We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 3 Lesson 3 Adjust Quotients**Â to make students experts in learning maths.

## HMH Into Math Grade 5 Module 3 Lesson 3 Answer Key Adjust Quotients

I Can adjust a digit in a whole-number quotient based on whether an estimate is too low or too high.

**Step It Out**

1. A ship with scientific equipment is mapping the ocean floor. The equipment can scan 24 square kilometers of ocean floor each day. How many days will the ship take to scan 941 square kilometers?

A. Use compatible numbers to estimate 941 Ă· 24.

________________

B. Use the first digit of your estimate as the first digit of the whole-number quotient. Is your estimate too low, too high, or correct?

________________

C. Adjust the first digit based on your results, and then divide. How many tens are left? _____

D. Divide the ones. Estimate the whole-number quotient and use the number. Is your estimate too low, too high, or correct?

________________

E. Adjust the second digit based on your results, and then divide. Interpret the remainder to answer the question.

Since 941 Ă· 24 is ___, it will take the ship ___ days to scan 941 square kilometers.

Answer:

A. 40,

B. 3, estimate is low,

C. 22 tens digits are left

D. 221, Estimate is correct,

E. Remainder is 5,

As 941 Ă· 24 is 39, it will take the ship 39 days to scan 941 square kilometers,

Explanation:

Given a ship with scientific equipment is mapping the ocean floor. The equipment can scan 24 square kilometers of ocean floor each day.

Number of days will the ship take to scan 941 square kilometers is

24)941(39

Â Â Â 72

Â Â Â 221

216

Â Â Â Â 5

A. The estimate for 941 Ă· 24 is 40,

B. The first digit 3 of my estimate as the first digit of the whole-number quotient. The estimate is low,

C. Adjusting the first digit based on my results, and then divide. Number of tens left are 22,

D. Dividing the ones. Estimate is 9 the whole-number quotient estimate is correct,

E. Adjusting the second digit based on my results, and then divide. The remainder is 5, therefore Since 941 Ă· 24 is 39, it will take the ship 39 days to scan 941 square kilometers.

**Turn and Talk** How do you know if your estimate for a digit in the whole-number quotient is too high or too low?

Answer:

By checking the divisor and quotient

Explanation:

we check the r estimate for a digit in the whole-number quotient is too high or too low,

If an estimate is too low the difference will be more than the divisor,

Example:

48)33,82(6

Â Â Â -288

Â Â Â Â 50

here 6 is too small,

If an estimate is too high the product with the first digit will be too large and cannot be subtracted

example

65) 453(7

Â Â Â -455

here 7 is too big.

**Step It Out**

2. A robot submarine is sent to collect fish deep underwater. The mission is to collect at least 2,150 fish. The submarine makes 35 trips and collects the same number of fish on each trip. How many fish does the submarine have to collect during each trip?

A. Use compatible numbers to estimate 2,150 Ă· 35.

____________________

B. Use the first digit of your estimate as the first digit of the whole-number quotient. Is your estimate too low, too high, or correct? ____________________

C. Adjust the first digit as needed, then divide. How many tens are left? ____________________

D. Divide the ones. Estimate the whole-number quotient and use the number. Is your estimate too low, too high, or correct? ____________________

E. Adjust the second digit as needed, then divide. Interpret the remainder to answer the question.

Since 2,150 Ă· 35 is ____, the submarine has to collect ___ fish on each of its trips.

Answer:

A. Estimate is 60,

B. 6, the estimate is correct,

C. 0 ten digits are left,

D. 50, estimate is low,

E. Remainder is 15,

As 2,150 Ă· 35 is 61, the submarine has to collect 61 fish on each of its trips,

Explanation:

Given a robot submarine is sent to collect fish deep underwater. The mission is to collect at least 2,150 fish. The submarine makes 35 trips and collects the same number of fish on each trip.

Number of fish does the submarine have to collect during each trip

2,150 Ă· 35.

35)2150(61

Â Â Â 210

Â Â Â Â Â 50

35

Â Â Â Â Â Â 15

A. The estimate for 2,150 Ă· 35 is 60,

B. The first digit 6 of my estimate as the first digit of the whole-number quotient. The estimate is correct

C. Adjusting the first digit based on my results, and then divide. Number of tens left are 0,

D. Dividing the ones. Estimate is 1 the whole-number quotient estimate is low,

E. Adjusting the second digit based on my results, and then divide. The remainder is 15,

since 2,150 Ă· 35 is 61, the submarine has to collect 61 fish on each of its trips.

