All the solutions provided inÂ **McGraw Hill My Math Grade 5 Answer Key PDF Chapter 4 Lesson 1 Estimate Quotients **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 4 Lesson 1 Estimate Quotients

You can use rounding and compatible numbers to estimate quotients when dividing by two-digit divisors. By estimating first, you can determine the reasonableness of your results.

**Math in My World**

**Example 1**

The school principal has 812 fliers to pass out equally to 19 different teachers. About how many fliers would each teacher receive?

Estimate 812 Ă· 19

1. Round the divisor to the nearest ten.

2. Round the dividend to the nearest hundred.

3. Divide mentally.

8 Ă· 2 = 4

80 Ă· 20 = 4

800 Ă· 20 = 40

So, each teacher would receive about ____________ fliers.

Answer: Each teacher would receive about 40 fliers.

Explanation: Given that,

The school principal has 812 fliers to pass out equally to 19 different teachers.

Now, we will find how many fliers would each teacher receive.

Based on the steps, we will find them easily.

So, the value is 812/19,

First, round the divisor to the nearest ten.

i.e., 812/20.

Next, round the dividend to the nearest hundred.

i.e., 800/20

Now, divide it.

800/20 = 40.

So, each teacher receives 40 fliers.

**Example 2**

Estimate 234 Ă· 41.

1. Round the divisor to the nearest ten.

41 â†’ ___________

2. Change the dividend to a number that is compatible with the rounded divisor, ____________.

234 â†’ ___________

3. Divide mentally.

___________ Ă· ___________ = ___________

So, 234 Ă· 41 is about ___________

Check: Use multiplication to check your answer.

___________ Ă— ___________ = ___________ and ___________ 234

Answer: 240

Explanation: Given that, the estimated value isÂ 234 Ă· 41.

First, round the divisor to the nearest ten.

i.e., 41 nearest to ten is 40.

Next, change the dividend to a number that is compatible with the rounded divisor.

So, the value is 234–> 240.

Now, divide it.

240 Ă· 40 = 6.

So, 234 Ă· 41 is about 6.

Use multiplication to check answers.

6 x 40 = 240.

i.e., 240 = 234.

Therefore, 234 is estimated to be 240.

**Talk Math**

Is it possible to have more than one estimate for a division problem? Explain. Give an example.

Answer: No, its not possible . Only one estimation is possible for a division problem. Because in division problem, we can estimate the values to nearest tens and estimate hundreds. So, it can easily divided then no need to estimate further more.

**Example:** He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends? There are 9 friends of seats on the bus. To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends.

i.e., 9/9 = 1.

He gave one apple to one friend.

**Guided Practice**

Question 1.

Estimate 312 Ă· 31. Show how you estimated.

Round the divisor to the nearest ten.

31 â†’ ___________

Round the dividend to the nearest hundred.

312 â†’ ___________

Divide mentally.

__________ Ă· ___________ = ____________

So, 312 Ă· 31 is about ____________.

Answer: 312 Ă· 31 is about 10.

Explanation: Given that, the estimated value is 312 Ă· 31.

Based on the steps, we will find the value quickly.

So, the value is 312 Ă· 31

First, round the divisor to the nearest ten.

i.e., 312/30.

Next, round the dividend to the nearest hundred.

i.e., 300/30

Now, divide it.

300/30 = 10.

So, 312 Ă· 31 is about 10.

**Independent Practice**

**Estimate by rounding. Show how you estimated.**

Question 2.

121 Ă· 42

Answer: 3

Explanation: Given that, the estimated value is 121 Ă· 42.

Based on the steps, we will find the value easily.

So, the value is 121 Ă· 42

First, round the divisor to the nearest ten.

i.e.,121/40.

Next, round the dividend to the nearest hundred.

i.e., 120/40

Now, divide it.

120/40 = 3.

So, 312 Ă· 31 is about 3.

Question 3.

400 Ă· 23

Answer: 20.

Explanation: Given that, the estimated value is 400 Ă· 23.

Based on the steps, we will find the value easily.

So, the value is 400 Ă· 23

First, round the divisor to the nearest ten.

i.e.,400/20.

Next, round the dividend to the nearest hundred.

i.e., 400/20

Now, divide it.

400/20 = 20.

So, 400 Ă· 23 is about 20.

Question 4.

642 Ă· 83

Answer: 642Ă· 83 is about 8.

Explanation: Given that, the estimated value is 642Ă· 83.

Based on the steps, we will find the value easily.

So, the value is 642Ă· 83

First, round the divisor to the nearest ten.

i.e.,642/80.

Next, round the dividend to the nearest hundred.

i.e., 640/80

Now, divide it.

640/80 = 8.

So, 642 Ă· 83 is about 8.

Question 5.

