – 10 = _____
The difference of 396 -10 is 386.

Explanation:
To find the difference of 396 -10, we will pick the ten’s digit number in 386 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
9-1= 8
therefore 396 -10= 386.

Question 13.
604 − 10 = _____
The difference of 604 -10 is 594.

Explanation:
To find the difference of 604 -10, we will pick the ten’s digit number in 604 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
60 – 1= 59
therefore 604 -10= 594.

Question 14.
799 – 100 = _____
The difference of 614 -10 is 604.

Explanation:
To find the difference of 614 -10, we will pick the ten’s digit number in 614 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
1-1= 0
therefore 614 -10= 604.

Question 15.
449 − _____ = 349
The difference of 449 – 100 is 349.

Explanation:
Let the blank be X,
so 449- X= 349,
Then X = 449-349
X = 100.
Let us cross-check that 100 is correct or not
449-100= 349.
So 100 is correct.

Question 16.
_____ – 10 = 227
The difference of 237-10 is 227.

Explanation:
Let the blank be X,
so X – 10 = 227,
Then X = 227 + 10
X = 237.
Let us cross-check that 237 is correct or not
237-10= 227.
So 237 is correct.

Question 17.
Number Sense
Use each number once to complete the equations.

_____ – 10 = ______
_____ – _____ = 460
470 – 10 = 460
560 – 10= 550.
560 – 100 = 460.
100 – 10= 90.

Explanation:
Let’s take 470,
then 470 – 10 = 460
and 470 – 10 = 460.
Let’s take 560,
then 560 – 10= 550.
and 560 – 100 = 460.
Let’s take 100
100 – 10= 90.

Think and Grow: Modeling Real Life

You have $106. You spend$10. How much money do you have left?

Subtraction equation:
$_____ Answer: Subtraction equation is$106 – $10=$96.

Explanation:
As we have $106 and$10 was spend, so the remaining money left are
$106 –$10= \$96.

Show and Grow

Question 18.
You have 334 tickets. You exchange 100 of them for a prize. How many tickets do you have left?

_____ tickets
The number of tickets left is 234 tickets.

Explanation:
As we have 334 tickets and in that 100 of them are exchanged for a prize, so the remaining tickets are
334 – 100= 234 tickets are remaining.

Question 19.
DIG DEEPER!
You score 745 points in a video game. You lose some points. Now you have 645. How many points did you lose?
_____ points
The number of points lost is 100 points.

Explanation:
The score in a video game is 745 points and after losing some points, we have 645 points. So the number of points lost is 745 – 645= 100 points.

Question 20.
How can you mentally subtract 10 or 100 from a number?
____________________
____________________
We will perform pick the ten’s digit number or hundred digit number. Then we will subtract both the numbers which we have picked with the given values. For example, if we take 452 – 10, we will pick the ten’s digit number in 452 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
5 – 1= 4
therefore 452 -10=442.

### Subtract 10 and 100 Homework & Practice 10.1

Question 1.
642 − 10 = ______
The difference of 642-10 is 632.

Explanation:
To find the difference of 642 -10, we will pick the ten’s digit number in 642 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
4 – 1= 3
therefore 642 -10= 632.

Question 2.
416 − 100 = _____
The difference of 416 -100 is 316.

Explanation:
To find the difference of 416 -100, we will pick the hundred’s digit number in 416 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
4 – 1= 3
therefore 416 -100= 316.

Question 3.
890 − 100 = _____
The difference of 890 -100 is 790.

Explanation:
To find the difference of 890 -100, we will pick the hundred’s digit number in 890 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
8 – 1= 7
therefore 890 -100= 790.

Question 4.
371 − 10 = _____
The difference of 371 -10 is 361.

Explanation:
To find the difference of 371 -10, we will pick the ten’s digit number in 371 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
7 – 1= 6
therefore 371-10= 361.

Question 5.
501 − 100 = _____
The difference of 501 -100 is 401.

Explanation:
To find the difference of 501 -100, we will pick the hundred’s digit number in 501 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
5 – 1= 4
therefore 501 -100= 401.

Question 6.
955 − 100 = _____
The difference of 955 -100 is 855.

Explanation:
To find the difference of 955 – 100, we will pick the hundred’s digit number in 955 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
9 – 1= 8
therefore 955 – 100= 855.

Question 7.
203 − 10 = ____
The difference of 203 – 10 is 193.

Explanation:
To find the difference of 203 – 10, we will pick the ten’s digit number in 203 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
20 – 1= 19
therefore 203 -10= 193.

Question 8.
888 − 100 = _____
The difference of 888 -100 is 788.

Explanation:
To find the difference of 888 – 100, we will pick the hundred’s digit number in 888 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
8 – 1= 7
therefore 888 – 100= 788.

Question 9.
690 − 10 = ____
The difference of 690 – 10 is 680.

Explanation:
To find the difference of 690 – 10, we will pick the ten’s digit number in 690 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
9 – 1= 8
therefore 690 – 10= 680.

Question 10.
107 − 10 = ____
The difference of 107 – 10 is 97.

Explanation:
To find the difference of 107 -10, we will pick the hundred’s digit number in 107 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
10 – 1= 9
therefore 107 – 10= 97.

Question 11.
723 − ____ = 713
The difference of 723 – 10 is 713.

Explanation:
Let the empty blank be X,
then 723 – X = 713
X = 723 – 713
= 10
Therefore X= 10.

Question 12.
____ − 100 = 433
The difference of 533 – 100 is 433.

Explanation:
Let the empty blank be X,
then X – 100 = 433
X = 433 + 100
= 533
Therefore X= 533.

Question 13.
YOU BE THE TEACHER
Your friend says that 678 − 100 = 668. Is your friend correct? Explain.
____________________
____________________
No, my friend is not correct.

Explanation:
My friend is not correct, because to find the difference of 678 – 100, we will pick the hundred’s digit number in 678 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
6 – 1= 5
therefore 678 – 100= 578.
As 678 – 100= 578, my friend is not correct.

Question 14.

582 – 10 < 683 – 100.

Explanation:

As 582 – 10= 572 and 683 – 100 = 583, so 583 is greater than 572. Which is
582 – 10 < 683 – 100.

Question 15.

985 – 100 = 895 – 10.

Explanation:

As 985 – 100= 885 and 895 – 10 = 885, and here 885 is equal to 885. Which is
985 – 100 = 895 – 10.

Question 16.
Modeling Real Life
Newton sends out 233 invitations. 100 people respond to the invitation. How many people have not responded yet?

_______ people
The number of people who didn’t respond is 133 people.

Explanation:
As Newton sends 233 invitations and in that 233 invitations 100 people responded, so the number of people who didn’t respond is 233 – 100 = 133 people.

Question 17.
Modeling Real Life
648 runners sign up for a marathon. 638 runners finish the race. How many runners do not finish?
______ runners
10 runners.

Explanation:
The total number of runners sign up for a marathon is 648 and of that 638 runners finish the race. So the number of persons who didn’t finish the race is 648-638= 10 runners.

Review & Refresh

Question 18.

____rows of ____
____ + ____ = ____
2 rows of 5 triangles

Explanation:
In the above image, we can see two rows of five triangles. And the total number of triangles in the above image is
5+5= 10.

Question 19.

____rows of ____
____ + ____ = ____
3 rows of 3 circles.
3+3+3= 9.

Explanation:
In the above image, we can see three rows of three circles. And the total number of circles are
3+3+3= 9.

### Lesson 10.2 Use a Number Line to Subtract Hundreds and Tens

Explore and Grow

Skip count back by tens five times on the number line.

555 – _____ = ______

The difference between 555-50 is 505.

Explanation:
Let’s start at 555 and then count back tens five times which is 10×5= 50 on the number line. So the number line is

Skip count back by hundreds five times on the number line.

555 – ____ = ______
555 – 500= 55.

Explanation:
Let’s start at 555 and then count back hundreds five times which is 100×5= 500 on the number line. So the number line is

Show and Grow

Question 1.
520 − 330 = ____

The difference between 520 − 330 is 190.

Explanation:
Let’s start from 520 and count back a hundred three times which is 3×100= 300 and the value will be
520 – 300= 220 and then we will count back tens three times, which is 3×10= 30 and the value will be
220-30= 190.

Question 2.
259 − 170 = _____

The difference between 259 – 170 is 89.

