# Go Math Grade 5 Chapter 2 Answer Key Pdf Divide Whole Numbers

## Divide Whole Numbers Go Math Grade 5 Chapter 2 Answer Key Pdf

Apply the math to real-time examples by learning the tricks using HMH Go Math Grade 5 Answer Key. The quick way of solving math problems will help the students to save time. So, students can practice more questions utilizing the time properly. If you want the best way of learning then you must use Go Math Grade 5 Chapter 2 Divide Whole Numbers Answer Key.

Lesson 1: Place the First Digit

Lesson 2: Divide by 1-Digit Divisors

Lesson 3: Investigate • Division with 2-Digit Divisors

Lesson 4: Partial Quotients

Mid-Chapter Checkpoint

Lesson 5: Estimate with 2-Digit Divisors

Lesson 6: Divide by 2-Digit Divisors

Lesson 7: Interpret the Remainder

Lesson 9: Problem Solving • Division

Review/Test

### Place the First Digit – Share and Show – Page No. 63

Divide.

Question 1.
3)$$\overline { 579 }$$
_____

193

Explanation:
Divide integers 57/3 = 19
Multiply 19 x 3 = 57; Subtract 57 – 57 = 0
Write down 9 and divide integers 9/3 = 3.
Multiply 3 x 3 = 9. Subtract 9 – 9 = 0.
The remainder is 0.

Question 2.
5)$$\overline { 1,035 }$$
_____

207

Explanation:
Divide integers 10/5 = 2
Multiply 2 x 5 = 10; Subtract 10 – 10 = 0
Write down 35 and divide integers 35/5 = 7.
Multiply 7 x 5 = 35. Subtract 35 – 35 = 0.
The remainder is 0.

Question 3.
8)$$\overline { 1,766 }$$
_____ R _____

220 R 6

Explanation:
Divide integers 17/8 = 2
Multiply 2 x 8 = 16; Subtract 17 – 16 = 1
Write down 16 and divide integers 16/8 = 2.
Multiply 2 x 8 = 16. Subtract 16 – 16 = 0.
Write down 6; 6 < 8. There are not enough tens
So, the remainder is 6

Divide.

Question 4.
8)$$\overline { 275 }$$
_____ R _____

43 R 3

Explanation:
Divide integers 27/8 = 3
Multiply 8 x 3 = 24; Subtract 27 – 24= 3
Write down 3 and divide integers 35/8 = 4.
Multiply 8 x 4 = 32. Subtract 35 – 32 = 3.
The remainder is 3.

Question 5.
3)$$\overline { 468 }$$
_____

155 R 3

Explanation:
Divide integers 46/3 = 15
Multiply 3 x 15 = 45; Subtract 46 – 45= 1
Write down 18 and divide integers 18/3 = 5.
Multiply 3 x 5 = 15. Subtract 18 – 15 = 3.
The remainder is 3.

Question 6.
4)$$\overline { 3,220 }$$
_____

805

Explanation:
Divide integers 32/4 = 8
Multiply 4 x 8 = 32; Subtract 32 – 32 = 0
Write down 20 and divide integers 20/4 = 5.
Multiply 4 x 5 = 20. Subtract 20 – 20= 0.
The remainder is 0.

Question 7.
6)$$\overline { 618 }$$
_____

103

Explanation:
Divide integers 61/6 = 10
Multiply 6 x 10 = 60; Subtract 61 – 60 = 1
Write down 18 and divide integers 18/6 = 3.
Multiply 6 x 3 = 18. Subtract 18 – 18 = 0.
The remainder is 0.

Question 8.
4)$$\overline { 716 }$$
_____

179

Explanation:
Divide integers 71/4 = 17
Multiply 4 x 17 = 68; Subtract 71 – 68 = 3
Write down 36 and divide integers 36/4 = 9.
Multiply 4 x 9 = 36. Subtract 36 – 36 = 0.
The remainder is 0.

Question 9.
9)$$\overline { 1,157 }$$
_____ R _____

128 R 5

Explanation:
Divide integers 11/9 = 1
Multiply 9 x 1 = 9; Subtract 11 – 9 = 2
Write down 25 and divide integers 25/9 = 2.
Multiply 9 x 2 = 18. Subtract 25 – 18 = 7.
Write down 77 and divide integers 77/9 = 8.
Multiply 9 x 8 = 72. Subtract 77 – 72= 5.
The remainder is 5.

Question 10.
6)$$\overline { 6,827 }$$
_____ R _____

1,137 R 5

Explanation:
Divide integers 6/6 = 1
Multiply 6 x 1 = 6; Subtract 6 – 6 = 0
Write down 82 and divide integers 82/6 = 13.
Multiply 6 x 13 = 78. Subtract 82 – 78 = 4.
Write down 47 and divide integers 47/6 = 7.
Multiply 6 x 7 = 42. Subtract 47 – 42= 5.
The remainder is 5.

Question 11.
7)$$\overline { 8,523 }$$
_____ R _____

1,217 R 4

Explanation:
Divide integers 8/7 = 1
Multiply 7 x 1 = 7; Subtract 8 – 7 = 1
Write down 15 and divide integers 15/7 = 2.
Multiply 7 x 2 = 14. Subtract 15 – 14 = 1.
Write down 12 and divide integers 12/7 = 1.
Multiply 7 x 1 = 7. Subtract 12 – 7= 5.
Write down 53 and divide integers 53/7 = 7.
Multiply 7 x 7 = 49. Subtract 53 – 49= 4.
The remainder is 4.

Practice: Copy and Solve Divide.

Question 12.
645 ÷ 8 = _____ R _____

645 ÷ 8 = 80 R 5

Explanation:
Divide integers 64/8 = 8
Multiply 8 x 8 = 64; Subtract 64 – 64 = 0
Write down 05; 5 < 8; There are not enough tens
The remainder is 5.

Question 13.
942 ÷ 6 = _____

157

Explanation:
Divide integers 9/6 = 1
Multiply 6 x 1 = 6; Subtract 9 – 6 = 3
Write down 34 and divide integers 34/6 = 5.
Multiply 6 x 5 = 30. Subtract 34 – 30 = 4.
Write down 42 and divide integers 42/6 = 7.
Multiply 6 x 7 = 42. Subtract 42 – 42 = 0.
The remainder is 0.

Question 14.
723 ÷ 7 = _____ R _____

103 R 2

Explanation:
Divide integers 7/7 = 1
Multiply 7 x 1 = 7; Subtract 7 – 7 = 0
Write down 23 and divide integers 23/7 = 3.
Multiply 7 x 3 = 21. Subtract 23 – 21 = 2.
The remainder is 2.

Question 15.
3,478 ÷ 9 = _____ R _____

386 R 4

Explanation:
Divide integers 34/9 = 3
Multiply 9 x 3 = 27; Subtract 34 – 27 = 7
Write down 77 and divide integers 77/9 = 8.
Multiply 9 x 8 = 72. Subtract 77 – 72 = 5.
Write down 58 and divide integers 58/9 = 6.
Multiply 9 x 6 = 54. Subtract 58 – 54= 4.
The remainder is 4.

Question 16.
3,214 ÷ 5 = _____ R _____

642 R 4

Explanation:
Divide integers 32/5 = 6
Multiply 5 x 6 = 30; Subtract 32 – 30 = 2
Write down 21 and divide integers 21/5 = 4.
Multiply 5 x 4 = 20. Subtract 21 – 20 = 1.
Write down 14 and divide integers 14/5 = 2.
Multiply 5 x 2 = 10. Subtract 14 – 10 = 4.
The remainder is 4.

Question 17.
492 ÷ 4 = _____

123

Explanation:
Divide integers 4/4 = 1
Multiply 4 x 1 = 4; Subtract 4 – 4 = 0
Write down 9 and divide integers 9/4 = 2.
Multiply 4 x 2 = 8. Subtract 9 – 8 = 1.
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12. Subtract 12 – 12 = 0.
The remainder is 0.

Question 18.
2,403 ÷ 9 = _____

267

Explanation:
Divide integers 24/9 = 2
Multiply 9 x 2 = 18; Subtract 24 – 18 = 6
Write down 60 and divide integers 60/9 = 6.
Multiply 9 x 6 = 54. Subtract 60 – 54 = 6.
Write down 63 and divide integers 63/9 = 7.
Multiply 9 x 7 = 63. Subtract 63 – 63 = 0.
The remainder is 0.

Question 19.
2,205 ÷ 6 = _____ R _____

367 R 3

Explanation:
Divide integers 22/6 = 3
Multiply 6 x 3 = 18; Subtract 22 – 18 = 4
Write down 40 and divide integers 40/6 = 6.
Multiply 6 x 6 = 36; Subtract 40 – 36 = 4
Write down 45 and divide integers 45/6 = 7.
Multiply 6 x 7 = 42; Subtract 45 – 42 = 3
The remainder is 3.

Question 20.
2,426 ÷ 3 = _____ R _____

808 R 2

Explanation:
Divide integers 24/3 = 8
Multiply 3 x 8 = 24; Subtract 24 – 24 = 0
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
The remainder is 2.

Question 21.
1,592 ÷ 8 = _____ R _____

199

Explanation:
Divide integers 15/8 = 1
Multiply 8 x 1 = 8; Subtract 15 – 8 = 7
Write down 79 and divide integers 79/8 = 9.
Multiply 8 x 9 = 72; Subtract 79 – 72 = 7
Write down 72 and divide integers 72/8 = 9.
Multiply 8 x 9 = 72; Subtract 72 – 72 = 0
The remainder is 0.

Question 22.
926 ÷ 4 = _____ R _____

231 R 2

Explanation:
Divide integers 9/4 = 2
Multiply 4 x 2 = 8; Subtract 9 – 8 = 1
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12; Subtract 12 – 12 = 0
Write down 6 and divide integers 6/4 = 1.
Multiply 4 x 1 = 4; Subtract 6 – 4 = 2
The remainder is 2.

Question 23.
6,033 ÷ 5 = _____ R _____

1,206 R 3

Explanation:
Divide integers 6/5 = 1
Multiply 5 x 1 = 5; Subtract 6 – 5 = 1
Write down 10 and divide integers 10/5 = 2.
Multiply 5 x 2 = 10; Subtract 10 – 10 = 0
Write down 33 and divide integers 33/5 = 6.
Multiply 5 x 6 = 30; Subtract 33 – 30 = 3
The remainder is 3.

### Place the First Digit – UNLOCK the Problem – Page No. 64

Question 24.
Rosa has a garden divided into sections. She has 125 daisy plants. If she plants an equal number of the daisy plants in each section of daisies, will she have any left over? If so, how many daisy plants will be left over?

a. What information will you use to solve the problem?
Type below:
__________

We can use the fact that she has 125 daisy plants and she plants an equal number of the daisy plants in each of 3 sections.

Question 24.
b. How will you use division to find the number of daisy plants left over?
Type below:
__________

We have to do 125/3
Divide integers 12/3 = 4
Multiply 3 x 4 = 12; Subtract 12 – 12 = 0
Write down 5 and divide integers 5/3 = 1.
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
The remainder is 2.
41 daisy plants in each section.
2 daisy plants left over

Question 24.
c. Show the steps you use to solve the problem. Estimate: 120 ÷ 3 = _____
Type below:
__________

Divide integers 12/3 = 4
Multiply 3 x 4 = 12; Subtract 12 – 12 = 0
The remainder is 0.