Answer: 21(9/28)

Explanation: Given the values are 28 and 597.

Now, see the step-by-step division process.

By dividing 597 by 28, we get the value is 21(9/28).

Question 6.

Answer: 6(8/19)

Explanation: Given the divisor is 38 and the dividend is 244.

Now, we will find the final value.

So, by dividing 244 by 38, we get the value is 6(16/38) = 6(8/19)

Question 7.

Answer: 39(7/24)

Explanation: As given in the question, the divisor is 24 and the dividend is 943.

Now, we will find the final value.

Below is the step-by-by process of division.

So, by dividing 943 by 24, to get the value is 39(7/24).

**Estimate using compatible numbers. Show how you estimated.**

Question 8.

653 Ă· 52

Answer: 653Ă· 52 is about 13.

Explanation: Given that, the estimated value is 653Ă· 52.

Based on the steps, we will find the value easily.

So, the value is 653Ă· 52

First, round the divisor to the nearest ten.

i.e.,653/50.

Next, round the dividend to the nearest hundred.

i.e., 650/50

Now, divide it.

650/50 = 13.

So, 653 Ă· 52 is about 13.

Question 9.

208 Ă· 51

Answer: 208 Ă· 51 is about 4.

Explanation: Given that, the estimated value is 208Ă· 51.

Based on the steps, we will find the value easily.

So, the value is 208 Ă·51

First, round the divisor to the nearest ten.

i.e.,208/50.

Next, round the dividend to the nearest hundred.

i.e., 200/50

Now, divide it.

200/50 = 4.

So, 200 Ă· 50 is about 4.

Question 10.

300 Ă· 59

Answer: 300Ă· 59 is about 5.

Explanation: Given that, the estimated value is 300Ă· 59.

Based on the steps, we will find the value quickly.

So, the value is 300Ă· 59

First, round the divisor to the nearest ten.

i.e.,300/60

Next, round the dividend to the nearest hundred.

i.e., 300/60Â Â (it is already rounded to a hundred)

Now, divide it.

300/60 = 5.

So, 300 Ă· 60 is about 5.

Question 11.

Answer: 19(11/32)

Explanation: Given the divisor is 32 and the dividend is 619.

Now, we can divide it. We get the final value.

So, by dividing 619 by 32, we get the value is 19(11/32).

Question 12.

Answer: 19(30/43)

Explanation: Given that, the divisor is 43 and the dividend is 847.

Now, we will find the final value.

So, dividing 847 by 43, we get the value is 19(30/43).

Question 13.

Answer: 8

Explanation: Given that, the divisor is 34 and the dividend is 272.

Now, we will divide it.

Therefore, by dividing 272 by 34, to get the value is 8.

**Problem Solving**

Question 14.

There are 598 goldfish divided equally among 23 fish tanks. About how many goldfish are in each tank?

Answer: 26 goldfish are in each tank.

Explanation: Given that,

There are 598 goldfish and 23 fish tanks.

Now, we will find how many goldfish are in each tank.

So, we divide 598 by 23, to get the value.

i.e., 598/23 = 26

So, 26 goldfish are in each tank.

Question 15.

The area of a rectangle is 138 square meters, and the length is 21 meters. About how many meters long is the width?

Answer: 6.57 meters long is the width.

Explanation: Given that,

The area of a rectangle is 138 square meters.

The length is 21 meters.

Now, we will find width of the rectangle.

We know, the area of a rectangle formula.

The formula is, Area of a rectangle is l x w.

Substitute the given values in a formula.

A = l x w.

138 = 21 x 3

138/21 = w

W = 6.57 meters

Question 16.

**Mathematical PRACTICE** Check for Reasonableness A box of cereal contains 340 grams of carbohydrates. If there are 12 servings, how many grams are there in one serving? Show how you estimated. Explain why your answer is reasonable.

Answer: Given that,

A box of cereal contains 340 grams of carbohydrates.

It servers to 12 then how many grams are there in one serving.

Now, we will find the grams of one serve.

So, 340 divided by 12.

i.e., 340/12 = 28.3 grams.

So, 28 grams are there in one serving.

The answer is reasonable because the packet contains only 340 grams of cereal, we can’t increase the quantity in cereal box. So, better to serve the given quantity to 12 servings equally. Therefore, we can divide 340 into 12 parts.

**HOT Problems**

Question 17.

**Mathematical PRACTICE** Which One Doesn’t Belong? Circle the equation that is not a reasonable estimate for 533 Ă· 57.

Answer: 420 Ă· 60 =7

Explanation: Given the value is 533 Ă· 57.

Now, we will find the not reasonable estimate value on given options.

533 is nearest to 540 and 57 is nearest to 60.

So, option A is reasonable.

Next, 533 is nearest to 500 and 57 is nearest to 50.

So, option B is also reasonable.