Explanation:
Let’s start from 259 and count back a hundred one time which is 1×100= 100 and the value will be
259 – 100= 159 and then we will count back tens seven times, which is 7×10= 70 and the value will be
159 – 70= 89.

Apply and Grow: Practice

Question 3.
640 – 150 = _____

The difference between 640 – 150 is 490.

Explanation:
Let’s start from 640 and count back a hundred one time which is 1×100= 100 and the value will be
640 – 100= 540 and then we will count back tens five times, which is 5×10= 50 and the value will be
540 – 50= 490.

Question 4.
453 – 210 = _____

The difference between 453 – 210 is 243.

Explanation:
Let’s start from 453 and count back a hundred one time which is 2×100= 200 and the value will be
453 – 200= 253 and then we will count back ten one time, which is 1×10= 10, and the value will be
253 – 10= 243.

Question 5.
329 – 220 = _____

The difference between 329 – 220 is 109.

Explanation:
Let’s start from 329 and count back a hundred two times which is 2×100= 200 and the value will be
329 – 200= 129 and then we will count back tens two times, which is 2×10= 20 and the value will be
129 – 20= 109.

Question 6.
Reasoning
Complete the number line and the equation.

_____ – _____ = _____
752 – 100= 652,
652 – 100= 552,
552 – 40= 512.

Explanation:
Given in the above image that 752 – 100= 652 and 652 – 100= 552, and in the next step we can see the result as 512. So the empty box be X and the equation is
552 – X= 512,
X= 552-512
= 40.
So the value of X is 40.

Think and Grow: Modeling Real Life

A batting cage has 360 baseballs. There are 130 fewer softballs are there?

Subtraction equation:
Model:

____ softballs
230 softballs.

Explanation:
The total number of baseballs in the batting cages is 360 baseballs and there are 130 fewer softballs. So the total number of softballs is 360 – 130= 230 softballs.

Show and Grow

Question 7.
A crocodile weighs 535 pounds. A kangaroo weighs 340 pounds less than the crocodile. How much does the kangaroo weigh?

______ pounds
The weight of the kangaroo is 195 pounds.

Explanation:
The weight of the crocodile is 535 pounds and the weight of the kangaroo is 340 pounds less than the crocodile, which means
535 – 340= 195 pounds.
So the weight of the kangaroo is 195 pounds.

Question 8.
DIG DEEPER!
A train has 850 seats. A plane has 390 fewer seats than the train. A bus has 370 fewer seats than the plane. How many seats does the bus have?
_____ seats
The number of seats on the bus is 90 seats.

Explanation:
As the train has 850 seats, and a plane has 390 fewer seats than the train, which means 850 – 390= 460. So the total number of seats on the train is 460 seats. And a bus has 370 fewer seats than the plane, which means
460 – 370= 90 seats. So the number of seats on the bus is 90 seats.

### Use a Number Line to Subtract Hundreds and Tens Homework & Practice 10.2

Question 1.
670 − 520 = ____

The difference between 670 – 520= 150.

Explanation:
Let’s start from 670 and count back a hundred five times which is 5×100= 500 and the value will be
670 – 500= 170 and then we will count back tens two times, which is 2×10= 20 and the value will be
170 – 20= 150.

Question 2.
749 − 150 = ____

The difference between 749 – 150 is 599.

Explanation:
Let’s start from 749 and count back a hundred one time which is 1×100= 100 and the value will be
749 – 100= 649 and then we will count back tens five times, which is 5×10= 50 and the value will be
649 – 50= 599.

Question 3.
583 − 320 = ____

The difference between 583 – 320 is 263.

Explanation:
Let’s start from 583 and count back a hundred three times which is 3×100= 300 and the value will be
583 – 300= 283 and then we will count back tens two times, which is 2×10= 20 and the value will be
283 – 20= 263.

Question 4.
Number Sense
Write the equation shown by the number line.

_____ – _____ = ______
The equation is 645 – 120= 525.

Explanation:
In the above image, we can see the starting point at 645 and it was counted back to 100 then the value will be 645 – 100= 545. Then from 545, it was counted back tens two times which is 10×2= 20. Then the value will be
545 – 20= 525.

Question 5.
Modeling Real Life
A bee pollinates 955 flowers in a day. A second bee pollinates 150 fewer flowers. How many flowers does the second bee pollinate?

_____ ﬂowers
855 flowers.

Explanation:
The number of flowers pollinated by the bee is 955 flowers and the second bee pollinates 150 fewer flowers, which means 955 – 150= 805 flowers were pollinated by the second bee.

Question 6.
DIG DEEPER!
A library has 990 books. It has 250 fewer movies than books. It has 410 fewer magazines than movies. How many magazines does the library have?
______ magazines
330 magazines.

Explanation:
The number of books in a library is 990 books and 250 fewer movies than books, which is 990 – 250= 740 movies. And 410 fewer magazines than movies, which means 740 – 410= 330 magazines.

Review & Refresh

Question 7.

How many students chose computer?
_____ students
3 students.

Explanation:
In the given graph the number of students who choose computer is 3 students.

### Lesson 10.3 Use a Number Line to Subtract Three-Digit Numbers

Explore and Grow

Use each difference as the starting number in the next equation.
425 − 200 = ____

425 – 200= 225,
225 – 20= 205,
205 – 2= 203.

Explanation:
Given the equation is 425 – 200. To represent the given equation in the number line, we will start from 425 and then count back hundred two times which is 2×100= 200 and the value will be
425 – 200= 225 and then we will count back tens two times, which is 2×10= 20 and the value will be
225 – 20= 205 and count back one two times, which is 1×2= 2and the value will be 205 – 2= 203.

______________________
________________________

Explanation:

Show and Grow

Question 1.
674 − 236 = _____

674 – 236= 438.

Explanation:
Let’s start from 674 and count back hundred two times which is 2×100= 200 and the value will be
674 – 200= 474 and then we will count back tens three times, which is 3×10= 30 and the value will be
474 – 30= 444 and then we will count back one six times, which is 6×1= 6, and the value will be 444 – 6 = 438.

Question 2.
438 −162 = _____

The difference between 438 – 162 is 276.

Explanation:
Let’s start from 438 and count back a hundred one time which is 1×100= 100 and the value will be
438 – 100= 338 and then we will count back tens six times, which is 6×10= 60 and the value will be
338 – 60= 278 and then we will count back one two times, which is 2×1= 2, and the value will be 278 – 2 = 276. And the difference between 438 – 162 is 276.

Apply and Grow: Practice

Question 3.
534 − 311 = _____

Explanation:
Let’s start from 438 and count back a hundred one time which is 1×100= 100 and the value will be
438 – 100= 338 and then we will count back tens six times, which is 6×10= 60 and the value will be
338 – 60= 278 and then we will count back one two times, which is 2×1= 2, and the value will be 278 – 2 = 276. And the difference between 438 – 162 is 276.

Question 4.
745 − 109 = ____

Question 5.
436 − 84 = ____

Question 6.
Number Sense
Write the equation shown by the number line.

____ – _____ = _____
678 – 354= 324.

Explanation:
In the above image, we can see the starting point at 678 and it was counted back to 300 then the value will be 678 – 300= 378. Then from 378, it was counted back 50 which is 378 – 50= 328. And then it was counted back to 4  then the value is 328 – 4= 324.

Think and Grow: Modeling Real Life

Your school recycles 762 bottles. 245 are glass. The rest are plastic. How many bottles are plastic?

Subtraction equation:
Model:

_____ bottles
517 bottles.

Explanation:

The number of bottles recycled by the school is 762 bottles and in that 245 are glass. So the number of plastic bottles is 762 – 245= 517 bottles.

Show and Grow

Question 7.
A squirrel collects 619 nuts for the winter. 421 are acorns. The rest are walnuts. How many walnuts are there?

_____ walnuts
198 walnuts.

Explanation:
The number of nuts was collected by the squirrel in the winter is 619 nuts and in that 421 are acorns, and the rest of all are walnuts, which means 619 – 421= 198 walnuts.

Question 8.
DIG DEEPER!
You have 384 photos. You put your photos into two photo albums. Each album can hold up to 208 photos. How many photos can you put in each album? Explain.
_____ photos in Album 1 _____ photos in Album 2
_________________________
________________________
208 photos in Album 1 and 176 photos in album 2.