Question 24.
d. Complete the sentences:
Rosa has _____ daisy plants.
She puts an equal number in each of _____ sections.
Each section has _____ plants.
Rosa has _____ daisy plants left over.
Type below:
__________

Rose has 125 daisy planes.
She puts an equal number in each of 3 sections.
Each section has 41 plants.
Rosa has 2 daisy plants left over.

Question 25.
One case can hold 3 boxes. Each box can hold 3 binders. How many cases are needed to hold 126 binders?
_____ cases

14 cases

Explanation:
One case can hold 3 boxes. Each box can hold 3 binders. 3 x 3 = 9.
For 12 binders,
126/ (3 x 3) = 126/9 = 14

Question 26.
Test Prep In which place is the first digit in the quotient 1,497 ÷ 5?
Options:
a. thousands
b. hundreds
c. tens
d. ones

b. hundreds

Explanation:
1,497 ÷ 5 = 499. the first digit 4 is in hundreds place.

### Divide by 1-Digit Divisors – Share and Show – Page No. 67

Question 1.
8)$$\overline { 624 }$$
Check
_____

78

Explanation:
Divide integers 62/8 = 7
Multiply 8 x 7 = 56; Subtract 62 – 56 = 6
Write down 64 and divide integers 64/8 = 8.
Multiply 8 x 8 = 64. Subtract 64 – 64 = 0.
The remainder is 0.
Check:
78 x 8 = 624;
624 = 624

Question 2.
4)$$\overline { 3,220 }$$
Check
_____

805

Explanation:
Divide integers 32/4 = 8
Multiply 4 x 8 = 32; Subtract 32 – 32 = 0
Write down 20 and divide integers 20/4 = 5.
Multiply 4 x 5 = 20. Subtract 20 – 20 = 0.
The remainder is 0.
Check:
805 x 4 = 3,220;
3,220 = 3,220.

Question 3.
4)$$\overline { 1,027 }$$
Check
_____ R _____

256 R 3

Explanation:
Divide integers 10/4 = 2
Multiply 4 x 2 = 8; Subtract 10 – 8 = 2
Write down 22 and divide integers 22/4 = 5.
Multiply 4 x 5 = 20. Subtract 22 – 20= 2.
Write down 27 and divide integers 27/4 = 6.
Multiply 4 x 6 = 24. Subtract 27 – 24 = 3.
The remainder is 3.
So, 256 R 3.
Check:
256 x 4 = 1,024;
1,024 + 3 = 1,027.
1,027 = 1,027

Divide.

Question 4.
6)$$\overline { 938 }$$
_____ R _____

156 R 2

Explanation:
Divide integers 9/6 = 1
Multiply 6 x 1 = 6; Subtract 9 – 6 = 3
Write down 33 and divide integers 33/6 = 5.
Multiply 6 x 5 = 30. Subtract 33 – 30 = 3.
Write down 38 and divide integers 38/6 = 6.
Multiply 6 x 6 = 36. Subtract 38 – 36 = 2.
The remainder is 2.
So, 156 R 2.

Question 5.
4)$$\overline { 762 }$$
_____ R _____

190 R 2

Explanation:
Divide integers 7/4 = 1
Multiply 4 x 1 = 4; Subtract 7 – 4 = 3
Write down 36 and divide integers 36/4 = 9.
Multiply 4 x 9 = 36. Subtract 36 – 36 = 0.
Write down 2. 2 < 4; There are not enough tens
The remainder is 2.
So, 190 R 2.

Question 6.
3)$$\overline { 5,654 }$$
_____ R _____

1884 R 2

Explanation:
Divide integers 5/3 = 1
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
Write down 25 and divide integers 25/3 = 8.
Multiply 3 x 8 = 24. Subtract 25 – 24 = 1.
Write down 14 and divide integers 14/3 = 4.
Multiply 3 x 4 = 12. Subtract 14 – 12 = 2.
The remainder is 2.
So, 1884 R 2.

Question 7.
8)$$\overline { 475 }$$
_____ R _____

59 R 3

Explanation:
Divide integers 47/8 = 5
Multiply 8 x 5 = 40; Subtract 47 – 40 = 7
Write down 75 and divide integers 75/8 = 9.
Multiply 9 x 8 = 72. Subtract 75 – 72 = 3.
The remainder is 3.
So, 59 R 3.

Practice: Copy and Solve Divide.

Question 8.
4)$$\overline { 671 }$$
_____ R _____

167 R 3

Explanation:
Divide integers 6/4 = 1
Multiply 4 x 1 = 4; Subtract 6 – 4 = 2
Write down 27 and divide integers 27/4 = 6.
Multiply 4 x 6 = 24. Subtract 27 – 24 = 3.
Write down 31 and divide integers 31/4 = 7.
Multiply 4 x 7 = 28. Subtract 31 – 28 = 3.
The remainder is 3.
So, 167 R 3.

Question 9.
9)$$\overline { 2,023 }$$
_____ R _____

224 R 7

Explanation:
Divide integers 20/9 = 2
Multiply 9 x 2 = 18; Subtract 20 – 18 = 2
Write down 22 and divide integers 22/9 = 2.
Multiply 9 x 2 = 18. Subtract 22 – 18 = 4.
Write down 43 and divide integers 43/9 = 4.
Multiply 9 x 4 = 36. Subtract 43 – 36 = 7.
The remainder is 7.
So, 224 R 7.

Question 10.
3)$$\overline { 4,685 }$$
_____ R _____

1,561 R 2

Explanation:
Divide integers 4/3 = 1
Multiply 3 x 1 = 3; Subtract 4 – 3 = 1
Write down 16 and divide integers 16/3 = 5.
Multiply 3 x 5 = 15. Subtract 16 – 15 = 1.
Write down 18 and divide integers 18/3 = 6.
Multiply 3 x 6 = 18. Subtract 18 – 18 = 0.
Write down 5 and divide integers 5/3 = 1.
Multiply 3 x 1 = 3. Subtract 5 – 3 = 2.
The remainder is 2.
So, 1,561 R 2.

Question 11.
8)$$\overline { 948 }$$
_____ R _____

118 R 4

Explanation:
Divide integers 9/8 = 1
Multiply 8 x 1 = 8; Subtract 9 – 8 = 1
Write down 14 and divide integers 14/8 = 1.
Multiply 8 x 1 = 8. Subtract 14 – 8 = 6.
Write down 68 and divide integers 68/8 = 8.
Multiply 8 x 8 = 64. Subtract 68 – 64 = 4.
The remainder is 4.
So, 118 R 4.

Question 12.
1,326 ÷ 4 = _____ R _____

331 R 2

Explanation:
Divide integers 13/4 = 3
Multiply 4 x 3 = 12; Subtract 13 – 12 = 1
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12. Subtract 12 – 12 = 0.
Write down 6 and divide integers 6/4 = 1.
Multiply 4 x 1 = 4. Subtract 6 – 4 = 2.
The remainder is 2.
So, 331 R 2.

Question 13.
5,868 ÷ 6 = _____

978

Explanation:
Divide integers 58/6 = 9
Multiply 6 x 9 = 54; Subtract 58 – 54 = 4
Write down 46 and divide integers 46/6 = 7.
Multiply 6 x 7 = 42. Subtract 46 – 42 = 4.
Write down 48 and divide integers 48/6 = 8.
Multiply 6 x 8 = 48. Subtract 48 – 48 = 0.
The remainder is 0.
So, 978.

Question 14.
566 ÷ 3 = _____ R _____

188 R 2

Explanation:
Divide integers 5/3 = 1
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
The remainder is 2.
So, 188 R 2.

Question 15.
3,283 ÷ 9 = _____ R _____

364 R 7

Explanation:
Divide integers 32/9 = 3
Multiply 9 x 3 = 27; Subtract 32 – 27 = 5
Write down 58 and divide integers 58/9 = 6.
Multiply 9 x 6 = 54. Subtract 58 – 54 = 4.
Write down 43 and divide integers 43/9 = 4.
Multiply 9 x 4 = 36. Subtract 43 – 36 = 7.
The remainder is 7.
So, 364 R 7.

Algebra Find the value of n in each equation. Write what n represents in the related division problem.

Question 16.
n = 4 × 58
Value of n = _______
Represents: _______

Value of n = 232
Represents: dividend

Explanation:
n = 4 × 58;
232 = 4 x 58;
n is the dividend

Question 17.
589 = 7 × 84 + n
Value of n = _______
Represents: _______

Value of n = 1
Represents: remainder

Explanation:
589 = 7 × 84 + n
589 = 588 + n;
589 – 588 = n;
1 = n
n is the remainder

Question 18.
n = 5 × 67 + 3
Value of n = _______
Represents: _______

Value of n = 338
Represents: dividend

Explanation:
n = 5 × 67 + 3
n = 335 + 3
n = 338
n is the dividend

### Divide by 1-Digit Divisors – Problem Solving – Page No. 68

Use the table to solve 19–20.

Question 19.
If the Welcome gold nugget were turned into 3 equal-sized gold bricks, how many troy ounces would each brick weigh?
_____ troy ounces

739 troy ounces

Explanation:
Welcome gold nugget = 2,217 troy ounces.
If it turned into 3 equal-sized gold bricks, 2,217/3 = 739.
739 troy ounces

Question 20.
Pose a Problem Look back at Problem 19. Write a similar problem by changing the nugget and the number of bricks. Then solve the problem.
Type below:
__________

571 troy ounces

Explanation:
If Welcome Stranger nugget were turned into 4 equal-sized gold bricks, how many troy ounces would each brick weigh?
Welcome Stranger nugget = 2,284.
If it turned into 4 equal-sized gold bricks, 2,217/3 = 571.
571 troy ounces

Question 21.
There are 246 students going on a field trip to pan for gold. If they are going in vans that hold 9 students each, how many vans are needed? How many students will ride in the van that isn’t full?
The number of vans: _________
_________ students in the van that isn’t full

The number of vans: 27
3 students will ride in the van that isn’t full

Explanation:
There are 246 students going on a field trip to pan for gold. If they are going in vans that hold 9 students each, 246/9 = 27 R 3
The number of vans: 27
3 students will ride in the van that isn’t full
Question 22.
One crate can hold 8 cases of trading cards. How many crates are needed to hold 128 cases of trading cards?
_____ crates

16 crates

Explanation:
One crate can hold 8 cases of trading cards. To hold 128 cases of trading cards, 128/8 = 16 crates needed.

Question 23.
Test Prep At a bake sale, a fifth-grade class sold 324 cupcakes in packages of 6. How many packages of cupcakes did the class sell?
Options:
a. 1,944
b. 108
c. 64
d. 54

d. 54

Explanation:
At a bake sale, a fifth-grade class sold 324 cupcakes in packages of 6. 324/6 = 54

### Division with 2-Digit Divisors – Share and Show – Page No. 71

Use the quick picture to divide.

Question 1.

143 ÷ 13 = _____

143 ÷ 13 = 11

Explanation:
143 = 100 + 40 + 3
Model the first partial quotient by making a rectangle with the hundred and 3 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10) = 100 + 30 = 130.
The rectangle shows 10 groups of 13.
Model the second partial quotient by making a line with the ten and 3 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1) = 10 + 3 = 13
130 + 13 = 143;
So, the answer is 10 + 1 = 11

Divide. Use base-ten blocks.

