We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 3 Lesson 2 Interpret the Remainder** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 3 Lesson 2 Answer Key Interpret the Remainder

I Can solve a division problem and interpret the remainder in the context of the problem.

**Step It Out**

1. A land surveyor rolls a wheeled device on the ground to measure distances. Each full turn of the wheel measures 14 inches. The surveyor measures 1,617 inches of land. How many turns of the wheel are needed to measure this distance?

A. Use division to represent the situation.

_____________________

B. Divide and write the whole-number quotient and the remainder. ______

C. The remainder indicates that the number of turns of the wheel is not a whole number. Use the remainder to find the fractional part of the last turn.

• What fraction of a turn is represented by the remainder?

_______________

D. Write the answer as a whole number of turns and a fractional part of a turn. How many turns of the wheel are needed to measure 1,617 inches? ____

Answer:

A. The situation is 1,617 ÷ 14,

B. Quotient is 115 and remainder is 7,

C. Fraction of a turn is represented by the remainder is 7/14,

D. 115(7/14), Number of turns of the wheel are needed to measure 1,617 inches are 115,

Explanation:

Given a land surveyor rolls a wheeled device on the ground to measure distances. Each full turn of the wheel measures 14 inches. The surveyor measures 1,617 inches of land.

The number of turns of the wheel are needed to measure this distance is

14)1617(115

14

21

14

77

70

7

A. The division to represent the situation is 1,617 ÷ 14,

B. The whole number quotient is 115 and remainder is 7,

C. Fraction of a turn is represented by the remainder is 7/14,

D. 115(7/14), Number of turns of the wheel are needed to measure 1,617 inches are 115.

**Turn and Talk** How are the divisor, whole-number quotient, and remainder used to represent the number of groups and the size of each group in this situation?

Answer:

Size of each group is divisor,

Number of groups is whole- number quotient,

Left over number are remainders,

Explanation:

The divisor, whole-number quotient, and remainder used to represent the number of groups and the size of each group in this situation as the size of each group is the divisor

Number of groups is whole- number quotient,

Left over number are remainders,

**Step It Out**

2. A large plot of farmland will be used for a new field. The seed that the farmers will plant on this field is sold in large tanks. Each tank can cover 72 acres with seed. How many tanks, are needed to cover the entire field with seed?

A. Represent the situation using a division problem. Identify the dividend and the divisor.

B. Divide to find the whole-number quotient and the remainder. Show your work.

C. The seed is sold only in full tanks. How many tanks must be purchased to cover the entire field?

_______________

D. How many acres will the seed from the last tank cover?

Answer:

A. 1,140 ÷ 72, Dividend is 1,140 and the divisor is 72,

B. Whole number quotient is 15 and remainder is 60,

C. 16 full tanks,

D. 60 acres,

Explanation:

Given a large plot of farmland will be used for a new field.

The seed that the farmers will plant on this field is sold in large tanks. Each tank can cover 72 acres with seed.

Number of tanks, are needed to cover the entire field 1,140 acres with seed are

72)1140(15

72

420

360

60

A. 1,140 ÷ 72, Dividend is 1,140 and the divisor is 72,

B. Whole number quotient is 15 and remainder is 60,

C. The seed is sold only in full tanks. So tanks must be purchased to cover the entire field is as quotient is 15 and we are getting the remainder so we need 16 full tanks,

D. As the remainder is 60 acres the seed from the last tank cover.

**Turn and Talk** If this remainder is expressed as a fraction, what information would the fraction give? Explain.

Answer:

If the remainder is expressed in fraction it means left over from the whole part,

**Check Understanding Math Board**

Question 1.

Milo will cut a 136-foot-long roll of wire into 16 equal lengths for fencing. He finds that 136 ÷ 16 is 8 r8. How long will each length of wire measure?

Answer:

8 foot,

Explanation:

Given Milo will cut a 136-foot-long roll of wire into 16 equal lengths for fencing. He finds that 136 ÷ 16 is 8 r8.

So long will each length of wire measure is 8 foot as the quotient is 8.

Question 2.

Trina has 232 books to put onto shelves. Each shelf can hold 38 books. She plans to fill each shelf before starting the next. She finds that 232 ÷ 38 is 6 r4. How many books will be on each shelf?

Answer:

6 books,

Explanation:

Given Trina has 232 books to put onto shelves.

Each shelf can hold 38 books.

She plans to fill each shelf before starting the next.

She finds that 232 ÷ 38 is 6 r4. As quotient is 6

The number of books will be on each shelf is 6 books.

**On Your Own**

Question 3.

**Reason** A vitamin company produces 4,514 tablets every hour. A machine drops the same number of tablets into each bottle. How many bottles does the machine completely fill every hour?

Answer:

71 bottles every hour,

Explanation:

Given a vitamin company produces 4,514 tablets every hour.

A machine drops the same number of tablets into each bottle.

So number of bottles does the machine completely fill every hour are 4514 ÷ 63

63)4514(71

441

104

63

41

71 bottles every hour.

Question 4.

**Reason** To watch a safety video, 294 employees will be arranged into conference rooms that each hold 30 people. The remaining people will watch the video in the cafe. How many people will watch the video in the cafe?