Explanation:
The number of photos we have is 384 photos and those photos were put into two albums and each album can hold 208 photos, which means we can put a total of 208+208= 416 photos. As we have 384 photos, so 208 photos we can put in one album and 384 – 208 = 176 photos in another album.

### Use a Number Line to Subtract Three-Digit Numbers Homework & Practice 10.3

Question 1.
953 − 328 = _____

Explanation:

Let’s start from 953 and count back a hundred three times which is 3×100= 300 and the value will be
953 – 300= 653 and then we will count back tens three times, which is 3×10= 30 and the value will be
474 – 30= 444 and then we will count back one six times, which is 6×1= 6, and the value will be 444 – 6 = 438.

Question 2.
674 − 218 = _____

674 – 218= 456.

Explanation:

Let’s start from 674 and count back hundred two times which is 2×100= 200 and the value will be
674 – 200= 474 and then we will count back tens one time, which is 1×10= 10 and the value will be
474 – 10= 464 and then we will count back one eight times, which is 8×1= 8, and the value will be 474 – 8 = 456.

Question 3.
594 − 107 = _____

594 – 107= 487.

Explanation:

Let’s start from 594 and count back a hundred one time which is 1×100= 100 and the value will be
594 – 100= 494 and then we will count back one seven times, which is 7×1= 7, and the value will be 494 – 7 = 487.

Question 4.
Structure
Use the number lines to show 531 − 396 two ways.

531 – 396 = ______

Question 5.
Modeling Real Life
You earn 631 points in a video game. You trade in 475 points for a special power. How many points do you have left?

____ points
156 points.

Explanation:
The number of points earned in a video game is 631 points and in that, we trade in 475 points for a special power, and the remaining points left are 631 – 475 = 156 points.

Question 6.
DIG DEEPER!
You have 137 books. You put your books on two bookshelves. Each shelf can hold up to 72 books. How many books can you put on each shelf? Explain.
_______ books on Shelf 1 _____ books on Shelf 2
____________________
____________________
72 books on shelf 1 and 65 books on shelf 2.

Explanation:
The number of books we have is 137 books and we need to put those books in two bookshelves and each shelf can hold up to 72 books. So for two shelves, the number of books can hold is 72+72= 144 books. So 72 books can be put in one bookshelf and in the other bookshelf we can keep remaining books which is 137 – 72= 65 books in another bookshelf.

Review & Refresh

Question 7.

_____ hundreds, ______ tens, and _____ ones is _______.
7 hundreds, 6 tens and 3 ones which is 763.

Explanation:

In the above image, we can see seven hundred and six tens and three ones which is
7×100 + 6×10 + 3×1
= 700+60+3
= 763.

### Lesson 10.4 Use Compensation to Subtract Three-Digit Numbers

Explore and Grow

Find 315 − 196.
315 – 196 = 119

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So here we will add 4 to 196, after adding we will get 196+4= 200. Now it is easy to subtract from 315,
so 315 – 200= 115 and we will add that 4 to the result 115. So 115+4= 119.

Find 319 − 200.
319 – 200= 119.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So here we will add 1 to 319, after adding we will get 319+1= 320. Now it is easy to subtract from 320,
so 320 – 200= 120 and we will subtract that 1 to the result 120. So 120 – 1= 119.

How are the problems the same? How are they different? Which problem can you solve using mental math?
__________________________
___________________________

Explanation:

Show and Grow

Use compensation to subtract.
Question 1.

654 – 197= 457.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above it shows that to add 3 to 197, so 197+3= 200,
now 654 – 200= 454 and now we will add 3 to the result,
so 454+3= 457.
654 – 197= 457.

Question 2.

835 – 309= 526.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above, it shows that to subtract 9 in 309, so 309 – 9= 300,
now 835 – 300= 535 and now we will subtract to the result,
so 835 – 309= 535 – 9
835 – 309= 526.

Question 3.

571 – 212= 359.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
571 – 212, so we will subtract 2 in 212, then the number will be 212 – 2= 210,
then 571 – 210= 361,
And now we will subtract -2 to the result,
so 361 – 2= 359.
571 – 210= 359.

Question 4.

611 – 392= 219.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
611 – 392, so we will subtract 92 in 392, then the number will be 392 – 92= 300,
then 611 – 300= 311,
And now we will subtract -92 to the result,
so 311 – 92= 219.
611 – 392= 219.

Apply and Grow: Practice

Use compensation to subtract.
Question 5.

428 – 212= 216.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
428 – 212, so we will subtract 2 in 212, then the number will be 212 – 2= 210,
then 428 – 210= 218,
And now we will subtract 2 to the result,
so 218 – 2= 216.
428 – 212= 216.

Question 6.

943 – 295= 648

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
943 – 295 so we will subtract 52 in 295,
then the number will be 295 – 52= 243,
then 943 – 243= 700,
And now we will subtract 52 to the result,
so 700 – 52= 648.
943 – 295= 648.

Question 7.

489 – 196= 293.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
489 – 196, so we will subtract 7 in 196, then the number will be 196 – 7= 189,
then 489 – 189= 300,
And now we will subtract 7 to the result,
so 300 – 7= 293.
489 – 196= 293.

Question 8.

709 – 503= 206.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
709 – 503, so we will subtract 3 in 503, then the number will be 503 – 3= 500,
then 709 – 500= 209,
And now we will subtract 3 to the result,
so 209 – 3= 206.
709 – 503= 206.

Question 9.
613 − 307 = _____
613 – 317= 306.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
The given numbers are
613 – 307, so we will subtract 7 in 307, then the number will be 307 – 7= 300,
then 613 – 307= 313,
And now we will subtract 7 to the result,
so 313 – 7= 306.
613 – 307= 306.

Question 10.
861 – 499 = _____
861 – 499= 362.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
The given numbers are
861 – 499, so we will subtract 99 in 499, then the number will be 499 – 99= 400,
then 861 – 400= 461,
And now we will subtract 99 to the result,
so 461 – 99= 362.
861 – 499= 362.

Question 11.
Writing
Should you add to or subtract from 194 to find the difference? Explain.

387 – 194= 193.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
387 – 194, so we will subtract 7 in 194, then the number will be 194 – 7= 187,
then 387 – 187= 200,
And now we will subtract 3 to the result,
so 200 – 7= 193.
387 – 194= 193.

Think and Grow: Modeling Real Life

A fish lays 861 eggs. A turtle lays 198 eggs. How many fewer eggs does the turtle lay than the fish?

Subtraction equation:
______ fewer eggs
663 fewer eggs.

Explanation:
As fish lays 861 eggs and a turtle lays 198 eggs, so the number of fewer eggs does the turtle lay than the fish is
861 – 198= 663 fewer eggs.

Show and Grow

Question 12.
A print shop has 650 sheets of white paper and 295 sheets of colored paper. How many fewer sheets of colored paper are there than white paper?

_____ fewer sheets of colored paper
355 fewer sheets of colored paper.

Explanation:
As a printer shop has 650 sheets of white paper and 295 sheets of colored paper. So the fewer sheets of colored paper are there than white paper is 650 – 295= 355 fewer sheets of colored paper.

Question 13.
A party store has 725 different cards and 506 different balloons. How many more cards are there than balloons?

____ more cards
219 more cards.

Explanation:
As a party store has 725 different cards and 506 different balloons, so the will be 725 – 506= 219 more cards are there than balloons.

Question 14.
How are Exercises 12 and 13 similar? How are they different?
____________________
_____________________

### Use Compensation to Subtract Three-Digit Numbers Homework & Practice 10.4

Use compensation to subtract.
Question 1.

972 – 415= 557

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
972 – 415, we will subtract 15 in 415, then the number will be 415 – 15= 400,
then 972 – 400= 572,
And now we will subtract 3 to the result,
so 572 – 15= 557.
972 – 415= 557.

Question 2.

328 – 186= 142.

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
328 – 186, we will add 14 to 186, then the number will be 186 + 14= 200,
then 328 – 200= 128,
And now we will add 14 to the result,
so 128 + 14= 142.
328 – 186= 142.

Question 3.

703 – 598= 105

Explanation:

Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
703 – 598, we will add 2 to 598, then the number will be 598 + 2= 600,
then 703 – 600= 103,
And now we will add 14 to the result,
so 103 + 2= 105.
703 – 598= 105.