Now, 533 is nearest to 550 and 57 is nearest to estimate 55.

So, option C is also reasonable.

Next, the option D is not reasonable to estimate. Because, there is much difference between 420 and 533.

So, we can’t estimate 533 to 420.

Therefore option 420 Ă· 60 =7 is not reasonable.

Question 18.

**Building on the Essential Question** Explains when it would be useful to estimate.

Answer: Estimation is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. ItÂ is very useful because it can help you to solve a problem quickly if only a rough answer is needed.

### McGraw Hill My Math Grade 5 Chapter 4 Lesson 1 My Homework Answer Key

**Practice**

**Estimate. Show how you estimated.**

Question 1.

512 Ă· 52

Answer: 512Ă· 52 is about 10.

Explanation: Given that, the estimated value is 512Ă· 52.

Based on the steps, we will find the value quickly.

So, the value is 512Ă· 52

First, round the divisor to the nearest ten.

i.e.,512/50

Next, round the dividend to the nearest hundred.

i.e., 500/50

Now, divide it.

500/50 = 10.

So, 512 Ă· 52 is about 10.

Question 2.

412 Ă· 97

Answer: 412Ă· 97 is about 4.

Explanation: Given that, the estimated value is 412Ă· 97.

Based on the steps, we will find the value quickly.

So, the value is 412Ă· 97

First, round the divisor to the nearest ten.

i.e.,412/100

Next, round the dividend to the nearest hundred.

i.e., 400/100

Now, divide it.

400/100 = 4.

So, 412 Ă· 97 is about 4.

Question 3.

Answer: 2(71/83)

Explanation: Given that, the divisor is 83 and the dividend is 237.

Now, we will find the value.

So, by dividing 237 by 83, to get the value is 2(71/83).

Question 4.

Answer: 14(24/31)

Explanation: As given in the question, the values are 458 and 31.

Now,we can divide it to get the final value.

So, dividing 458 by 31, to get the value is 14(24/31).

**Problem Solving**

Question 5.

The Booster Club is having a bake sale. The members place 25 baked goods in each bag. There are 630 baked goods donated. About how many bags will the club have for sale?

Answer: 25 bags

Explanation: Given that,

The booster club is having a bake sale.

There are 25 members are baked goods in each bag.

The total 630 goods are donated.

Now, we will find how many bags will the club have sale.

So, estimate divide the given values.

i.e., 630/25 = 25.2

Therefore, 25 bags will the club have to sale.

Question 6.

A farmer has 212 acres of land for sale. He divides the land into 18 equal sections. About how many acres are in each section?

Answer: 11.7 acres are in each section.

Explanation: As given in the question, the data is,

A farmer has 212 acres of land for sale.

He divides the land into 18 equal parts.

Now, we will find how many acres are in each section.

So, the values are 212 and 18.

Divide 212 acres/ 18 equal parts. To get the value.

i.e., 212/ 18 = 11.7

Therefore, 11.7 acres are there in each section.

Question 7.

Alexander has 418 songs on his MP3 player. He divides the songs into 11 equal groups. About how many songs are in each group?

Answer: 38 songs are in each group.

Explanation: Given in the question, the data is,

Alexander has 418 songs on his MP3 player.

He divides the songs into 11 equal groups.

Now, we will find how many songs are in each section.

So, the values are 418 and 11.

Divide 418 songs/ 11 equal groups. To get the value.

i.e., 418/ 11 = 38

Therefore, 38 songs are there in each group.

Question 8.

**Mathematical PRACTICE** If Check for Reasonableness A restaurant ordered 833 ounces of chicken. There are 16 ounces in a pound. About how many pounds of chicken did the restaurant order?

Answer: 52 pounds of chicken did the restaurant ordered.

Explanation: Given that,

A restaurant ordered 833 ounces of chicken.

There are 16 ounces in a pound.

Now, we have to find out how many pounds of chicken did the restaurant ordered.

So, the values are 833 and 16.

Divide 833/ 16

i.e., 418/ 11 = 52.06

Hence, 52 pounds of chicken the restaurant will be ordered.

**Test Practice**

Question 9.

Ms. Robbins has 600 sheets of paper for a project. She has 48 students. Which is the best estimate for the number of sheets of paper she can give to each student?

(A) 10 sheets

(B) 12 sheets

(C) 15 sheets

(D) 20 sheets

Answer: OptionB

Explanation: As given in the question,

Ms. Robbins has 600 sheets of paper for a project.

She has 48 students.

Now, find out the best estimate for the number of sheets of paper she can given to each student.

So, divide 600 by 48.

i.e., 600/48= 12.5 which is 12.

(or)

48 is rounded to nearest to 10.

i.e., 600/50 = 12.

So, the best estimate for the number of sheets of paper is 12.