**Check Understanding Math Board**

Question 1.

Cindy wants to back up 1,562 computer files by dividing them equally onto 44 thumb drives. She estimates 1,600 Ă· 40 = 40. How does she know that her estimate of 40 tens is too high for

the whole-number quotient?_____

Answer:

The whole number quotient is 35 but estimate is 40 so estimate is high,

Explanation:

Given Cindy wants to back up 1,562 computer files by dividing them equally onto 44 thumb drives,

The whole number quotient is

44)1562(35

Â Â Â Â 132

Â Â Â Â 242

Â Â Â Â 220

Â Â Â Â Â 22

Cindy estimates 1,600 Ă· 40 = 40.

As the whole number quotient is 35 so she knows that her estimate of 40 tens is too high than 35.

**On Your Own**

Question 2.

**Attend to Precision** A new theater complex opens and sells 1,296 tickets. The same number of tickets is sold for each of its theaters. To find this number of tickets, the theater owner makes an estimate: 1,200 Ă· 20 = 60. Explain how to find the number of tickets sold for each theater using this estimate.

Answer:

The number of tickets sold for each theater is 60,

Explanation:

Given new theater complex opens and sells 1,296 tickets.

The same number of tickets is sold for each of its theaters.

To find this number of tickets, the theater owner makes an estimate: 1,200 Ă· 20 = 60.

The number of tickets sold for each theater using this estimate is when 1,200 is divided we got quotient 60, so 60 is the number of tickets sold for each theater.

**Describe the estimated digit in the whole-number quotient as too high, too low, or correct. Adjust the estimated digit if needed. Then divide.**

Question 3.

Answer:

The estimated digit in the whole-number quotient is too high,

Explanation:

Given 3735 Ă·Â 81

81)3735(46

Â Â Â 324

Â Â Â Â 495

486

Â Â 9

Given estimated quotient as 5 as we are getting 4, the estimated digit in the whole-number quotient is too high.

Question 4.

Answer:

The estimated digit in the whole-number

quotient is correct,

Explanation:

Given 4,473 Ă· 63

63)4473(71

Â Â Â 441

Â Â Â Â Â 63

Â 63

Â Â Â Â Â 0

Given estimated quotient as 7 as we are getting 7, the estimated digit in the whole-number quotient is correct.

Question 5.

Answer:

The estimated digit in the whole-number

quotient is too low,

Explanation:

Given 6388 Ă· 97

97)6388(65

Â Â Â 582

Â Â Â Â 568

Â Â Â Â 485

Â Â Â Â 83

Given estimated quotient as 5 as we are getting 6, the estimated digit in the whole-number

quotient is too low.

Question 6.

Answer:

The estimated digit in the whole-number quotient is too low,

Explanation:

Given 3,619 Ă· 45

45)3619(80

Â Â Â 360

Â Â Â Â 19

Given estimated quotient as 7 as we are getting 8,the estimated digit in the whole-number quotient is too low.

Question 7.

Answer:

The estimated digit in the whole-number quotient is too high,

Explanation:

Given 1,398 Ă·Â 28

28)1398(49

Â Â Â 112

Â Â Â Â 278

Â Â Â Â 252

Â Â Â Â Â 26

Given estimated quotient as 5 as we are getting 4, the estimated digit in the whole-number quotient is too high.

Question 8.

Answer:

The estimated digit in the whole-number

quotient is correct,

Explanation:

Given 6429 Ă· 79

79)6429(81

Â Â Â 632

Â Â Â Â 109

Â Â Â Â Â 79

Â Â Â Â Â Â 30

Given estimated quotient as 8 as we are getting 8, the estimated digit in the whole-number

quotient is correct.

Question 9.

Answer:

The estimated digit in the whole-number quotient is too high,

Explanation:

Given 2136 Ă· 32

32)2136(66

Â Â Â 192

Â Â Â 216

Â Â Â 192

Â Â Â 24

Given the estimated quotient as 7 as we are getting 6, the estimated digit in the whole-number

quotient is too high.

Question 10.

Answer:

The estimated digit in the whole-number

quotient is correct,

Explanation:

Given 2,128 Ă· 53

53)2,128(40

Â Â Â 2120

Â Â Â Â Â Â 8

Given estimated quotient as 4 as we are getting 4, the estimated digit in the whole-number

quotient is correct.