Question 4.

On compensation subtraction 841 – 603, we will get the result as 105.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
841 – 603, we will subtract 3 in 603, then the number will be 603 – 3= 600,
then 841 – 600= 541,
And now we will subtract -3 to the result,
so 541 – 3= 105 and on subtracting 841 – 603 we will get the result as 105.

Question 5.
439 – 210 = ______
On compensation subtraction 439 -210 we will get the result as 229.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
439 – 210, we will subtract 1 in 210, then the number will be 210 – 1= 209,
then 439 – 209= 230,
And now we will subtract -1 to the result,
so 230 – 1= 229. On compensation subtraction 439 -210 we will get the result as 229.

Question 6.
719 – 302 = ______
On compensation subtraction 719 -302 we will get the result as 417.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
In the above figure, the given numbers are
719 – 302, we will subtract 2 in 302, then the number will be 302 – 2= 300,
then 719 – 300= 419,
And now we will subtract -2 to the result,
so 419 – 2= 417. On compensation subtraction 719 -302 we will get the result as 417.

Question 7.
YOU BE THE TEACHER
Your friend uses compensation to find 796 − 304. Is your friend correct? Explain.

On compensation subtraction 796 -304 we will get the result as 492.

Explanation:
Yes, my friend is correct. As compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction. So in the above figure, the given numbers are
796 – 304, we will subtract 4 in 304, then the number will be 304 – 4= 300,
then 796 – 300= 496,
And now we will subtract 4 to the result,
so 496 – 4= 492. On compensation subtraction 796 -304 we will get the result as 492.

Question 8.
Modeling Real Life
You write a 225-word essay. Your friend writes a 598-word essay. How many fewer words do you write?
_______ fewer words
The number of fewer words written by me is 373 words.

Explanation:
The number of words written by me is 225 easy words and my friend writes 598 essay words. So the fewer words were written by me than my friend is 598 – 225= 373 words.

Question 9.
Modeling Real Life
How many more students like math than science?

_____ more students
151 more students like math than science.

Explanation:
Given the number of students like math is 348 and the number of students like science is 197. So the number of students who like math more than science is 348 – 197= 151 students.

Review & Refresh

Find the missing digits.
Question 10.

By adding 35 + 46 we will get the result as 81.

Explanation:

In the above image, we can see the result as 81. So to get 1 in one’s place we will take 6 in the empty box, so by adding 5 and 6 we will get 11. So we got 1 in one’s place. Now we know the one value, so to get the other value we will subtract the value which we got in the result. So 81 – 46= 35, and the other number 35. So 35 + 46= 81.

Question 11.

By adding 61 + 37 we will get the result of 81.

Explanation:

In the above image, we can see the result as 98. So to get 8 in one’s place we will take 7 in the empty box, so by adding 1 and 7 which is 7 + 1= 8, we will get 8. So we got 8 in one’s place. Now we know the one value which is 37, so to get the other value we will subtract the value which we got in the result. So 98 – 37= 61, and the other number 37. So 61 + 37= 98.

Question 12.

By adding 27 + 17 we will get the result of 81.

Explanation:

In the above image, we can see the result as 44. So to get 4 in one’s place we will take 7 in the empty box, so by adding 7 and 7 which is 7 + 7= 14, we will get 14. So we got 4 in one’s place. Now we know the one value which is 17, so to get the other value we will subtract the value which we got in the result. So 44 – 17= 27, and the other number 27. So 27 + 17= 44.

### Lesson 10.5 Use Models to Subtract Three-Digit Numbers

Explore and Grow

Model to solve. Make a quick sketch of your model.

323 – 219 = _____
On subtracting 323 – 219 we will get the result as 104.

Explanation:

To model 323 – 219 which is 104, we will take square for hundred, the line for ten, and dot for ones. To subtract 323 – 219, we can see that 9 is greater than 1. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, we can see the model for 104.

Show and Grow

Question 1.
429 – 165 = ?

On subtracting 429 – 165 we will get the result as 264.

Explanation:

To model 429 – 165 which is 264, we will take square for hundred, the line for ten, and dot for ones. To subtract 429 – 165, we can see that 6 is greater than 2. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, we can see the model for 264.

Apply and Grow: Practice

Question 2.
359 – 167 = ?

On subtracting 359 – 167 we will get the result as 192.

Explanation:
To model 359 – 167 which is 192, we will take square for hundred, the line for ten, and dot for ones. To subtract 359 – 167, we can see that 6 is greater than 5. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, we can see the model for 192.

Question 3.
527 – 384 = ?

On subtracting 527 – 384 we will get the result as 143.

Explanation:
To model 527 – 384 which is 143, we will take square for hundred, the line for ten, and dot for ones. To subtract 527 – 143, we can see that 4 is greater than 2. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, we can see the model for 143.

Question 4.
673 – 245 = ?

On subtracting 673 – 245 we will get the result as 428.

Explanation:
To model 673 – 245 which is 428, we will take square for hundred, the line for ten, and dot for ones. To subtract 673 – 245, we can see that 5 is greater than 3. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, we can see the model for 428.

Question 5.
Patterns
Write and solve the next problem in the pattern.

So on subtracting 629 – 141 we will get the result as 488.
So on subtracting 529 – 241 we will get the result as 288.
So on subtracting 429 – 341 we will get the result as 088.

Explanation:

As we can see in the above image that hundreds place was increasing by a hundred times in minuend and in hundreds place hundred was decreasing in subtrahend, so that the next problem will be 629 – 141. To subtract 629 – 141, we can see that 4 is greater than 2. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. So on subtracting 629 – 141 we will get the result as 488. To subtract 529 – 241, we can see that 4 is greater than 2. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. So on subtracting 529 – 241 we will get the result as 288. To subtract 429 – 341, we can see that 4 is greater than 2. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. So on subtracting 429 – 341 we will get the result as 088.

Think and Grow: Modeling Real Life

There are 549 people in a parade. 158 of them are in the marching band. How many people are not in the marching band?
Models:

_____ people
The number of people who are not in the marching band is 549 – 158= 391.

Explanation:
The number of people in a parade is 549 and in that 158 people are in the marching band. So the number of people who are not in the marching band is 549 – 158= 391.

Show and Grow

Question 6.
A school library has 784 books. 256 of them are checked out. How many books are not checked out?
_____ books
586 books are not checked.

Explanation:
The number of books in a school library is 784 books and in that 256 are checked out. So the number of books not checked out is 784 – 256= 586.

Question 7.
A horse weighs 371 pounds more than a pig. The horse weighs 914 pounds. How much does the pig weigh?

_____ pounds
The weight of the pig is 543 pounds.

Explanation:
Given the weight of the horse is 371 pounds more than the pig and the weight of the horse is 914 pounds. So to find the weight of the pig we will subtract 914 – 371= 543. So the weight of the pig is 543 pounds.

### Use Models to Subtract Three-Digit Numbers Homework & Practice 10.5

Question 1.
738 – 544 = ?

On subtracting 738 – 544 we will get the result as 194.

Explanation:
To model 738 – 544 which is 194, we will take square for hundred, the line for ten, and dot for ones. To subtract 738 – 544, we can see that 4 is greater than 3. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, on subtracting 738 – 544 we will get the result as 194.

Question 2.
519 – 248 = ?

On subtracting 519 – 248 we will get the result as 271.

Explanation:
To model 519 – 248 which is 194, we will take square for hundred, the line for ten, and dot for ones. To subtract 519 – 248, we can see that 4 is greater than 1. So we will need a little bit extra in order to subtract, and then we will use an amount from the column to the left. So in this subtraction, we will borrow when we are subtracting one number that is greater than another. And in the above image, on subtracting 519 – 248 we will get the result as 271.

Question 3.
DIG DEEPER!
Complete the subtraction problem so that you need to regroup to subtract.

On subtracting 749 – 345 the result will be 404.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Let the blank be 5 and 749 – 345 will be 404.

Question 4.
Modeling Real Life
A clown makes 315 balloon animals. 156 are giraffes. How many balloon animals are not giraffes?

_____ balloon animals
159 balloon animals are not giraffes.

Explanation:
As a clown makes 315 balloon animals and of that 156 are giraffes, so the number of balloons that are not giraffes is 315 – 156= 159 balloon animals.