Question 2.
168 ÷ 12 = _____

168 ÷ 12 = 14

Explanation:
168 ÷ 12
Model the first partial quotient by making a rectangle with the hundred and 2 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10) = 100 + 20 = 120.
The rectangle shows 10 groups of 12.
Model the second partial quotient by making a line with the ten and 2 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1) = 10 + 2 = 12.
Repeat the above step more three times to get
120 + 12 + 12 + 12 + 12 = 168;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 3.
154 ÷ 14 = _____

154 ÷ 14 = 11

Explanation:
154 ÷ 14
Model the first partial quotient by making a rectangle with the hundred and 4 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10) = 100 + 40 = 140.
The rectangle shows 10 groups of 14.
Model the second partial quotient by making a line with the ten and 4 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1) = 10 + 4 = 14.
Repeat the above step more three times to get
140 + 14 = 154;
So, the answer is 10 + 1 = 11

Question 4.
187 ÷ 11 = _____

187 ÷ 11 = 17

Explanation:
187 ÷ 11 =
Model the first partial quotient by making a rectangle with the hundred and 1 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10) = 100 + 10 = 110.
The rectangle shows 10 groups of 11.
Model the second partial quotient by making a line with the ten and 1 ones. In the Record section, cross out the ten and ones you use.
10 + (1) = 10 + 1 = 11.
Repeat the above step more six times to get
110 + 11 + 11 + 11 + 11 + 11 + 11 + 11 = 187;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 17

Divide. Draw a quick picture.

Question 5.
165 ÷ 11 = _____

165 ÷ 11 = 15

Explanation:
165 ÷ 11
Model the first partial quotient by making a rectangle with the hundred and 1 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10) = 100 + 10 = 110.
The rectangle shows 10 groups of 11.
Model the second partial quotient by making a line with the ten and 1 ones. In the Record section, cross out the ten and ones you use.
10 + (1) = 10 + 1 = 11.
Repeat the above step more four times to get
110 + 11 + 11 + 11 + 11 + 11 = 165;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 = 15

Question 6.
216 ÷ 18 = _____

216 ÷ 18 = 12

Explanation:
216 ÷ 18
Model the first partial quotient by making a rectangle with the hundred and 8 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10 + 10 + 10 + 10 + 10) = 100 + 80 = 180.
The rectangle shows 10 groups of 18.
Model the second partial quotient by making a line with the ten and 8 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = 10 + 8 = 18.
Repeat the above step to get
180 + 18 + 18 = 216;
So, the answer is 10 + 1 + 1 = 12

Question 7.
196 ÷ 14 = _____

196 ÷ 14 = 14

Explanation:
196 ÷ 14
Model the first partial quotient by making a rectangle with the hundred and 4 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10) = 100 + 40 = 140.
The rectangle shows 10 groups of 14.
Model the second partial quotient by making a line with the ten and 4 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1) = 10 + 4 = 14.
Repeat the above step more three times to get
140 + 14 + 14 + 14 + 14 = 196;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 8.
195 ÷ 15 = _____

195 ÷ 15 = 13

Explanation:
195 ÷ 15
Model the first partial quotient by making a rectangle with the hundred and 5 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10 + 10) = 100 + 50 = 150.
The rectangle shows 10 groups of 15.
Model the second partial quotient by making a line with the ten and 5 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1 + 1) = 10 + 5 = 15.
Repeat the above step more three times to get
150 + 15 + 15 + 15 = 195;
So, the answer is 10 + 1 + 1 + 1 = 13

Question 9.
182 ÷ 13 = _____

182 ÷ 13 = 14

Explanation:
182 ÷ 13
Model the first partial quotient by making a rectangle with the hundred and 3 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 ) = 100 + 30 = 130.
The rectangle shows 10 groups of 13.
Model the second partial quotient by making a line with the ten and 3 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1) = 10 + 3 = 13.
Repeat the above step more four times to get
130 + 13 + 13 + 13 + 13 = 182;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 10.
228 ÷ 12 = _____

228 ÷ 12 = 19

Explanation:
228 ÷ 12
Model the first partial quotient by making a rectangle with the hundred and 2 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10) = 100 + 20 = 120.
The rectangle shows 10 groups of 12.
Model the second partial quotient by making a line with the ten and 2 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1) = 10 + 2 = 12.
Repeat the above step more eight times to get
120 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 228;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 19

### Division with 2-Digit Divisors – Connect to Social Studies – Page No. 72

Pony Express

The Pony Express used men riding horses to deliver mail between St. Joseph, Missouri, and Sacramento, California, from April, 1860 to October, 1861. The trail between the cities was approximately 2,000 miles long. The first trip from St. Joseph to Sacramento took 9 days 23 hours. The first trip from Sacramento to St. Joseph took 11 days 12 hours.

Solve.

Question 11.
Suppose two Pony Express riders rode a total of 165 miles. If they replaced each horse with a fresh horse every 11 miles, how many horses would they have used?
_____ horses

16 horses

Explanation:
Suppose two Pony Express riders rode a total of 165 miles. If they replaced each horse with a fresh horse every 11 miles. Then, 16 horses used.

Question 12.
Suppose a Pony Express rider was paid $192 for 12 weeks of work. If he was paid the same amount each week, how much was he paid for each week of work?$ _____

$16 Explanation: Suppose a Pony Express rider was paid$192 for 12 weeks of work.
For each week. $192/12 =$16.

Question 13.
Suppose three riders rode a total of 240 miles. If they used a total of 16 horses, and rode each horse the same number of miles, how many miles did they ride before replacing each horse?
_____ miles

15 miles

Explanation:
Assuming each horse was only ridden once then a total of 16 horses were ridden for a total of 240 miles
240 miles/16 horses = 15 miles/horse
if each horse was ridden more than once before being replaced the distance between replacements could be reduced.
The fact that there were 3 riders is irrelevant.

Question 14.
Suppose it took 19 riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento. If they all rode the same number of hours, how many hours did each rider ride?
_____ hours

15 hours

Explanation:
Suppose it took 19 riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento.
(11 x 24 + 21)/19 = (264 + 21)/19 = 285/19 = 15 hours.

### Partial Quotients – Share and Show – Page No. 75

Divide. Use partial quotients.

Question 1.
18)$$\overline { 648 }$$
_____

36

Explanation:
Multiply 18 x 10 = 180; Subtract: 648 – 180 = 468.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 468 – 180= 288.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 288- 180= 108.
partial quotient = 10
Multiply 18 x 6 = 108; Subtract: 108 – 108 = 0.
partial quotient = 6;
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 6 = 36 R 0

Question 2.
62)$$\overline { 3,186 }$$
_____ R _____

Explanation:
Multiply 62 x 10 = 620; Subtract: 3,186 – 620 = 2,566.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 2,566 – 620 = 1,946.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 1,946 – 620 = 1,326.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 1,326 – 620 = 706.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 706 – 620 = 86.
partial quotient = 10
Multiply 62 x 1 = 62; Subtract: 86 – 62 = 24.
partial quotient = 1
The remainder is 24;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 1 = 51 R 24

Question 3.
858 ÷ 57
_____ R _____

Explanation:
Multiply 57 x 10 = 570; Subtract: 858 – 570 = 288.
partial quotient = 10
Multiply 57 x 5 = 285; Subtract: 288 – 285 = 3.
partial quotient = 5
The remainder is 3;
Add partial quotient to find the wholenumber quotient;
10 + 5 = 15 R 3

Divide. Use partial quotients.

Question 4.
73)$$\overline { 584 }$$
_____

8

Explanation:
Multiply 73 x 8 = 584; Subtract: 584 – 584 = 0.
partial quotient = 8
The remainder is 0;

Question 5.
51)$$\overline { 1,831 }$$
_____ R _____

35 R 46

Explanation:
Multiply 51 x 10 = 510; Subtract: 1,831 – 510 = 1,321.
partial quotient = 10
Multiply 51 x 10 = 510; Subtract: 1,321 – 510 = 811.
partial quotient = 10
Multiply 51 x 10 = 510; Subtract: 811 – 510 = 301.
partial quotient = 10
Multiply 51 x 5 = 255; Subtract: 301 – 255 = 46.
partial quotient = 5
The remainder is 46;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 5 = 35 R 46

Question 6.
82)$$\overline { 2,964 }$$
_____ R _____

36 R 12

Explanation:
Multiply 82 x 10 = 820; Subtract: 2,964 – 820 = 2,144.
partial quotient = 10
Multiply 82 x 10 = 820; Subtract: 2,144 – 820 = 1,324.
partial quotient = 10
Multiply 82 x 10 = 820; Subtract: 1,324 – 820 = 504.
partial quotient = 10
Multiply 82 x 6 = 492; Subtract: 504 – 492= 12.
partial quotient = 6
The remainder is 12;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 6 = 36 R 12

Question 7.
892 ÷ 26
_____ R _____

34 R 8

Explanation:
Multiply 26 x 10 = 260; Subtract: 892 – 260 = 632.
partial quotient = 10
Multiply 26 x 10 = 260; Subtract: 632 – 260 = 372.
partial quotient = 10
Multiply 26 x 10 = 260; Subtract: 372 – 260 = 112.
partial quotient = 10
Multiply 26 x 4 = 104; Subtract: 112 – 104 = 8.
partial quotient = 4
The remainder is 8;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 4 = 34 R 8

Question 8.
1,056 ÷ 48
_____

22

Explanation:
Multiply 48 x 10 = 480; Subtract: 1,056 – 480 = 576.
partial quotient = 10
Multiply 48 x 10 = 480; Subtract: 576 – 480 = 96.
partial quotient = 10
Multiply 48 x 2 = 96; Subtract: 96 – 96 = 0.
partial quotient = 2
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 2 = 22

Question 9.
2,950 ÷ 67
_____ R _____

44 R 2

Explanation:
Multiply 67 x 10 = 670; Subtract: 2,950 – 670 = 2,280.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 2,280 – 670 = 1,610.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 1,610 – 670 = 940.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 940 – 670 = 270.
partial quotient = 10
Multiply 67 x 4= 268; Subtract: 270 – 268 = 2.
partial quotient = 4
The remainder is 2;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 4 = 44 R 2

Practice: Copy and Solve Divide. Use partial quotients.