Answer:

The number of people will watch the video in the cafe are 24,

Explanation:

Given to watch a safety video, 294 employees will be arranged into conference rooms that each hold 30 people.

So 294 ÷ 30 is

30)294(9

270

24

As the remaining people will watch the video in the cafe.

So number of people will watch the video in the cafe are 24.

Question 5.

**Attend to Precision** A fabric store orders 2,345 spools of thread. If each shipping box holds 84 spools, how many shipping boxes are needed for this order? Explain your thinking.

Answer:

Number of boxes are needed 28 boxes,

Explanation:

Given a fabric store orders 2,345 spools of thread.

If each shipping box holds 84 spools, So shipping boxes are needed for this order are 2,345 ÷ 84

84)2345(27

168

665

588

77

as there is a remainder we need 27 + 1 = 28 boxes.

Divide. Interpret the remainder to solve.

Question 6.

A company ships new basketballs in boxes that fit up to 14 basketballs. How many boxes are needed for an order of 202 basketballs?

Answer:

Number of boxes needed are 15,

Explanation:

Given a company ships new basketballs in boxes that fit up to 14 basketballs. Number of boxes are needed for an order of 202 basketballs are

202 ÷ 14

14)202(14

14

62

56

6

Question 7.

At a banquet hall, each table requires 18 plates. The kitchen has 387 plates available. How many full tables can be set?

Answer:

21 full tables can be set,

Explanation:

Given at a banquet hall, each table requires 18 plates.

The kitchen has 387 plates available.

So full tables can be set are 387 ÷ 18

18)387(21

36

27

18

9

21 tables.

Question 8.

A spacecraft collects 234 pounds of rocks from the moon. The rocks are divided evenly among 36 groups of scientists for study. What weight of rocks does each group receive?

Answer:

Weight of rocks does each group receive are 6 pounds,

Explanation:

Given a spacecraft collects 234 pounds of rocks from the moon.

The rocks are divided evenly among 36 groups of scientists for study.

The weight of rocks does each group receive are

234 ÷ 36

36)234(6

216

18

6 pounds .

Question 9.

At the Kennedy Space Center, 138 people are divided into 15 equal groups. The remaining people will form a sixteenth group. How many people will be in the sixteenth group?

Answer:

Number of people will be in the sixteenth group are 3 people,

Explanation:

Given at the Kennedy Space Center,

138 people are divided into 15 equal groups,

The remaining people will form a sixteenth group.

Number of people will be in the sixteenth group are

15)138(9

135

3

3 people.

**On Your Own**

Question 10.

**Open Ended** Write two word problems that can be represented by using 200 ÷ 12.

- Write a word problem for which the answer is 17.

_______________________ - Write a word problem for which the answer is 8.

_______________________

_______________________

Answer:

A word problem for which the answer is 17 is

Tina wants to distribute pencils, Each box holds 12 pencils she has 200 pencils how many pencil boxes are required to hold 200 pencils?,

Write a word problem for which the answer is 8.

How many pencils will be left in the last box?

Question 11.

Uma brings 600 fluid ounces of lemonade to a picnic. She also brings a package of 48 plastic cups.

- If she fills each cup with the same amount of lemonade, how much will be in each cup? _______________

- Why does it make sense to express this quotient using a fraction?

Answer:

Each cup will have 12 ounces,

whole number is obtained,

Explanation:

Given Uma brings 600 fluid ounces of lemonade to a picnic.

She also brings a package of 48 plastic cups.

If she fills each cup with the same amount of lemonade,

in each cup it will be

48)600(12

48

120

96

24

It makes sense to express this quotient using a fraction, the quotient of a fraction is the whole number that is obtained when we simplify the fraction.

Question 12.

**Reason** Pulp Paper Company is having a paper airplane design contest. They receive 391 submissions. The judges review the paper airplanes in groups of 16. How many equal groups of paper airplanes will the judges review? How many paper airplanes will be left after the equal groups are judged?

Answer:

24 number of equal groups of paper airplanes will the judges review and 7 paper airplanes will be left after the equal groups are judged,

Explanation:

Given Pulp Paper Company is having a paper airplane design contest. They receive 391 submissions.

The judges review the paper airplanes in groups of 16.

The number of equal groups of paper airplanes will the judges review

16)391(24

32

71

64

7,

Therefore 24 number of equal groups of paper airplanes will the judges review and 7 paper airplanes will be left after the equal groups are judged.

Question 13.

**Construct Arguments** Mr. Torres has 212 coins in his collection. He wants to keep all of his coins in a binder. He can store 24 coins on each binder page. He finds 212 ÷ 24 to be 8 r20, so he buys 8 pages. Does Mr. Torres buy the correct number of pages? Explain.

Answer:

No,

Explanation:

Given Mr. Torres has 212 coins in his collection. He wants to keep all of his coins in a binder.

He can store 24 coins on each binder page. He finds 212 ÷ 24 to be 8 r20, so he buys 8 pages.

No, Mr.Torres did not buy the correct number of pages as we have the remainder of 20 coins to keep sufficient number of coins in a binder he should have taken

9 pages, not 8 pages.