Question 5.
Modeling Real Life

Explanation:

Review & Refresh

Question 6.

463 + 194= 657.

Explanation:

By subtracting 463 + 194 we will get the result of 657.

Question 7.

186 + 567= 753.

Explanation:

By adding 186 + 567 we will get the result of 753.

Question 8.

623 + 298= 921.

Explanation:

By adding 623 + 298 we will get the result of 921.

### Lesson 10.6 Subtract Three-Digit Numbers

Explore and Grow

Find each difference.

The difference between 529 – 218 is 311.
The difference between 553 – 316 is 237.
The difference between 323 – 194 is 129.

Explanation:

Compare the problems. How are they the same? How are they different?
_________________________
_________________________

Show and Grow

Question 1.

By regrouping in the subtraction of 423 – 174 we will get the result as 249.

Explanation:

Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 423- 174 we get 249.

Question 2.

By regrouping in the subtraction of 542 – 367 we will get the result of 175.

Explanation:

Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 542- 367 we get 175

Question 3.

By regrouping in the subtraction of 315 – 151 we will get the result of 164.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 315- 151 we get 164

Question 4.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 568 – 276 we get 292

Question 5.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 821- 346 we get 475

Question 6.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 727- 289 we get 438

Question 7.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 434 – 188 we get 246

Question 8.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 963- 335 we get 628

Question 9.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 741- 254 we get 487

Apply and Grow: Practice

Question 10.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 345- 185 we get 160

Question 11.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 627 – 418 we get 209

Question 12.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 916- 723 we get 193

Question 13.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 829- 367 we get 462

Question 14.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 541- 291 we get 250

Question 15.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 351- 182  we get 169

Question 16.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 465- 197 we get 268

Question 17.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 643 – 289  we get 354

Question 18.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 673- 498 we get 175

Question 19.
DIG DEEPER!
Find the missing digits

The missing digit in the first image is 3.
The missing digit in the first image is 8.
The missing digit in the first image is 4.

Explanation:

To find the missing digits in the above figure, we will subtract the difference and minuend. So for the first image we can see that minuend is greater than subtrahend that i 5  is greater than 0, so there is no carry forward. And we can subtract the minuend and difference which is 4 – 1=3. So the missing digit is 3. We can find in another way also by subtracting minuend and the difference which is in the second image we will subtract 957 – 279 which is 678 and the missing digit is 8. For the third image we will add subtrahend and the difference which is
484 + 158 which is 642 and the missing digit is 4.

Think and Grow: Modeling Real Life

A jeweler has 616 bracelets and 668 necklaces. He sells 269 bracelets. How many bracelets are left?

Subtraction equation:
______ bracelets
Subtraction equation: 616 – 269= 347
347 bracelets left.

Explanation:
Aa a jeweler has 616 bracelets and 668 necklaces and he sells 269 bracelets. So the number of bracelets left is
616 – 269= 347 bracelets left.

Show and Grow

Question 20.
A vendor has 354 hats and 294 pairs of sunglasses. She sells 186 hats. How many hats are left?

_____ hats
168 hats left.

Explanation:
As the vendor has 354 hats and 294 pairs of sunglasses and she sold 186 hats, the number of hats lefts are
354 – 186= 168 hats left.

Question 21.
There are 449 watercolor paintings and 373 oil paintings in a school art show. 238 paintings win a ribbon. How many do not win a ribbon?

_____ paintings
584 paintings didn’t win the ribbon.

Explanation:
The total number of watercolor paintings are 449 and the number of oil paintings is 373 and of that 238 won a ribbon, so the number of paintings that didn’t win the ribbon is, first we will add watercolor paintings and oil painting and then we will subtract 238 from the result. So 449 +373= 822 paintings and in that 238 paintings win a ribbon. So the number of paintings that didn’t win the ribbon is 822 – 238= 584 paintings didn’t win the ribbon.

Question 22.
Explain how Exercises 20 and 21 are different.
_________________________
_________________________
In exercise 20 the given objects are hats and sunglasses and asked to find about hats only. But in exercise 21 asked about both water color paintings and oil paintings which didn’t win the ribbon.

### Subtract Three-Digit Numbers Homework & Practice 10.6

Question 1.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 873 – 438 we get 435

Question 2.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 341 – 278 we get 063

Question 3.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 913 – 156 we get 757

Question 4.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 456- 187 we get 269

Question 5.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 625 – 297 we get 328

Question 6.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 951 – 682 we get 269

Question 7.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 452 – 374 we get 078

Question 8.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 961 – 593  we get 368

Question 9.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. as shown in the above image
Hence 746 – 289 we get 457

Question 10.
Number Sense
Complete the subtraction problem so that you do not need to regroup to subtract.

The difference without regrouping is 453 – 241 which is 212.

Explanation:
Let the blank be the any number which is less than 5. As given that we do not need to regroup to subtract, so we will pick any number from 0 to 5. So let the number be 4, then 453 – 241= 212.

Question 11.
YOU BE THE TEACHER
Descartes finds 731 − 246. Is he correct? Explain.

No, Descartes is not correct.

Explanation:
No, Descartes is not correct. In the above image we can see that 1 is less than 6. So we need to borrow from 3 to subtract the digit 6 from 1. Then 731 – 246 will be 485.

Question 12.
Modeling Real Life
453 bananas and 456 apples are shipped to a store. When they arrive, 268 of the bananas are rotten. How many bananas are not rotten?

____ bananas
185 bananas are not rotten.

Explanation:
The total number of bananas is 453 and the number of apples in the store is 456. And in that 268 bananas are rotten, so the number of bananas not rotten is 453 – 268= 185 bananas are not rotten.

Question 13.
Modeling Real Life
There are 432 red shirts and 293 blue shirts in stock. 516 shirts are sold. How many shirts are left?
_____ shirts
209 shirts left.

Explanation:
The total number of red shirts is 432 and the number of blue shirts in stock is 293. So the total number of shirts is
432 + 293= 725 shirts. And in that 516 shirts are sold out, so the number of shirts left is 725 – 516= 209 shirts left.

Review & Refresh

Question 14.
Count by fives.
680, 685, ____, _____, _____, _____, ______
680, 685, 690, 695, 700, 705, 710, 715.

Explanation:
By adding five to the given numbers we will get the result as
680 + 5= 685,
685 + 5= 690,
690 + 5= 695,
695 + 5= 700,
700 + 5= 705,
705 + 5= 710,
710 + 5= 715.

### Lesson 10.7 Subtract from Numbers That Contain Zeros

Explore and Grow

Find each difference.

The difference between 400 – 178 is 222.
The difference between 399 – 177 is 222.

Explanation:
For the image 1 we should follow regrouping method, as the digits contains 0. So by regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend. So to subtract 400 – 178 we will borrow from 4 as the 0 is less than 7 and 8. Then 400 – 178 will be 222. For the image 2 we don’t need any regrouping as minuend is greater than subtrahend. So
399 – 177= 222.

How are the problems the same? How are they different? Which problem can you solve without regrouping?
______________________________
______________________________
The problems are same by their result and the problem is different as their minuend and subtrahend are different. The second problem can solve without using regrouping. As minuend is greater than subtrahend, so we don’t need regrouping.

Show and Grow

Use regrouping or compensation to subtract.
Question 1.
300 − 139 = _____
300 – 139= 161.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 1 for both the numbers. Then 300 – 1= 299 and 139 – 1= 138. Now we will subtract 299 – 138= 161.

Question 2.
402 − 265 = _____
402 – 265= 137.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 3 for both the numbers. Then 402 – 3= 399 and 265 – 3= 262. Now we will subtract 399 – 262= 137.

Question 3.
800 − 547 = _____
800 – 547= 253.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 1 for both the numbers. Then 800 – 1= 799 and 547 – 1= 546. Now we will subtract 799 – 546= 253.

Question 4.
910 − 252 = _____
910 – 252= 658.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 52 in 252 then 252 – 52= 200. Now we will subtract
910 – 200= 710. Now we will subtract 52 from the result 710, which is 710 – 52= 658. So 910 – 252= 658.

Apply and Grow: Practice

Use regrouping or compensation to subtract.
Question 5.
310 – 186 = ____
310 – 186= 124.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 86 in 186 then 186 – 86= 100. Now we will subtract
310 – 100= 210. Now we will subtract 86 from the result 210, which is 210 – 86= 124. So 310 – 186= 124.