Question 10.
653 ÷ 42
_____ R _____

15 R 23

Explanation:
Multiply 42 x 10 = 420; Subtract: 653 – 420 = 233.
partial quotient = 10
Multiply 42 x 5 = 210; Subtract: 233 – 210 = 23.
partial quotient = 5
The remainder is 23;
Add partial quotient to find the wholenumber quotient;
10 + 5 = 15 R 23

Question 11.
946 ÷ 78
_____ R _____

12 R 10

Explanation:
Multiply 78 x 10 = 780; Subtract: 946 – 780 = 166.
partial quotient = 10
Multiply 78 x 2 = 156; Subtract: 166 – 156 = 10.
partial quotient = 2
The remainder is 10;
Add partial quotient to find the wholenumber quotient;
10 + 2 = 12 R 10

Question 12.
412 ÷ 18
_____ R _____

22 R 16

Explanation:
Multiply 18 x 10 = 180; Subtract: 412 – 180 = 232.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 232 – 180 = 52.
partial quotient = 10
Multiply 18 x 2 = 36; Subtract: 52 – 36 = 16.
partial quotient = 2
The remainder is 16;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 2 = 22 R 16

Question 13.
871 ÷ 87
_____ R _____

10 R 1

Explanation:
Multiply 87 x 10 = 870; Subtract: 871 – 870 = 1.
partial quotient = 10
The remainder is 1;
10 R 1

Question 14.
1,544 ÷ 34
_____ R _____

45 R 14

Explanation:
Multiply 34 x 10 = 340; Subtract: 1,544 – 340 = 1,204.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 1,204 – 340 = 864.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 864 – 340 = 524.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 524 – 340 = 184.
partial quotient = 10
Multiply 34 x 5 = 170; Subtract: 184 – 170 = 14.
partial quotient = 5
The remainder is 14;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 5 = 45 R 14

Question 15.
2,548 ÷ 52
_____ R _____

47 R 14

Explanation:
Multiply 52 x 10 = 520; Subtract: 2,548 – 520 = 2028.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 2028- 520 = 1508.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 1508- 520 = 988.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 988 – 520 = 468.
partial quotient = 10
Multiply 52 x 9 = 468; Subtract: 468 – 468= 0.
partial quotient = 9
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 9 = 49 R 0

Question 16.
2,740 ÷ 83
_____ R _____

33 R 1

Explanation:
Multiply 83 x 10 = 830; Subtract: 2,740 – 830= 1910.
partial quotient = 10
Multiply 83 x 10 = 830; Subtract: 1910 – 830= 1080.
partial quotient = 10
Multiply 83 x 10 = 830; Subtract: 1080 – 830= 250.
partial quotient = 10
Multiply 83 x 3 = 249; Subtract: 250 – 249 = 1.
partial quotient = 3
The remainder is 1;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 3 = 33 R 1

Question 17.
4,135 ÷ 66
_____ R _____

62 R 43

Explanation:
Multiply 66 x 10 = 660; Subtract: 4,135 – 660 = 3475.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 3475 – 660 = 2815.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 2815 – 660 = 2155.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 2155 – 660 = 1495.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 1495 – 660 = 835.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 835 – 660 = 175.
partial quotient = 10
Multiply 66 x 2 = 132; Subtract: 175 – 132 = 43.
partial quotient = 2
The remainder is 43;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 10 + 10 + 2 = 62 R 43

### Partial Quotients – Problem Solving – Page No. 76

Use the table to solve 18–20 and 22.

Question 18.
How many years would it take for a person in the United States to eat 855 pounds of apples?
_____ years

45 years

Explanation:
Each year a person eats 19 pounds of apples. So, to eat 855 pounds of apples, it takes 855/19 = 45 years.

Question 19.
How many years would it take for a person in the United States to eat 1,120 pounds of turkey?
_____ years

80 years

Explanation:
Each year a person eats 14 pounds of turkey. So, to eat 1,120 pounds of turkey, it takes 1,120/14 = 80 years.

Question 20.
If 6 people in the United States each eat the average amount of popcorn for 5 years, how many quarts of popcorn will they eat?
_____ quarts

2,040 quarts

Explanation:
1 person eats 68 quarts of popcorn each year. 6 people = 6 x 68 quarts of popcorn = 408 quarts of popcorn for each year.
For 5 years, they will eat popcorn = 5 x 408 = 2,040 quarts

Question 21.
In a study, 9 people ate a total of 1,566 pounds of potatoes in 2 years. If each person ate the same amount each year, how many pounds of potatoes did each person eat in 1 year?
_____ pounds

87 pounds

Explanation:
9 people ate a total of 1,566 pounds of potatoes in 2 years. If each person ate the same amount each year, 1,566/2 = 783.
To calculate how many pounds of potatoes did each person eat in 1 year, 783/9 = 87 pounds.

Question 22.
Sense or Nonsense? In the United States, a person eats more than 40,000 pounds of bread in a lifetime if he or she lives to be 80 years old. Does this statement make sense, or is it nonsense? Explain.
__________

nonsense; 40,000 pounds / 80 years = 4,000 pounds / 8 years = 2,000 pounds (1 ton) / 4 years = 1,000 pounds / 2 years = 1,000 pounds / 2 years = 500 pounds per year = almost 1 and 1/2 pounds of bread every day of your life.

Question 23.
Test Prep The school auditorium has 448 seats arranged in 32 equal rows. How many seats are in each row?
Options:
a. 14,336
b. 480
c. 416
d. 14

d. 14

Explanation:
The school auditorium has 448 seats arranged in 32 equal rows.
Each row = 448/32 = 14

### Mid-Chapter Checkpoint – Page No. 77

Concepts and Skills

Question 1.
Explain how estimating the quotient helps you place the first digit in the quotient of a division problem.
Type below:
__________

Let’s do 5980 divided by 347
Estimate: 6000/300 = 20
So, I now know my first digit will go into the 10’s place
or 57890 divided by 34
that is 60,000 divided by 30 = 2000
my first digit goes into the thousands place.

Question 2.
Explain how to use multiplication to check the answer to a division problem.
Type below:
__________

Take 739/9 = 82 R 1.
Check: 9 x 82 + 1 = 739.
divisor x quotient + remainder = dividend.

Divide.

Question 3.
633 ÷ 3 = _____

211

Explanation:
Divide integers 6/3 = 2
Multiply 3 x 2 = 6; Subtract 6 – 6 = 0
Write down 3 and divide integers 3/3 = 1.
Multiply 3 x 1 = 3. Subtract 3 – 3 = 0.
Write down 3 and divide integers 3/3 = 1.
Multiply 3 x 1 = 3. Subtract 3 – 3 = 0.
The remainder is 0.

Question 4.
487 ÷ 8 = _____ R _____

60 R 7

Explanation:
Divide integers 48/8 = 6
Multiply 8 x 6 = 48; Subtract 48 – 48 = 0
Write down 7;7 < 8.
The remainder is 7.
So, 60 R 7.

Question 5.
1,641 ÷ 4 = _____ R _____

410 R 1

Explanation:
Divide integers 16/4 = 4
Multiply 4 x 4 = 16; Subtract 16 – 16 = 0
Write down 4 and divide integers 4/4 = 1.
Multiply 4 x 1 = 4; Subtract 4 – 4 = 0
Write down 1; 1<4
The remainder is 1.
So, 410 R 1.

Question 6.
2,765 ÷ 9 = _____ R _____

307 R 2

Explanation:
Divide integers 27/9 = 3
Multiply 9 x 3 = 27; Subtract 27 – 27 = 0
Write down 65 and divide integers 65/9 = 7.
Multiply 9 x 7 = 63. Subtract 65 – 63 = 2.
The remainder is 2.
So, 307 R 2.

Divide. Use partial quotients.

Question 7.
156 ÷ 13 = _____

12

Explanation:
Multiply 13 x 10 = 130; Subtract: 156 – 130 = 26.
partial quotient = 10
Multiply 13 x 2 = 26; Subtract: 26 – 26 = 0.
partial quotient = 2
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 +2 = 12 R 0

Question 8.
318 ÷ 53 = _____

6

Explanation:
Multiply 53 x 6 = 318; Subtract: 318 – 318= 0.
partial quotient = 6
The remainder is 0;
quotient = 6

Question 9.
1,562 ÷ 34 =
_____ r _____

45 R 32

Explanation:
Multiply 34 x 10 = 340; Subtract: 1,562 – 340 = 1,222.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 1,222 – 340 = 882.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 882 – 340 = 542.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 542 – 340 = 202.
partial quotient = 10
Multiply 34 x 5 = 170; Subtract: 202 – 170 = 32.
partial quotient = 5
The remainder is 32;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 5 = 45 R 32

Question 10.
4,024 ÷ 68 =
_____ r _____

59 R 12

Explanation:
Multiply 68 x 10 = 680; Subtract: 4,024 – 680 = 3,344.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 3,344 – 680= 2664.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 2664 – 680 = 1984.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 1984 – 680= 1304.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 1304 – 680 = 624.
partial quotient = 10
Multiply 68 x 9 = 612; Subtract: 624 – 612 = 12.
partial quotient = 9
The remainder is 12;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 10 + 9 = 59 R 12

### Mid-Chapter Checkpoint – Page No. 78

Question 11.
Emma is planning a party for 128 guests. If 8 guests can be seated at each table, how many tables will be needed for seating at the party?
_____ tables

16 tables

Explanation:
Emma is planning a party for 128 guests. If 8 guests can be seated at each table 128/8 = 16.

Question 12.
Tickets for the basketball game cost $14 each. If the sale of the tickets brought in$2,212, how many tickets were sold?
_____ tickets

158 tickets

Explanation:
Tickets for the basketball game cost $14 each. If the sale of the tickets brought in$2,212, $2,212/$14 = 158

Question 13.
Margo used 864 beads to make necklaces for the art club. She made 24 necklaces with the beads. If each necklace has the same number of beads, how many beads did Margo use for each necklace?
_____

Explanation:
Margo used 864 beads to make necklaces for the art club. She made 24 necklaces with the beads. If each necklace has the same number of beads, 864/24 = 36 beads

Question 14.
Angie needs to buy 156 candles for a party. Each package has 8 candles. How many packages should Angie buy?
_____ packages

20 packages

Explanation:
Angie needs to buy 156 candles for a party. Each package has 8 candles.
156/8 = 20

Question 15.
Max delivers 8,520 pieces of mail in one year. About how many pieces of mail does he deliver in 2 months? Explain your steps.
_____ pieces

1,420 pieces

Explanation:
Max delivers 8,520 pieces of mail in one year.
So, for 12 months, 8,520/12 = 710.
To deliver in 2 months, 710 x 2 = 1,420

### Share and Show – Page No. 81

Use compatible numbers to find two estimates.

Question 1.
22)$$\overline { 154 }$$
140 ÷ 20 = _____
160 ÷ 20 = _____
Estimate: _____ ; _____

140 ÷ 20 = 7
160 ÷ 20 = 8
Estimate: 7 ; 8

Explanation:
Two sets of compatible numbers to find two different estimates are
140 ÷ 20
14 ÷ 2 = 7
140 ÷ 20 = 7
160 ÷ 20
16 ÷ 2 = 8
160 ÷ 20 = 8

Question 2.
68)$$\overline { 503 }$$
Estimate: _____ ; _____

476 ÷ 68= 7
544 ÷ 68 = 8
Estimate: 7 ; 8

Explanation:
Multiples of 68:
68 136 204 272 340 408 476 544
Find multiples that are close to the dividend. Use either or both numbers to estimate the quotient.
476/68 = 7
544/68 = 8
The quotient is between 7 and 8.

Question 3.
81)$$\overline { 7,052 }$$
Estimate: _____ ; _____

6400 ÷ 80 = 80
7200 ÷ 80 = 90
Estimate: 80 ; 90

Explanation:
6400/80
64/8 = 8
640 / 80 = 8
6400/80 = 800
7200/80
72/8 = 9
720/80 =9
7200/80 = 90
Estimate: 80, 90

Question 4.
33)$$\overline { 291 }$$
Estimate: _____ ; _____

240 ÷ 30= 8
270 ÷ 30 = 9
Estimate: 8 ; 9

Explanation:
240/30
24/3 = 8
240/30 = 8
270/30
27/3 = 9
270/30 = 9
Estimate: 8, 9

Question 5.
58)$$\overline { 2,365 }$$
Estimate: _____ ;

2400 ÷ 60= 40
3000 ÷ 60 = 50
Estimate: 40 ; 50

Explanation:
2400/60
24/6 = 4
240/60 = 4
2400/60 = 40
3000/60
30/6 = 5
300/60 = 5
3000/60 = 50
Estimate: 40, 50

Question 6.
19)$$\overline { 5,312 }$$
Estimate: _____ ; _____

5300 ÷ 20= 7
5320 ÷ 20 = 8
Estimate: 265 ; 266

Explanation:
5300/20
5300/20 = 265
5320/20
5320/20 = 266

Use compatible numbers to find two estimates.