Question 11.

Answer:

The estimated digit in the whole-number

quotient is too high,

Explanation:

Given 4391 Ă· 64

64)4391(68

Â Â Â 384

Â Â Â Â 551

Â Â Â Â Â 512

Â Â Â Â Â 39

Given estimated quotient as 7 as we are getting 6, the estimated digit in the whole-number

quotient is too high.

**Write a division equation that estimates the value of the expression. Then use your estimate to divide, adjusting numbers as needed.**

Question 12.

1,598 Ă· 34

Answer:

1600 Ă· 30 = 53,

Explanation:

The division equation that estimates 1,598 Ă· 34 is

1600 Ă· 30

30)1600(53

Â Â Â 150

Â Â Â Â Â 100

Â Â Â Â Â Â 90

Â Â Â Â Â Â 10

Question 13.

4,398 Ă· 59

Answer:

4000 Ă· 60Â = 66,

Explanation:

The division equation that estimates 4,398 Ă· 59 is

4,000 Ă· 60

60)4000(66

Â Â Â 360

Â Â Â Â 400

Â Â Â Â 360

Â Â Â Â 40

Question 14.

2,964 Ă· 78

Answer:

3,000 Ă·Â 80 = 40,

Explanation:

The division equation that estimates 2,964 Ă· 78 is

3000 Ă· 80

80)3000(37

Â Â Â 240

Â Â Â Â 600

560

Â Â Â Â Â 40

**On Your Own**

Question 15.

**Critique Reasoning** Amanda and Jessica each make a different estimate before dividing 1,305 Ă· 26.

- Amandaâ€™s estimate is 1,200 Ă· 30 = 40. How did Amanda adjust the first digit from the estimate to find the first digit in the whole-number quotient?
- Jessicaâ€™s estimate is 1200 Ă· 20 = 60. How did Jessica adjust the first digit from the estimate to find the first digit in the whole-number quotient?

Answer:

Amanda used place value to place the first digit,

Jessica used place value to place the first digit,

Explanation:

Given Amanda and Jessica each make a different estimate before dividing 1,305 Ă· 26.

Amandaâ€™s estimate is 1,200 Ă· 30 = 40.

Amanda adjusted the first digit from the estimate to find the first digit in the whole-number quotient by place value to place the first digit.

The place value minus one for the first digit of the estimate tells where to place the first digit of the quotient.

The first digit should be placed in the tens place.

Jessica adjusted the first digit from the estimate to find the first digit in the whole-number quotient by place value to place the first digit.

The place value minus one for the first digit of the estimate tells where to place the first digit of the quotient.

The first digit should be placed in the tens place.

Question 16.

**Attend to Precision** A new machine can cut 2,576 blocks each day. This is 28 times as many blocks as the current machine can cut each day. How many blocks can the current machine cut each day? Make an estimate. Then use your estimate to divide.

Answer:

100 blocks can the current machine cut each day,

Explanation:

Given A new machine can cut 2,576 blocks each day. This is 28 times as many blocks as the current machine can cut each day. So blocks can the current machine. cut each day estimate is 3,000 Ă· 30 = 100.

Question 17.

Jaime wants to put 2,936 movie posters into 85 tubes, with the same number in each tube. He finds two estimates for the expression 2,936 Ă· 85: 2,700 Ă· 90 = 30 and 3,200 Ă· 80 = 40.

- Use each estimate to divide. What adjustments, if any, must be made using each estimate?

______________________

______________________ - What does your work tell you about finding different estimates for the same division expression?

______________________

______________________

Answer:

1. Instead of 2,700 Ă· 90 = 30 it should be 3,000 Ă· 90 = 33,

Instead of 3,200 Ă· 80 = 40 it should be 3,000 Ă· 90 = 33,

2. In adjustments only we find different estimates for the same division expression,

Explanation:

Given Jaime wants to put 2,936 movie posters into 85 tubes, with the same number in each tube.

finds two estimates for the expression 2,936 Ă· 85:

2,700 Ă· 90 = 30 and 3,200 Ă· 80 = 40.

1. Instead of taking 2,700 Ă· 90 = 30,

it should be taken 3,000 Ă· 90 = 33,

Instead of taking 3,200 Ă· 80 = 40,

it should be taken 3,000 Ă· 90 = 33,

2. In adjustments only we find different estimates for the same division expression, for 2,936 we should have taken 3,000 and for 85 if we taken 90 we would have got same estimate.