Question 6.
620 – 458 = _____
On compensation subtraction of 620 – 458, the result will be 162.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 58 in 458 then 458 – 58= 400. Now we will subtract
620 – 400= 220. Now we will subtract 58 from the result 220, which is 220 – 58= 162. So 620 – 458= 162.

Question 7.
906 – 729 = _____
On compensation subtraction of 906 – 729, the result will be 177.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 29 in 729 then 729 – 29= 700. Now we will subtract
906 – 700= 206. Now we will subtract 29 from the result 206, which is 206 – 29= 177. So 906- 729= 177.

Question 8.
807 – 389 = _____
On compensation subtraction of 807 – 389, the result will be 418.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 89 in 389 then 389 – 89= 300. Now we will subtract
807 – 300= 507. Now we will subtract 89 from the result 507, which is 807 – 389= 418. So 807 – 389= 418.

Question 9.
503 – 296 = _____
On compensation subtraction of 503 – 296, the result will be 207.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 96 in 296 then 296 – 96= 200. Now we will subtract
503 – 200= 303. Now we will subtract 96 from the result 303, which is 303 – 96= 207. So 503 – 296= 207.

Question 10.
301 – 282 = _____
On compensation subtraction of 301 – 282, the result will be 19.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 82 in 282 then 282 – 82= 200. Now we will subtract
301 – 200= 101. Now we will subtract 82 from the result 101, which is 101 – 82= 19. So 301 – 282= 19.

Question 11.
400 – 197 = _____
On compensation subtraction of 400 – 197, the result will be 203.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 97 in 197 then 197 – 97= 100. Now we will subtract
400 – 100= 300. Now we will subtract 97 from the result 300, which is 300 – 97= 203. So 400 – 197= 203.

Question 12.
600 – 289 = _____
On compensation subtraction of 600 – 289, the result will be 311.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 89 in 289 then 289 – 89= 200. Now we will subtract
600 – 200= 400. Now we will subtract 89 from the result 400, which is 400 – 89= 311. So 600 – 289= 311.

Question 13.
Structure
Show two ways to find 500 −314.

Think and Grow: Modeling Real Life

There are 400 paper lanterns. 279 of them are let go. How many paper lanterns are left?

Subtraction equation:
_____ paper lanterns
The number of paper lanterns left is 121.

Explanation:
The number of paper lanterns is 400 and in that 279 of them are let go and the remaining left are
400 – 279= 121. So the number of paper lanterns left is 121.

Show and Grow

Question 14.
There are 803 fans at a stadium. 226 of them leave. How many fans are left?

_____ fans
The number of fans left is 577.

Explanation:
The total number of fans in the stadium is 803 and in that 226 of them are left. So the remaining number of fans left is 803 – 226= 577. So the number of fans left is 577.

Question 15.
DIG DEEPER!
A florist plants 600 flowers. The table shows how many have bloomed. How many flowers have not bloomed yet?

_____ flowers
The number of flowers not bloomed is 72.

Explanation:
The number of plants did the florist plant is 600 flowers. In the table given that the number of blooms in May is 296 and the number of blooms in June is 232. So the total number of blooms in the month of May and June is
296 + 232= 528. And the number of flowers not bloomed is 600 – 528= 72.

### Subtract from Numbers That Contain Zeros Homework & Practice 10.7

Use regrouping or compensation to subtract
Question 1.
700 − 465 = _____
On compensation subtraction of 700 – 465, the result will be 235.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 65 in 465 then 465 – 65= 400. Now we will subtract
700 – 400= 300. Now we will subtract 65 from the result 300, which is 300 – 82= 19. So 301 – 282= 19.

Question 2.
302 − 176 = _____
On compensation subtraction of 302- 176, the result will be 126.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 76 in 176 then 176 – 76= 100. Now we will subtract
302 – 100= 202. Now we will subtract 76 from the result 202, which is 202 – 76= 126. So 302 – 176= 126.

Question 3.
910 − 186 = ______
By compensation subtraction of 910- 186, the result will be 724.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 86 in 186 then 186 – 86= 100. Now we will subtract
910 – 100= 810. Now we will subtract 86 from the result 810, which is 810 – 86= 724. So 910 – 186= 724.

Question 4.
800 − 691 = _____
By compensation subtraction of 800 – 691, the result will be 109.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will add 9 for 691 then 691 + 9= 700. Now we will subtract
800 – 700= 100. Now we will add 9 for the result 100, which is 100 + 9= 109. So 800 – 691= 109.

Question 5.
Writing
Explain why you might want to use compensation to subtract. Give an example.
_______________________________
_______________________________
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction. So we will use compensation subtract. For example, if we take 420 – 326. So by the compensation method, we will subtract 26 in 326 then
326 – 26= 300. Now we will subtract 420 – 300= 120. Now we will subtract 26 for the result 120, which is
120 – 26= 109. So 420 – 326= 94.

Question 6.
Modeling Real Life
There are 300 coins on a desk. 178 fall off. How many coins are left on the desk?

_____ coins
The number of coins left on the desk is 122.

Explanation:
The number of coins on a desk is 300 coins and in that 178 coins fall off. So the number of coins left on the desk is, here we will use compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 78 for 178 then 178 – 78= 100. Now we will subtract
300 – 100= 200. Now we will subtract 78 for the result 200, which is 200 – 78= 122. So 300 – 178= 122.

Question 7.
Modeling Real Life
There are 500 students in a school. How many students are absent?

______ students
The number of students absent is 88 students.

Explanation:
The total number of students is 500 students and in that the attendance of boy students is 234 and the attendance of girl students is 178. So the total number of students who attended is 234 + 178= 412. And the number of students absent is 500 – 412= 88 students.

Review & Refresh

Question 8.
29 + 34 = _____
29 + 34= 63.

Explanation:
On adding 29 + 34, we will get the result as 63.

Question 9.
46 + 13 = _____
46 + 13= 29.

Explanation:
On adding 46 + 13, we will get the result of 59.

### Lesson 10.8 Use Addition to Subtract

Explore and Grow

Use the number lines to solve.
445 – 220 = _____

How are the equations the same? How are they different?
__________________________
__________________________

Show and Grow

Question 1.
488 − 137 = _____

The difference between 488 – 137 is 351.

Explanation:
Let’s start at 137 and add hundred three times which is 3×100= 300 and the value will be
137 + 300= 437 and then we will add fifty which is 437+50= 487 and then we will add one. The value will be
487 + 1=488. So the difference between 438 – 137 is 351.

Question 2.
792 − 446 = _____

The difference between 792 – 446 is 346.

Explanation:
Let’s start at 446 and add hundred three times which is 3×100= 300 and the value will be
446 + 300= 746 and then we will add four tens which is 746+40= 786 and then we will add six. The value will be
786 + 6=792. So the difference between 792 – 446 is 346.

Apply and Grow: Practice

Question 3.
521 − 364 = _____

The difference between 521 – 364 is 157.

Explanation:
Let’s start at 364 and add hundred once which is 1×100= 100 and the value will be 364 + 100= 464 and then we will add five tens which is 464+50= 514 and then we will add seven. The value will be 514 + 7=521. So the difference between 521 – 364 is 157.

Question 4.
856 – 213 = ______

The difference between 856 – 213 is 643

Explanation:
Let’s start at 213 and add hundred six times which is 6×100= 600 and the value will be 213 + 600= 813 and then we will add four tens which is 813+40= 853 and then we will add three. The value will be 853 + 3=856. So the difference between 856 – 213 is 643.

Question 5.
492 − 137 = _____

The difference between 492 – 137 is 355.

Explanation:
Let’s start at 137 and add hundred three times which is 3×100= 300 and the value will be 137 + 300= 437 and then we will add eight tens which is 437+50= 487 and then we will add five. The value will be  487+ 5=492. So the difference between 492 – 137 is 355.

Question 6.
Number Sense
Write the equation shown by the number line.

_____ – ______ = ______
The number line equation is 642 – 221= 421.

Explanation:
In the above figure, to find the number line equation we will add all the numbers which are counted back. So the counted back numbers are 1+10+10+100+100 which is 221. So the number line equation is 642 – 221= 421.

Think and Grow: Modeling Real Life

A machine has some bouncy balls. 115 are sold. There are 227 left. How many bouncy balls were there to start?