Question 7.
42)$$\overline { 396 }$$
Estimate: _____ ; _____

360 ÷ 40 = 9
400 ÷ 40 = 10
Estimate: 9 ; 10

Explanation:
360/40 = 9
400/40 = 10
Estimate: 9,10

Question 8.
59)$$\overline { 413 }$$
Estimate: _____ ; _____

420 ÷ 60= 7
480 ÷ 60 = 8
Estimate: 7 ; 8

Explanation:
420/60 = 7
480/60 = 8

Question 9.
28)$$\overline { 232 }$$
Estimate: _____ ; _____

240 ÷ 30 = 8
270÷ 30 = 9
Estimate: 8 ; 9

Explanation:
240/30 = 8
270/30 = 9
Estimate: 8 ; 9

Question 10.
22)$$\overline { 368 }$$
Estimate: _____ ; _____

320 ÷ 20= 16
340 ÷ 20 = 17
Estimate: 16 ; 17

Explanation:
320/20 = 16
340/20 = 17
Estimate: 16 ; 17

Question 11.
78)$$\overline { 375 }$$
Estimate: _____ ; _____

320 ÷ 80 = 4
400 ÷ 80 = 5
Estimate: 4 ; 5

Explanation:
320/80 = 4
400/80 = 5
Estimate: 16 ; 17

Question 12.
88)$$\overline { 6,080 }$$
Estimate: _____ ; _____

6210÷ 90= 69
6300 ÷ 90 = 70
Estimate: 69 ; 70

Explanation:
6210/90 = 69
6300/90 = 70

Question 13.
5,821 ÷ 71
Estimate: _____ ; _____

5180 ÷ 70 = 74
5250÷ 70 = 75
Estimate: 74 ; 75

Explanation:
5180/70 = 74
5250/70 = 75
Estimate: 74 ; 75

Question 14.
1,565 ÷ 67
Estimate: _____ ; _____

1610 ÷ 70 = 23
1680 ÷ 70 = 24
Estimate: 23 ; 24

Explanation:
1610/70 = 23
1680/70 = 24
Estimate: 23 ; 24

Question 15.
7,973 ÷ 91
Estimate: _____ ; _____

476 ÷ 90 = 87
544 ÷ 90 = 88
Estimate: 87 ; 88

Explanation:
6960/90 = 87
7920/90 = 88
Estimate: 87 ; 88

Use compatible numbers to estimate the quotient.