Equation:
Model:
______ bouncy balls
The total number of bouncy balls is 342.

Explanation:
As there are 115 bouncy balls sold and 227 are sold. So the total number of bouncy balls is 115+227= 342 bouncy balls.

Show and Grow

Question 7.
There are some fans at a baseball game. 148 leave early. There are 182 left. How many fans were at the baseball game?
_____ fans
The total number of fans at the baseball game is 330.

Explanation:
The number of fans left early in the baseball game is 148 fans and after that 182 fans left. So the total number of fans at the baseball game is 148 + 182= 330.

Question 8.
DIG DEEPER!
Your school collects 518 cans for a food drive. Your class collects 142 cans. Another class collects 204. How many cans did the rest of the classes collect?

_____ cans
The number of cans did the rest of the classes collected is 172 cans.

Explanation:
The number of food cans that the school collects for a food drive is 518 cans and my class collects 142 cans and another class collects 204 cans. The total number of food cans collected by both classes is 142 + 204 which is 346. And the total number of cans collected by the rest of the classes is 518 – 346. Here, we will use compensation subtraction as a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 46 in 346 then 346 – 46= 300. Now we will subtract
518 – 300= 218. Now we will subtract 46 from the result 218, which is 218 – 46= 172. So 518 – 346= 172 cans.

### Use Addition to Subtract Homework & Practice 10.8

Question 1.
721 − 314 = ____

The difference between 721 – 314= 407.

Explanation:

Let’s start at 314 and add hundred four times which is 4×100= 400 and the value will be
314 + 400= 714 and then we will add seven by dividing the seven into two parts by 5+2 tens, which is
714+7= 721 and the value will be 314 + 407= 721. So the difference between 721 – 314= 407.

Question 2.
654 − 334 = _____

The difference between 654 – 334 is 320.

Explanation:

Let’s start at 334 and add hundred three times which is 3×100= 300 and the value will be
334 + 300= 634 and then we will add twenty by dividing the twenty into two parts by 10+10, which is
634+20= 654 and the value will be 334 + 320= 654. So the difference between 654 – 334= 320.

Question 3.
Descartes adds to find 400 − 279. Is he correct? Explain.

Yes, Descartes is correct.

Explanation:
Yes, Descartes is correct. By adding the number of jumps 1+20+100 we will get 121. So by adding 121+279 we will get 400. So Descartes is correct.

Question 4.
Modeling Real Life
There are some people in a national park. 124 of them leave. There are 535 people left. How many people were in the park to start?
______ people
The number of people in the park yet to start is 411 people.

Explanation:
The number of people leave is 124 and after that, there are 535 people left. So the total number of people were in the park to start is 535 – 124= 411 people.

Question 5.
Modeling Real Life
You have 514 tickets. You spend 220 tickets on a mug and 156 on stickers. How many tickets do you have left?
______ tickets
The number of tickets left is 138 tickets.

Explanation:
The number of tickets we have is 514 and 220 tickets are spent on a mug and 156 tickets on stickers. So the total number of tickets left is, we will add both the tickets that were spent on mug and stickers, which is 220+156= 376 tickets. So the number of tickets left are 514-376= 138.

Review & Refresh

Question 6.

_____ flat surfaces
______ vertices
_____ edges
Two flat surfaces,
One vertex,
One edge.

Explanation:
The above image is a cone that has two flat surfaces, one vertex, and 1 edge.

Question 7.

_____ flat surfaces
______ vertices
_____ edges
Six flat surfaces,
Twelve edges,
Eight vertices.

Explanation:
The above image is a cube that has six flat surfaces, twelve edges, and eight vertices.

### Lesson 10.9 Explain Subtraction Strategies

Explore and Grow

Use two different strategies to find 474 − 119.

The two different strategies used are Regrouping and Compensation.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So 474 – 119 we get 355.
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 19 in 119 then 119 – 19= 100. Now we will subtract
474 – 100= 374. Now we will subtract 19 from the result 374, which is 374 – 19= 355. So 474 – 119= 355.

Explain why you chose one of your strategies.
________________________
________________________
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So we will choose compensation subtraction.

Show and Grow

Choose any strategy to solve. Explain how you solved.
Question 1.
477 − 224 = _____
___________________________
___________________________
By regrouping subtraction 477 – 224= 253.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So we will subtract by regrouping the numbers 477 – 224= 253.

Question 2.
686 − 397 = _____
___________________________
___________________________
By regrouping subtraction 686 – 397= 289.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So we will subtract by regrouping the numbers 686 – 397= 289.

Apply and Grow: Practice

Choose any strategy to solve. Explain how you solved.
Question 3.
502 − 321 = _____
_______________________
_______________________
By regrouping subtraction 502 – 321= 181.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So we will subtract by regrouping the numbers 502 – 321= 181.

Question 4.
900 − 756 = _____
________________________
_______________________
By regrouping subtraction 900 – 756= 144.

Explanation:
Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So we will subtract by regrouping the numbers 900 – 756= 144.

Question 5.
Reasoning
Your friend solves a subtraction problem. Write the problem your friend solves. Explain what strategy was used to solve.

______ – _____ = _____
__________________________
__________________________
The number line equation is 335 – 125= 210.

Explanation:
The strategy which was used by my friend to solve is using the number line. And the problem which was solved by my friend is, the count jump starts from 125 and the count is  100+100+10 which is 210, and the number line equation is 335 – 125= 210.

Think and Grow: Modeling Real Life

Choose any strategy to solve. Explain how you solved.
There are 941 songs in a music library. 365 of them are pop songs. 189 are rock songs. How many songs are not pop songs?
Subtraction equation:
______ songs
The number of songs that are not pop songs is 576 songs.

Explanation:
The total number of songs in a music library is 941 songs. And in that 365 of them are pop songs and 189 are rock songs. So the number of songs that are not pop songs is 941 – 365 which is 576 songs are not pop songs.

Show and Grow

Choose any strategy to solve. Explain how you solved.
Question 6.
There are 743 penguins in a colony. 235 are in the water. 159 are in caves. How many penguins are not in the water?

_____ penguins
The number of penguins that are not in water is 508 penguins.

Explanation:
The total number of penguins in a colony is 743 penguins. And a number of penguins in the water is 235 penguins, and in caves, there are 159 penguins. So the number of penguins that are not in water is 743 – 235= 508 penguins.

### Explain Subtraction Strategies Homework & Practice 10.9

Choose any strategy to solve. Explain how you solved.
Question 1.
408 − 196 = _____
__________________________________
__________________________________
By compensation subtraction 408 – 196= 212.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will add 4 to the number 196 then 196 + 4= 200. Now we will subtract
408 – 200= 208. Now we will add 4 to the result 208, which is 208 + 4= 212. So 408 – 196= 212.

Question 2.
723 − 515 = ____
______________________________
______________________________
By compensation subtraction 723 – 515= 208.

Explanation:
Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, we will subtract 15 from the number 515 then 515 – 15= 500. Now we will subtract 723 – 500= 223. Now we will subtract 15 to the result 223, which is 223 – 15= 208. So 723 – 515= 208.

Question 3.
DIG DEEPER!
Newton wants to use mental math to find 452 − 239. Is this a good strategy for him to use? Explain.
___________________________
___________________________
By compensation subtraction 452 – 239= 213.

Explanation:
Compensation subtraction is a good strategy because compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is quite an effective way of subtraction. So by the compensation method, we will subtract 39 from the number 239 then
239 – 39= 200. Now we will subtract 452 – 200= 252. Now we will subtract 39 to the result 252, which is
252 – 39= 213. So 452 – 239= 213.

Question 4.
Modeling Real Life
767 people work at a store. 205 are cashiers. 314 stock shelves. How many people are not cashiers? Explain.
______ people
_____________________________
_____________________________
The number of people who are not cashiers is 562 people.

Explanation:
The total number of people in the work at a store is 767. And the cashiers are 205 people, and the stock shelves are 314. So the people who are not cashiers is 767 – 205= 562 people are not cashiers.

Question 5.
Modeling Real Life
You have a pack of 900 craft sticks. You use 638 for a project. Your friend uses 127. How many craft sticks were not used? Explain.
______ craft sticks
____________________________
____________________________
The number of sticks that are not used is 135 sticks.