Question 16.
19)$$\overline { 228 }$$
Estimate: _____

240 ÷ 20 = 12
260 ÷ 20 = 13
Estimate: 12 ; 13

Explanation:
240/20 = 12
260/20 = 13
Estimate: 12 ; 13

Question 17.
25)$$\overline { 595 }$$
Estimate: $_____ Answer: 575 ÷ 25 = 23 600 ÷ 25 = 24 Estimate: 23 ; 24 Explanation: 575/25 = 23 600/25 = 24 Estimate: 23 ; 24 Question 18. 86)$$\overline { 7,130 }$$ Estimate: _____ Answer: 7380 ÷ 90 = 82 7470 ÷ 90 = 83 Estimate: 82 ; 83 Explanation: 7380/90 = 82 7470/90 = 83 Estimate: 82 ; 83 Question 19. 83)$$\overline { 462 }$$ Estimate: _____ Answer: 400 ÷ 80 = 5 480 ÷ 80 = 6 Estimate: 5 ; 6 Explanation: 400/80 = 5 480/80 = 6 Estimate: 5 ; 6 Question 20. 27)$$\overline { 9,144 }$$ Estimate: _____ Answer: 10,140 ÷ 30 = 338 10,170 ÷ 30 = 339 Estimate: 338 ; 339 Explanation: 10,140/30 = 338 10,170/30 = 339 Estimate: 338 ; 339 Question 21. 68)$$\overline { 710 }$$ Estimate: _____ Answer: 700 ÷ 70 = 10 770 ÷ 70 = 11 Estimate: 10 ; 11 Explanation: 700/70 = 10 770/70 = 11 Estimate: 10 ; 11 Question 22. 707 ÷ 36 Estimate: _____ Answer: 760 ÷ 40 = 19 800 ÷ 40 = 20 Estimate: 19 ; 20 Explanation: 760/40 = 19 800/40 = 20 Estimate: 19 ; 20 Question 23. 1,198 ÷ 41 Estimate: _____ Answer: 1160 ÷ 40 = 29 1200 ÷ 40 = 30 Estimate: 29 ; 30 Explanation: 1160/40 = 29 1200/40 = 30 Estimate: 29 ; 30 Question 24. 5,581 ÷ 72 Estimate: _____ Answer: 5390 ÷ 70 = 77 5460 ÷ 70 = 78 Estimate: 77 ; 78 Explanation: 5390/70 = 77 5460/70 = 78 Estimate: 77 ; 78 ### Problem Solving – Page No. 82 Use the picture to solve 25–26. Question 25. About how many meters tall is each floor of the Williams Tower? _____ m Answer: 4.29 meters Explanation: Williams Tower has 275 meters and 64 floors. 275/64 = 4.29 meters Question 26. About how many meters tall is each floor of the Chrysler Building? _____ m Answer: 4.142 m Explanation: Chrysler Building has 319 meters and 77 floors 319/77 = 4.142 Question 27. Eli needs to save$235. To earn money, he plans to mow lawns and charge $21 for each. Write two estimates Eli could use to determine the number of lawns he needs to mow. Decide which estimate you think is the better one for Eli to use. Explain your reasoning. Type below: __________ Answer: 220/20 = 11 Explanation: Calculate$235/$21 210/21 = 10 220/20 = 11 number 220 is closer to 235. So, the better estimate is 220/20 = 11. Question 28. Explain how you know whether the quotient of 298 ÷ 31 is closer to 9 or to 10. Type below: __________ Answer: 270/30 = 9 310/31 = 10 298 is closer to 270. So, the quotient is closer to 9 than 10. Question 29. Test Prep Anik built a tower of cubes. It was 594 millimeters tall. The height of each cube was 17 millimeters. About how many cubes did Anik use? Options: a. 10 b. 16 c. 30 d. 300 Answer: c. 30 Explanation: 594/17 540/18 = 30 600/15 = 40 So, Anik use 30 cubes ### Share and Show – Page No. 85 Divide. Check your answer. Question 1. 28)$$\overline { 620 }$$ _____ R _____ Answer: 22 R 4 Explanation: Divide integers 62/28 = 2 Multiply 28 x 2 = 56; Subtract 62 – 56 = 6 Write down 60 and divide integers 60/28 = 2. Multiply 28 x 2 = 56. Subtract 60 – 56 = 4. The remainder is 4. So, 22 R 4. Check: 22 x 28 = 616; 616 + 4 = 620 620 = 620 Question 2. 64)$$\overline { 842 }$$ _____ R _____ Answer: 13 R 10 Explanation: Divide integers 84/64 = 1 Multiply 64 x 1 = 64; Subtract 84 – 64 = 20 Write down 202 and divide integers 202/64 = 3. Multiply 64 x 3 = 192. Subtract 202 – 192 = 10. The remainder is 10. So, 13 R 10. Check: 64 x 13 = 832; 832 + 10 = 842 842 = 842 Question 3. 53)$$\overline { 2,340 }$$ _____ R _____ Answer: 44 R 8 Explanation: Divide integers 234/53 = 4 Multiply 53 x 4 = 212; Subtract 234 – 212 = 22 Write down 220 and divide integers 220/53 = 4. Multiply 53 x 4 = 212. Subtract 220 – 212 = 8. The remainder is 8. So, 44 R 8. Check: 53 x 44 = 2332; 2332 + 8 = 2340 2340 = 2340 Question 4. 723 ÷ 31 _____ R _____ Answer: 23 R 10 Explanation: Divide integers 72/31 = 2 Multiply 31 x 2 = 62; Subtract 72 – 62 = 10 Write down 103 and divide integers 103/31 = 3. Multiply 31 x 3 = 93. Subtract 103 – 93 = 10. The remainder is 10. So, 23 R 10. Check: 31 x 23 = 713; 713 + 10 = 723 723 = 723 Question 5. 1,359 ÷ 45 _____ R _____ Answer: 30 R 9 Explanation: Divide integers 135/45 = 3 Multiply 45 x 3 = 62; Subtract 135 – 135 = 0 Write down 9; 9<45 The remainder is 9. So, 30 R 9. Check: 45 x 30 = 1350; 1350 + 9 = 1359 1359 = 1359 Question 6. 7,925 ÷ 72 _____ R _____ Answer: 110 R 5 Explanation: Divide integers 79/72 = 1 Multiply 72 x 1 = 72; Subtract 79 – 72 = 7 Write down 72 and divide integers 72/72= 1. Multiply 72 x 1 = 72; Subtract 72 – 72 = 0 Write down 5; 5<72 The remainder is 5. So, 110 R 5. Check: 72 x 110 = 7920; 7920 + 5 = 7925 7925 = 7925 On Your Own Divide. Check your answer. Question 7. 16)$$\overline { 346 }$$ _____ R _____ Answer: Explanation: Divide integers 34/16 = 2 Multiply 16 x 2 = 32; Subtract 34 – 32 = 2 Write down 26 and divide integers 26/16= 1. Multiply 16 x 1 = 16; Subtract 26 – 16 = 10 The remainder is 10. So, 21 R 10. Check: 16 x 21 = 336; 336 + 10 = 346 346 = 346 Question 8. 34)$$\overline { 241 }$$ _____ R _____ Answer: 7 R 3 Explanation: Divide integers 241/34 = 7 Multiply 34 x 7 = 238; Subtract 241 – 238= 3 The remainder is 3. So, 7 R 3 Check: 34 x 7 = 238; 238 + 3 = 241 241 = 241 Question 9. 77)$$\overline { 851 }$$ _____ R _____ Answer: 11 R 4 Explanation: Divide integers 85/77 = 1 Multiply 77 x 1 = 77; Subtract 85 – 77 = 8 Write down 81 and divide integers 81/77= 1. Multiply 77 x 1 = 77; Subtract 81 – 77 = 4 The remainder is 4. So, 11 R 4. Check: 77 x 11 = 847; 847 + 4 = 851 851 = 851 Question 10. 21)$$\overline { 1,098 }$$ _____ R _____ Answer: 52 R 6 Explanation: Divide integers 109/21 = 5 Multiply 21 x 5 = 105; Subtract 109 – 105= 4 Write down 48 and divide integers 48/21 = 2. Multiply 21 x 2 = 42; Subtract 48 – 42 = 6 The remainder is 6. So, 52 R 6. Check: 21 x 52 = 1092; 1092 + 6 = 1098 1098 = 1098 Question 11. 32)$$\overline { 6,466 }$$ _____ R _____ Answer: 202 R 2 Explanation: Divide integers 64/32= 2 Multiply 32 x 2 = 64; Subtract 64 – 64 = 0 Write down 66 and divide integers 66/32 = 2. Multiply 32 x 2 = 64; Subtract 66 – 64 = 2 The remainder is 2. So, 202 R 2. Check: 32 x 202 = 6464; 6464 + 2 = 6466 6466 = 6466 Question 12. 45)$$\overline { 9,500 }$$ _____ R _____ Answer: 211 R 5 Explanation: Divide integers 95/45 = 2 Multiply 45 x 2 = 90; Subtract 95 – 90 = 5 Write down 50 and divide integers 50/45 = 1. Multiply 45 x 1 = 45; Subtract 50 – 45 = 5 Write down 50 and divide integers 50/45 = 1. Multiply 45 x 1 = 45; Subtract 50 – 45 = 5 The remainder is 5. So, 211 R 5. Check: 45 x 211 = 9495; 9495 + 5 = 9500 9500 = 9500 Question 13. 483 ÷ 21 _____ Answer: 23 Explanation: Divide integers 48/21 = 2 Multiply 21 x 2 = 42; Subtract 48 – 42 = 6 Write down 63 and divide integers 63/21 = 3. Multiply 21 x 3 = 63; Subtract 63 – 63 = 0 The remainder is 0. So, 23 R 0. Check: 23 x 21 = 483; 483 = 483 Question 14. 2,292 ÷ 19 _____ R _____ Answer: 120 R 12 Explanation: Divide integers 22/19 = 1 Multiply 19 x 1 = 19; Subtract 22 – 19 = 3 Write down 39 and divide integers 39/19 = 2. Multiply 19 x 2 = 38; Subtract 39 – 38 = 1 Write down 12; 12<19 The remainder is 12. So, 120 R 12. Check: 19 x 120 = 2280; 2280 + 12 = 2,292 2,292 = 2,292 Question 15. 4,255 ÷ 30 _____ R _____ Answer: 141 R 25 Explanation: Divide integers 42/30 = 1 Multiply 30 x 1 = 30; Subtract 42 – 30 = 12 Write down 125 and divide integers 125/30 = 4. Multiply 30 x 4 = 120; Subtract 125 – 120 = 5 Write down 55 and divide integers 55/30 = 1. Multiply 30 x 1 = 30; Subtract 55 – 30 = 25 The remainder is 25. So, 141 R 25. Check: 30 x 141 = 4230; 4230 + 25 = 4,255 4,255 = 4,255 Practice: Copy and Solve Divide. Check your answer. Question 16. 775 ÷ 35 _____ R _____ Answer: 22 R 5 Explanation: Divide integers 77/35 = 2 Multiply 35 x 2 = 70; Subtract 77 – 70 = 7 Write down 75 and divide integers 75/35 = 2. Multiply 35 x 2 = 70; Subtract 75 – 70 = 5 The remainder is 5. So, 22 R 5. Check: 22 x 35 = 770; 770 + 5 = 775 775 = 775 Question 17. 820 ÷ 41 _____ Answer: 20 Explanation: Divide integers 82/41 = 2 Multiply 41 x 2 = 82; Subtract 82 – 82= 0 The remainder is 0. So, 20 R 0. Check: 41 x 20 = 820; 820 = 820 Question 18. 805 ÷ 24 _____ R _____ Answer: 33 R 13 Explanation: Divide integers 80/24 = 3 Multiply 24 x 3 = 72; Subtract 80 – 72 = 8 Write down 85 and divide integers 85/24 = 3. Multiply 24 x 3 = 72; Subtract 85 – 72 = 13 The remainder is 13. So, 33 R 13. Check: 24 x 33 = 792; 792 + 13 = 805 805 = 805 Question 19. 1,166 ÷ 53 _____ R _____ Answer: 22 R 0 Explanation: Divide integers 116/53 = 2 Multiply 53 x 2 = 106; Subtract 116 – 106= 10 Write down 106 and divide integers 106/53 = 2. Multiply 53 x 2 = 106; Subtract 106 – 106= 0 The remainder is 0. So, 22 R 0. Check: 53 x 22 = 1166; 1166 = 1166 Question 20. 1,989 ÷ 15 _____ R _____ Answer: 132 R 9 Explanation: Divide integers 19/15 = 1 Multiply 15 x 1 = 15; Subtract 19 – 15 = 4 Write down 48 and divide integers 48/15 = 3. Multiply 15 x 3 = 45; Subtract 48 – 45 = 3 Write down 39 and divide integers 39/15 = 2. Multiply 15 x 2 = 30; Subtract 39 – 30= 9 The remainder is 9. So, 132 R 9. Check: 15 x 132 = 1980; 1980 + 9 = 1989 1989 = 1989 Question 21. 3,927 ÷ 35 _____ R _____ Answer: 112 R 7 Explanation: Divide integers 39/35 = 1 Multiply 35 x 1 = 35; Subtract 39 – 35 = 4 Write down 42 and divide integers 42/35 = 1. Multiply 35 x 1 = 35; Subtract 42 – 35 = 7 Write down 77 and divide integers 77/35 = 2. Multiply 35 x 2 = 70; Subtract 77 – 70 = 7 The remainder is 7. So, 112 R 7. Check: 35 x 112 = 3920; 3920 + 7 = 3927 3927 = 3927 ### Problem Solving – Page No. 86 Use the list at the right to solve 22–24. Question 22. A smoothie shop receives a delivery of 980 ounces of grape juice. How many Royal Purple smoothies can be made with the grape juice? _____ smoothies Answer: 45 smoothies Explanation: A smoothie shop receives a delivery of 980 ounces of grape juice. 980 ounces of grape juice/22 ounces of grape juice = 45 Question 23. The shop has 1,260 ounces of cranberry juice and 650 ounces of passion fruit juice. If the juices are used to make Crazy Cranberry smoothies, which juice will run out first? How much of the other juice will be left over? Type below: _________ Answer: The shop has 1,260 ounces of cranberry juice and 650 ounces of passion fruit juice. If the juices are used to make Crazy Cranberry smoothies, passion fruit juice will run out first. Because 650<1,260. So, passion fruit juice will run out first. 1,260 – 650 =610 Crazy Cranberry juice will be left over. Question 24. In the refrigerator, there are 680 ounces of orange juice and 410 ounces of mango juice. How many Orange Tango smoothies can be made? Explain your reasoning. _____ smoothies Answer: In the refrigerator, there are 680 ounces of orange juice and 410 ounces of mango juice. So, 410 Orange Tango smoothies can be made. Because there are 410 ounces of mango juices available. Question 25. Test Prep James has 870 action figures. He decides to divide them equally among 23 boxes. How many action figures will James have left over? Options: a. 19 b. 23 c. 31 d. 37 Answer: d. 37 Explanation: James has 870 action figures. He decides to divide them equally among 23 boxes. 870/23 = 37 ### Share and Show – Page No. 89 Interpret the remainder to solve. Question 1. Erika and Bradley want to hike the Big Cypress Trail. They will hike a total of 75 miles. If Erika and Bradley plan to hike for 12 days, how many miles will they hike each day? a. Divide to find the quotient and remainder. _____ R _____ Answer: 6 R 3 Explanation: 75/12 = 6 The remainder is 3 6 R 3 Question 1. b. Decide how to use the quotient and remainder to answer the question. Type below: _________ Answer: 75/12 = 6 1/4 So, Each day they will hike 6$$\frac{1}{4}$$ miles. Question 2. What if Erika and Bradley want to hike 14 miles each day? How many days will they hike exactly 14 miles? _____ days Answer: 196 days Explanation: If Erika and Bradley want to hike 14 miles each day, 14 x 14 = 196 days Question 3. Dylan’s hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 154 hikers. How many rooms will they need? _____ rooms Answer: 11 rooms Explanation: Dylan’s hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 154 hikers. So, 154/15 = 10 and the remainder is 4. Dylan’s hiking club require 10 rooms for 150 hikers and other room for 4 hikers. So, in total they need 10 + 1 = 11 rooms. On Your Own Interpret the remainder to solve. Question 4. The students in a class of 24 share 84 cookies equally among them. How many cookies did each student eat? _____ $$\frac{□}{□}$$ cookies Answer: 3$$\frac{1}{2}$$ cookies Explanation: The students in a class of 24 share 84 cookies equally among them. So, 84/24 = 3$$\frac{12}{24}$$ = 3$$\frac{1}{2}$$ Question 5. A campground has cabins that can each hold 28 campers. There are 148 campers visiting the campground. How many cabins are full if 28 campers are in each cabin? _____ cabins Answer: 5$$\frac{1}{7}$$ cabins Explanation: A campground has cabins that can each hold 28 campers. There are 148 campers visiting the campground. 184/28 = 5$$\frac{1}{7}$$ Question 6. A total of 123 fifth-grade students are going to Fort Verde State Historic Park. Each bus holds 38 students. All of the buses are full except one. How many students will be in the bus that is not full? _____ students Answer: 9 students Explanation: A total of 123 fifth-grade students are going to Fort Verde State Historic Park. Each bus holds 38 students. 123/38 = 3 and the remainder is 9. 3 x 38 = 114 students. 1 bus is not full. So, 9 students will be in the bus that is not full Question 7. What’s the Error? Sheila is going to divide a 36-inch piece of ribbon into 5 equal pieces. She says each piece will be 7 inches long. Type below: _________ Answer: Sheila is going to divide a 36-inch piece of ribbon into 5 equal pieces. 36/5 = 7$$\frac{1}{5}$$. She said each piece will be 7 inches long and forgot about $$\frac{1}{5}$$ part. ### UNLOCK the Problem – Page No. 90 Question 8. Maureen has 243 ounces of trail mix. She puts an equal number of ounces in each of 15 bags. How many ounces of trail mix does Maureen have left over? a. What do you need to find? Answer: We need to find how many ounces of trail mix does Maureen have left over? Question 8. b. How will you use division to find how many ounces of trail mix are left over? Type below: _________ Answer: The division is 243/15 Question 8. c. Show the steps you use to solve the problem. Type below: _________ Answer: 243/15 Divide integers 24/15 = 1 Multiply 15 x 1 = 15; Subtract 24 – 15 = 9 Write down 93 and divide integers 93/3 = 6. Multiply 15 x 6 = 90. Subtract 93 – 90 = 3. The remainder is 3. So, 16 R 3. Question 8. d. Complete the sentences. Maureen has _______ ounces of trail mix. She puts an equal number in each of _______ bags. Each bag has _______ ounces. Maureen has _______ ounces of trail mix left over. Type below: _________ Answer: Maureen has 243 ounces of trail mix. She puts an equal number in each of 15 bags. Each bag has 16 ounces. Maureen has 3 ounces of trail mix left over. Question 8. e. Fill in the bubble completely to show your answer. Options: a. 3 ounces b. 15 ounces c. 16 ounces d. 17 ounces Answer: c. 16 ounces Question 9. Mr. Field wants to give each of his 72 campers a certificate for completing an obstacle course. If there are 16 certificates in one package, how many packages will Mr. Field need? Options: a. 4 b. 5 c. 16 d. 17 Answer: b. 5 Explanation: Mr. Field wants to give each of his 72 campers a certificate for completing an obstacle course. If there are 16 certificates in one package, 72/16 = 4.5 Question 10. James has 884 feet of rope. There are 12 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive? Options: a. 12 b. 73 c. 73 $$\frac{2}{3}$$ d. 74 Answer: b. 73 Explanation: James has 884 feet of rope. There are 12 teams of hikers. If James gives an equal amount of rope to each team, 884/12 = 73 ### Share and Show – Page No. 92 Adjust the estimated digit in the quotient, if needed. Then divide. Question 1. 4 41)$$\overline { 1,546 }$$ _____ R _____ Answer: 37 R 29 Explanation: 41 x 4 = 164; Subtract: 154 – 164 the estimate too high. Change the quotient to 3 41 x 3 = 123; Subtract: 154 – 123 = 31 Write down 316 and divide integers 316/41 41 x 7 = 287; Subtract: 316 – 287 = 29 37 R 29 Question 2. 2 16)$$\overline { 416 }$$ _____ Answer: 26 Explanation: 16 x 2 = 32; Subtract: 41 – 32 = 9 Write down 96 and divide integers 96/16 16 x 6 = 96; Subtract: 96 – 96 = 0 26 Question 3. 9 34)$$\overline { 2,831 }$$ _____ R _____ Answer: 83 R 9 Explanation: 34 x 9 = 306; Subtract: 283 – 306 the estimate too high. Change the quotient to 8 34 x 8 = 272; Subtract: 283 – 272 = 11 Write down 111 and divide integers 111/34 34 x 3 = 102; Subtract: 111 – 102 = 9 83 R 9 Divide. Question 4. 19)$$\overline { 915 }$$ _____ R _____ Answer: 48 R 3 Explanation: 900/18 = 50 19 x 5 = 95; Subtract: 91 – 95 the estimate too high. Change the quotient to 4 19 x 4 = 76; Subtract: 91 – 76 = 15 Write down 155 and divide integers 155/19 19 x 7 = 133; Subtract: 155 – 133 = 22 22 > 19; So Change the quotient to 8 19 x 8 = 152; Subtract: 155 – 152 = 3 48 R 3 Question 5. 28)$$\overline { 1,825 }$$ _____ R _____ Answer: Explanation: 1800/30 = 60 28 x 6 = 168; Subtract: 182 – 168 = 14 Write down 145 and divide integers 145/28 28 x 5 = 140; Subtract: 145 – 140 = 5 65 R 5 Question 6. 45)$$\overline { 3,518 }$$ _____ R _____ Answer: Explanation: 3600/40 = 90 45 x 9 = 405; Subtract: 351 – 405 the estimate too high. Change the quotient to 7 45 x 7 = 315; Subtract: 351 – 315 = 36 Write down 368 and divide integers 368/45 45 x 8 = 360; Subtract: 368 – 315 = 8 78 R 8 ### On Your Own – Page No. 93 Adjust the estimated digit in the quotient, if needed. Then divide. Question 7. 2 26)$$\overline { 541 }$$ _____ R _____ Answer: 20 R 21 Explanation: 500/25 = 2 26 x 2 = 52; Subtract: 54 – 52 = 2 Write down 21 and divide integers 21/26 20 R 21 Question 8. 1 43)$$\overline { 688 }$$ _____ Answer: 16 Explanation: 800/40 = 20 43 x 2 = 86; Subtract: 68 – 86 the estimate is too high. Change the quotient to 1 43 x 1 = 43; Subtract: 68 – 43 = 25 Write down 258 and divide integers 258/43 43 x 6 = 258; Subtract: 258 – 258 = 0 So, 16 Question 9. 6 67)$$\overline { 4,873 }$$ _____ R _____ Answer: 72 R 49 Explanation: 4800/70 = 60 67 x 6 = 402; Subtract: 487 – 402 = 85 the estimate is too low. Change the quotient to 7 67 x 7 = 469; Subtract: 487 – 469 = 18 Write down 183 and divide integers 183/67 67 x 2 = 134; Subtract: 183 – 134 = 49 72 R 49 Question 10. 15)$$\overline { 975 }$$ _____ Answer: 65 Explanation: 15 x 6 = 90; Subtract 97 – 90 = 7 Write down 75 and divide integers 75/15 15 x 5 = 75; Subtract: 75 – 75 = 0 So, 65 Question 11. 37)$$\overline { 264 }$$ _____ R _____ Answer: 7 R 5 Explanation: 240/40 = 6 37 x 6 = 222; Subtract: 264 – 222 = 42 the estimate is too low. Change the quotient to 7 37 x 7 = 259; Subtract: 264 – 259 = 5 7 R 5 Question 12. 22)$$\overline { 6,837 }$$ _____ R _____ Answer: 310 R 17 Explanation: 6300/20 = 325 22 x 3 = 66; Subtract: 68 – 66 = 2 Write down 23 and divide integers 23/22 22 x 1 = 22; Subtract: 23 – 22 = 1 Write down 17; 17 < 22 310 R 17 Practice: Copy and Solve Divide. Question 13. 452 ÷ 31 _____ $$\frac{□}{□}$$ Answer: 14$$\frac{18}{31}$$ Explanation: Divide integers 45/31 = 1 Multiply 31 x 1 = 31; Subtract 45 – 31 = 14 Write down 142 and divide integers 142/31 = 4. Multiply 31 x 4 = 124. Subtract 142 – 124 = 18. The remainder is 18. So, 14 R 18. 14$$\frac{18}{31}$$ Question 14. 592 ÷ 74 _____ Answer: 8 Explanation: Divide integers 592/74 = 8 So, 8. Question 15. 785 ÷ 14 _____ R _____ Answer: 56$$\frac{1}{14}$$ Explanation: Divide integers 78/14 = 5 Multiply 14 x 5 = 70; Subtract 78 – 70 = 8 Write down 85 and divide integers 85/14 = 6. Multiply 14 x 6 = 84. Subtract 85 – 84 = 1. The remainder is 1. So, 56 R 1. 56$$\frac{1}{14}$$ Question 16. 601 ÷ 66 _____ R _____ Answer: 9 R 7 Explanation: Divide integers 601/66 = 9 Multiply 66 x 9 = 594 ; Subtract 601 – 594= 7 The remainder is 7. So, 9 R 7. 9$$\frac{7}{66}$$ Question 17. 1,067 ÷ 97 _____ Answer: 11 Explanation: Divide integers 106/97 = 1 Multiply 97 x 1 = 97; Subtract 106 – 97 = 9 Write down 97 and divide integers 97/97 = 1 Multiply 97 x 1 = 97; Subtract 97 – 97 = 0 The remainder is 0. So, 11 is the answer. Question 18. 2,693 ÷ 56 _____ R _____ Answer: 48 R 5 Explanation: Divide integers 269/56 = 4 Multiply 56 x 4 = 224; Subtract 269 – 224 = 45 Write down 453 and divide integers 453/56 = 8 Multiply 56 x 8 = 448. Subtract 453 – 448 = 5. The remainder is 5. So, 48 R 5. Question 19. 1,488 ÷ 78 _____ R _____ Answer: 19 R 6 Explanation: Divide integers 148/78 = 1 Multiply 78 x 1 = 78; Subtract 148 – 78 = 70 Write down 708 and divide integers 708/78 = 9. Multiply 78 x 9 = 702. Subtract 708 – 702 = 6. The remainder is 6. So, 19 R 6. Question 20. 2,230 ÷ 42 _____ R _____ Answer: 53 R 4 Explanation: Divide integers 223/42 = 5 Multiply 42 x 5 = 210; Subtract 223 – 210 = 13 Write down 130 and divide integers 130/42 = 3. Multiply 42 x 3 = 126. Subtract 130 – 126 = 4. The remainder is 4. So, 53 R 4. Question 21. 4,295 ÷ 66 _____ R _____ Answer: 65 R 5 Explanation: Divide integers 429/66 = 6 Multiply 66 x 6 = 396; Subtract 429 – 396 = 33 Write down 335 and divide integers 335/66 = 5. Multiply 66 x 5 = 330. Subtract 335 – 330 = 5. The remainder is 5 So, 65 R 5 Algebra Write the unknown number for each ■. Question 22. ■ ÷ 33 = 11 ■ = _____ Answer: 363 Explanation: n ÷ 33 = 11 n = 11 x 33 = 363 Question 23. 1,092 ÷ 52 = ■ ■ = _____ Answer: 21 Explanation: 1,092 ÷ 52 = 21 Question 24. 429 ÷ ■ = 33 ■ = _____ Answer: 13 Explanation: 429 ÷ n = 33 n = 429 ÷ 33 n = 13 ### UNLOCK the Problem – Page No. 94 Question 25. A banquet hall serves 2,394 pounds of turkey during a 3-week period. If the same amount is served each day, how many pounds of turkey does the banquet hall serve each day? a. What do you need to find? Type below: _________ Answer: How many Lbs at turkey they serve each day? Question 25. b. What information are you given? Type below: _________ Answer: Every 3 weeks, serves 2,394 lbs. Question 25. c. What other information will you use? Type below: _________ Answer: Same each day, 3 weeks = 21 days Question 25. d. Find how many days there are in 3 weeks. There are ______ days in 3 weeks. Type below: _________ Answer: There are ______ days in 3 weeks Explanation: 1 week = 7 days. 3 x 7 = 21 days Question 25. e. Divide to solve the problem. Type below: _________ Answer: 2394/3 = t t = 798 798/7 = 114 pounds Question 25. f. Fill in the bubble for the correct answer choice. Options: a. 50,274 pounds b. 798 pounds c. 342 pounds d. 114 pounds Answer: d. 114 pounds Question 26. Marcos mixes 624 ounces of lemonade. He wants to fill the 52 cups he has with equal amounts of lemonade. How much lemonade should he put in each cup? Options: a. 8 ounces b. 12 ounces c. 18 ounces d. 20 ounces Answer: b. 12 ounces Explanation: Marcos mixes 624 ounces of lemonade. He wants to fill the 52 cups he has with equal amounts of lemonade. 624/52 = 12 ounces. 12 ounces should he put in each cup Question 27. The Box of Sox company packs 18 pairs of socks in a box. How many boxes will the company need to pack 810 pairs of socks? Options: a. 40 b. 45 c. 55 d. 56 Answer: b. 45 Explanation: The Box of Sox company packs 18 pairs of socks in a box. So, for 810 pairs of socks, 810/18 = 45 ### Share and Show – Page No. 97 Question 1. Paula caught a tarpon with a weight that was 10 times as great as the weight of a permit fish she caught. The total weight of the two fish was 132 pounds. How much did each fish weigh? First, draw one box to represent the weight of the permit fish and ten boxes to represent the weight of the tarpon. Next, divide the total weight of the two fish by the total number of boxes you drew. Place the quotient in each box. Last, find the weight of each fish. The permit fish weighed _____ pounds. The tarpon weighed _____ pounds. Type below: _________ Answer: The permit fish weighed 12 pounds. The tarpon weighed 120 pounds. Explanation: Let S be the weight of a permit fish Paula caught. The weight of the tarpon is 10 times as great as the weight of a permit fish she caught = 10 S The total weight of the two fish was 132 pounds. S + 10S = 132 11S = 132 S = 132/11 = 12 So, Paula caught a fish with the weight of 12 pounds. The tarpon weighted 120 pounds. Question 2. What if the weight of the tarpon was 11 times the weight of the permit fish, and the total weight of the two fish was 132 pounds? How much would each fish weigh? permit fish: _________ pounds tarpon: _________ pounds Answer: permit fish: 11 pounds tarpon: 11 x 11 = 121 pounds Explanation: Let S be the weight of a permit fish Paula caught. The weight of the tarpon is 11 times as great as the weight of a permit fish she caught = 11S Total weight is 132 11S + S = 132 12S = 132 S = 132/12 = 11. permit fish: 11 pounds tarpon: 11 x 11 = 121 pounds Question 3. Jon caught four fish that weighed a total of 252 pounds. The kingfish weighed twice as much as the amberjack and the white marlin weighed twice as much as the kingfish. The weight of the tarpon was 5 times the weight of the amberjack. How much did each fish weigh? amberjack: _________ pounds kingfish: _________ pounds marlin: _________ pounds tarpon: _________ pounds Answer: amberjack: 21 pounds kingfish: 42 pounds marlin: 84 pounds tarpon: 105 pounds Explanation: Let S be the weight of the amberjack. The kingfish weighed twice as much as the amberjack = 2S The white marlin weighed twice as much as the kingfish = 2 X 2S = 4S The weight of the tarpon was 5 times the weight of the amberjack = 5S Total weight = 252 pounds. 2S + 4S + 5S + S = 252 12S = 252 S = 252/12 S = 21. The kingfish weighed twice as much as the amberjack = 2S = 2 x 21 = 42 pounds. The white marlin weighed twice as much as the kingfish = 2 X 2S = 4S = 4 x 21 = 84 pounds. The weight of the tarpon was 5 times the weight of the amberjack = 5S = 5 x 21 = 105 pounds. ### On Your Own – Page No. 98 Use the table to solve 4–7. Question 4. Kevin is starting a saltwater aquarium with 36 fish. He wants to start with 11 times as many damselfish as clown fish. How many of each fish will Kevin buy? How much will he pay for the fish? Type below: _________ Answer: Kevin is starting a saltwater aquarium with 36 fish. He uses 1 damselfish and 11 clown fish. So, three groups form for 36 fishes. 1 damselfish and 11 clown fish =$7 + (11 x $20) = 7 + 220 = 227 He buys 3 damselfish and 33 clown fish. 3 x 7 = 21$ for damselfish and 33 x 20 = 660 for clown fish.
Each fish = 681/36 = 19