Explanation:
The total number of craft sticks in a pack is 900 sticks. And in that 638 sticks are used for a project, and a friend uses 127 sticks. So the total number of sticks that are not used is 638 + 127= 765. And the number of craft sticks that are not used is 900 – 765= 135 sticks.

Review & Refresh

Question 6.
Circle the longer object.

The pen is longer than the eraser.

Explanation:

In the above image, we can see that the pen is longer than the eraser. So we will round off the pen.

### Subtract Numbers within 1,000 Performance Task

The table shows the number of laps that four cars complete in a racing season.

Question 1.
How many fewer laps does the blue car complete than the yellow car?
_____ laps
57 fewer laps do the blue car complete than the yellow car.

Explanation:
The number of laps for the blue car is 217 laps and the laps of the yellow car is 274. So 274 – 217= 57 fewer laps does the blue car complete than the yellow car.

Question 2.
How many more laps does the red car complete than the green car?
_____ laps
66 more laps the red car complete than the green car.

Explanation:
The number of laps does the red car completes is 300, and the number of laps does the green car completes is 234. So 300 – 234= 66 many more laps does the red car complete than the green car.

Question 3.
The purple car completes 500 laps and the orange car completes 250 laps. Order the cars from the greatest number of laps to the least number of laps.

_____, _____, _____, _____, _____, ______
500, 300, 274, 250, 234, 217.

Explanation:
The number of laps completed by the red car is 300 laps,
The number of laps completed by the yellow car is 274 laps,
The number of laps completed by the green car is 234 laps,
The number of laps completed by the blue car is 217 laps,
The number of laps completed by the purple car is 500 laps,
The number of laps completed by the orange car is 250 laps.
So the order of the cars from the greatest number of laps to the least number of laps is
purple car, red car, yellow car, orange car, green car, and the blue car which is
500, 300, 274, 250, 234, 217.

Question 4.
How many cars complete an even number of laps?
_____ cars
The total number of cars that complete an even number of laps is 3 laps.

Explanation:
The number of cars that complete an even number of laps is a red car with 300 laps, yellow car with 274 laps, a green car with 234 laps. So the total number of cars that complete an even number of laps is 3 laps.

Question 5.
The red and yellow cars are on Team Go Fast. The green and blue cars are on Team Speed. Which team completes more laps? How many more laps?

The team go fast completes more laps than the team speed. And the number of more laps is 123 laps.

Explanation:
The red car completes 300 laps and the yellow car completes 274 laps. As the red and yellow cars are the team, so the total number of laps that both cars completed is 300 + 274= 574 laps. And the green car completes 234 laps and the blue car completes 217 laps. So the total number of laps that both cars completed is 234 + 217=  451 laps. So the team go fast completes more laps than the team speed. And the number of more laps is
574 – 451= 123 laps.

### Subtract Numbers within 1,000 Activity

Greatest and Least
To Play: Roll a die 3 times and record each number. Use the numbers to write the greatest and the least three-digit numbers. Find the difference and record your answer.

### Subtract Numbers within 1,000 Chapter Practice

10.1 Subtract 10 and 100

Question 1.
230 −10 = _____
The difference between 230 – 10 is 220.

Explanation:
To find the difference of 230-10, we will pick the tens digit number in 230 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
3 – 1= 2
therefore 230 – 10= 220.

Question 2.
956 − 10 = _____
The difference between 956 – 10 is 946.

Explanation:
To find the difference of 956 -10, we will pick the tens digit number in 956 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
5 – 1= 4
therefore 956 – 10= 946.

Question 3.
597 − 100 = _____
The difference between 597 – 100 is 497.

Explanation:
To find the difference of 597 – 100, we will pick the hundred digit number in 597 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
5 – 1= 4
therefore 597 – 100= 497.

Question 4.
384 − 100 = _____
The difference between 384 – 100 is 284.

Explanation:
To find the difference of 384-100, we will pick the hundred digit number in 384 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
3 – 1= 2
therefore 384 – 100= 284.

Question 5.
705 − 10 = _____
The difference between 705 – 10 is 695.

Explanation:
To find the difference of 705-10, we will pick the tens digit number in 705 and in 10. Then we will subtract both the numbers which we have picked. So the result will be
70 – 1= 69
therefore 705 – 10= 695.

Question 6.
157 − 100 = _____
The difference between 157 – 100 is 57.

Explanation:
To find the difference of 157-100, we will pick the hundred digit number in 157 and in 100. Then we will subtract both the numbers which we have picked. So the result will be
1 – 1= 0
therefore 157 – 100= 057.

10.2 Use a Number Line to Subtract Hundreds and Tens

Question 7.
481 − 250 = ______

The difference between 481 – 250 is 231.

Explanation:
Let’s start at 250 and add hundred two times which is 2×100= 200 and the value will be 250 + 200= 450 and then we will add three tens which is 450+30= 480 and then we will add one. The value will be 480 + 1=481. So the difference between 481 – 250 is 231.

Question 8.
Modeling Real Life
325 crackers come in a box. You set out 160 for a party. How many crackers are left in the box?

_____ crackers
The number of crackers left is 165.

Explanation:
The total number of crackers in the box is 325, and in that 160 are set for a party. So the number of crackers left in the box is 325 – 160= 165 crackers left.

10.3 Use a Number Line to SubtractThree-Digit Numbers

Question 9.
604 −97 = _____

The difference between 604 – 97 is 507.

Explanation:
Let’s start from 604 and count back ninety once and the value will be 604 – 90= 514 and then we will count back seven, and the value will be 514 – 7=507. So the difference between 604 – 97= 507.

Question 10.
Number Sense
Write the equation shown by the number line.

_____ – _____ = ______
The equation is 782 – 325= 457.

Explanation:
In the above image, given it is started from 782 and count back to 300 then the result is 782 – 300= 482, and then it was counted back to 20 then the value is 482 – 20= 462, then the value is counted back to 5 and the value is 462 – 5= 457.

10.4 Use Compensation to Subtract Three-Digit Numbers

Use compensation to subtract.
Question 11.

Question 12.

Question 13.
YOU BE THE TEACHER
Descartes uses compensation to find 331 − 214. Is he correct? Explain.

Yes, Descartes is correct.

Explanation:
Yes, Descartes is correct. As Compensation subtraction is a mental math strategy for multi-digit addition which means taking away more than we need and then adding some back which is a quite effective way of subtraction.
So by the compensation method, Descartes subtracted 14 to the number 214 then 214 – 14= 200. Now Descartes subtracted 331 – 200= 131.

10.5 Use Models to Subtract Three-Digit Numbers

Question 14.
992 – 645 = ?

10.6 Subtract Three-Digit Numbers

Question 15.

Question 16.

Question 17.

Question 18.
Modeling Real Life
There are 420 T-shirts and120 pairs of shorts at a store. 135 T-shirts are sold. How many T-shirts are left?
_____ T-shirts
The number of t-shirts left is 285.

Explanation:
The number of t-shirts is 420 and there are 120 pairs of shorts at a store. And in that 135 tshits are sold out. The remaining t-shirts is 420 – 135= 285.

10.7 Subtract from Numbers that Contain Zeros

Question 19.
600 − 365 = _____
By regrouping the numbers 600 – 365= 235.

Explanation:
By regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So we will subtract by regrouping the numbers 600 – 365= 235.

Question 20.
402 − 195 = _____
By regrouping the numbers 402 – 195= 207.

Explanation:
By regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtrahend.
So we will subtract by regrouping the numbers 402 – 195= 207.

Question 21.
213 − 102 = _____

The difference between 213 – 102 is 111.

Explanation:
Let’s start at 102 and add hundred once which is 1×100= 100 and the value will be 102 + 100= 202 and then we will add ten which is 202+10= 212 and then we will add one. The value will be 212 + 1=213. So the difference between 213 – 102 is 111.

Question 22.
564 − 317 = _____

The difference between 564 – 317 is 247.

Explanation:
Let’s start at 317 and add hundred two time which is 2×100= 200 and the value will be 317 + 200= 517 and then we will add four tens which is 517+40= 557 and then we will add seven. The value will be 557 + 7=564. So the difference between 564 – 317 is 247.

10.9 Explain Subtraction Strategies

Choose any strategy to solve. Explain how you solved.
Question 23.
573 − 309 = ____
______________________________
______________________________
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