Question 5.
Kevin used a store coupon to buy a 40-gallon tank, an aquarium light, and a filtration system. He paid a total of $240. How much money did Kevin save by using the coupon?$ _____

$25 Explanation: 40-gallon tank =$170
aquarium light = $30 filtration system =$65
170 + 30 + 65 = 265
He paid a total of $240; 265 -240 =$25
Kevin save by using the coupon $25. Question 6. Kevin bought 3 bags of gravel to cover the bottom of his fish tank. He has 8 pounds of gravel left over. How much gravel did Kevin use to cover the bottom of the tank? _____ pounds Answer: 37 pounds. Explanation: 15lb bag of gravel =$13.
3 bags of gravel = 45lb.
He has 8 pounds of gravel left over = 45 – 8 = 37
Kevin use 37 pounds of gravel to cover the bottom of the tank

Question 7.
Pose a Problem Look back at Problem 6. Write a similar problem by changing the number of bags of gravel and the amount of gravel left.
Type below:
_________

If he bought 5 bags of gravel to cover the bottom of his fish tank. He has 10 pounds of gravel left over.
5 bags of gravel = 15 x 5 = 75lbs
He has 10 pounds of gravel left over = 75 – 10 lbs = 65 lbs
65lbs

Explanation:

Question 8.
Test Prep Captain James offers a deep-sea fishing tour. He charges $2,940 for a 14-hour trip. How much does each hour of the tour cost? Options: a.$138
b. $201 c.$210
d. $294 Answer: c.$210

Explanation:
Captain James offers a deep-sea fishing tour. He charges $2,940 for a 14-hour trip. Each hour =$2940/14 = 210

### Chapter Review/Test – Vocabulary – Page No. 99

Choose the best term from the box.

Question 1.
You can to estimate quotients because they are easy
use _________ to compute with mentally

Compatible Numbers

Question 2.
To decide where to place the first digit in the
quotient, you can estimate or use _________

Place Value

Concepts and Skills

Use compatible numbers to estimate the quotient.

Question 3.
522 ÷ 6 = _____

90

Explanation:
522 is close to 540. 540 ÷ 6 = 90

Question 4.
1,285 ÷ 32 = _____

40

Explanation:
1,280 ÷ 32 = 40

Question 5.
6,285 ÷ 89 = _____

70

Explanation:
6,300 ÷ 90 = 70

Question 6.
2)$$\overline { 554 }$$ = _____

277

Explanation:
Divide integers 5/2 = 2
Multiply 2 x 2 = 4; Subtract 5 – 4 = 1
Write down 15 and divide integers 15/2 = 7.
Multiply 2 x 7 = 14. Subtract 15 – 14 = 1
Write down 14 and divide integers 14/2 = 7.
Multiply 2 x 7 = 14. Subtract 14 – 14 = 0
The remainder is 0.

Question 7.
8)$$\overline { 680 }$$ = _____

85

Explanation:
Divide integers 68/8 = 8
Multiply 8 x 8 = 64; Subtract 68 – 64 = 4
Write down 40 and divide integers 40/8 = 5.
Multiply 8 x 5 = 40. Subtract 40 – 40 = 0
The remainder is 0.

Question 8.
5)$$\overline { 462 }$$ = _____ R _____

92 R 2

Explanation:
Divide integers 46/5 = 9
Multiply 5 x 9 = 45; Subtract 46 – 45 = 1
Write down 12 and divide integers 12/5 = 2.
Multiply 5 x 2 = 10. Subtract 12 – 10 = 2
The remainder is 2.
So, 92 R 2
Check:
(92 x 5) + 2 = 460 + 2 = 462

Question 9.
522 ÷ 18 = _____

29

Explanation:
Divide integers 52/18 = 2
Multiply 18 x 2 = 36; Subtract 52 – 36 = 16
Write down 162 and divide integers 162/8 = 9.
Multiply 8 x 9 = 162. Subtract 162 – 162 = 0
The remainder is 0

Question 10.
529 ÷ 37 = _____ R _____

14 R 11

Explanation:
Divide integers 52/37 = 1
Multiply 37 x 1 = 37; Subtract 52 – 37 = 15
Write down 159 and divide integers 159/37 = 4.
Multiply 37 x 4 = 148. Subtract 159 – 148 = 11
The remainder is 11.
So, 14 R 11
Check:
(14 x 37) + 11 = 518 + 11 = 529

Question 11.
987 ÷ 15 = _____ R _____

65 R 12

Explanation:
Divide integers 98/15 = 6
Multiply 15 x 6 = 90; Subtract 98 – 90 = 8
Write down 87 and divide integers 87/15 = 5.
Multiply 15 x 5 = 75. Subtract 87 – 75 = 12
The remainder is 12.
So, 65 R 12
Check:
(15 x 65) + 12 = 975 + 12 = 987

Question 12.
1,248 ÷ 24 = _____

52

Explanation:
Divide integers 124/24 = 5
Multiply 24 x 5 = 120; Subtract 124 – 120 = 4
Write down 48 and divide integers 48/24 = 2.
Multiply 24 x 2 = 48. Subtract 48 – 48 = 0
The remainder is 0

Question 13.
5,210 ÷ 17 = _____ R _____

306 R 8

Explanation:
Divide integers 52/17 = 3
Multiply 17 x 3 = 51; Subtract 52 – 51 = 1
Write down 110 and divide integers 110/17 = 6.
Multiply 17 x 6 = 102. Subtract 110 – 102 = 8
The remainder is 8.
So, 306 R 8
Check:
(306 x 17) + 8 = 5202 + 8 = 5210

Question 14.
8,808 ÷ 42 = _____ R _____

209 R 30

Explanation:
Divide integers 88/42 = 2
Multiply 42 x 2 = 84; Subtract 88 – 84 = 4
Write down 408 and divide integers 408/42 = 9.
Multiply 42 x 9 = 378. Subtract 408 – 378 = 30
The remainder is 30.
So, 209 R 30
Check:
(209 x 42) + 30 = 8778 + 30 = 8808

### Chapter Review/Test – Page No. 100

Question 15.
Samira bought 156 ounces of trail mix. She wants to divide the amount equally into 24 portions. How many ounces of trail mix will be in each portion?
Options:
A. 6 ounces
B. 6 $$\frac{1}{2}$$ ounces
C. 7 ounces
D. 12 ounces

B. 6 $$\frac{1}{2}$$ ounces

Explanation:
Samira bought 156 ounces of trail mix. She wants to divide the amount equally into 24 portions.156/24 = 6.5 = 6 $$\frac{1}{2}$$ ounces

Question 16.
A school band performed 6 concerts. Every seat for each performance was sold. If a total of 1,248 seats were sold for all 6 concerts, how many seats were sold for each performance?
Options:
A. 28
B. 200
C. 206
D. 208

D. 208

Explanation:
A school band performed 6 concerts. Every seat for each performance was sold. If a total of 1,248 seats were sold for all 6 concerts, then 1,248/6 = 208.

Question 17.
Dylan’s dog weighs 12 times as much as his pet rabbit. The dog and rabbit weigh 104 pounds altogether. How much does Dylan’s dog weigh?
Options:
A. 104 pounds
B. 96 pounds
C. 88 pounds
D. 8 pounds

D. 8 pounds

Explanation:
Dylan’s dog weighs 12 times as much as his pet rabbit. The dog and rabbit weigh 104 pounds altogether.
rabbit weight = S
dog weighs = 12S
S + 12S = 104; 13S = 104; S = 104/13 =8.

Question 18.
Jamie is sewing 14 identical costumes for the school play. She needs 210 buttons to complete all of the costumes. How many buttons will she sew onto each costume?
Options:
A. 15
B. 14
C. 11
D. 9

A. 15

Explanation:
Jamie is sewing 14 identical costumes for the school play. She needs 210 buttons to complete all of the costumes. 210/14 = 15

### Chapter Review/Test – Page No. 101

Question 19.
A book publishing company is shipping an order of 300 books. The books are packaged in boxes that each can hold 24 books. How many boxes are needed to ship the order of books?
Options:
A. 10
B. 11
C. 12
D. 13

D. 13

Explanation:
A book publishing company is shipping an order of 300 books. The books are packaged in boxes that each can hold 24 books.
300/24 = 12.5. That is 12 and above boxes. So, the answer is 13

Question 20.
Richard is planning a trip to Italy. He thinks he will need $2,750 for the trip. If the trip is 40 weeks away, which is the best estimate of how much money Richard needs to save each week? Options: A.$60
B. $70 C.$600
D. $700 Answer: B.$70

Explanation:
Richard is planning a trip to Italy. He thinks he will need $2,750 for the trip. If the trip is 40 weeks away,$2,750/40 = $68.75. That is equal to$70

Question 21.
A school club raises $506 to spend on a field trip. There are 23 people going on the trip. How much money did the club raise for each person going? Options: A.$27
B. $22 C.$18
D. $12 Answer: B.$22

Explanation:
A school club raises $506 to spend on a field trip. There are 23 people going on the trip.$506/23 = \$22.

Question 22.
A local orange grower processes 2,330 oranges from his grove this year. The oranges are packaged in crates that each hold 96 oranges. All but one crate is full. How many oranges are in this last crate?
Options:
A. 24
B. 25
C. 26
D. 27

C. 26

Explanation:
2330 oranges / 96 orange/crate = 24.2708333 crates the decimal portion is the fraction of 96 in the last crate= 96 x .2708333 = 26 oranges in the last crate.

### Chapter Review/Test – Page No. 102

Constructed Response

Question 23.
On Monday, 1,900 bottles of perfume are delivered to a warehouse. The bottles are packed in boxes. Each box can hold 32 bottles. How many boxes were delivered? Explain how you found your answer.
_____ boxes

I need to divide 1,900 by 32, which is 59 r12. That means the bottles will completely fill 59 boxes. But there will be 12 bottles left over. These would be packed in another box, which makes a total of 60 boxes.

Question 24.
Quincy needs 322 yards of ribbon to decorate quilts for a craft fair.The ribbon comes in rolls of 15 yards.
_____ rolls

I need to divide 322 by 15. The answer is 21 R 7. Since he can’t buy a part of a roll, I need to add 1 to the quotient. So, the final answer is 22.

Question 24.
B. Alice needs twice as many yards of ribbon as Quincy. How many rolls of ribbon does Alice need? Explain your answer.
_____ rolls