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

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

When you estimate which digit to place in the quotient, your estimate might be too small or too large. So, you need to adjust the quotient.

**Math in My World**

**Example 1**

During lunch, there were 144 students in the cafeteria. The cafeteria has a total of 16 tables. How many students can sit at each table?

Let s represent the number of students at each table. Write an equation to find the value of s.

___________ ÷ ____________ = s

1. Estimate by using compatible numbers. 140 ÷ 20 = ___________

2. Try the estimate

Since 32 > 16, the estimated digit is too low.

3. Adjust. Try 8.

Since 16 = 16, the estimated digit is too low.

4. Adjust again. Try 9.

So, 144 ÷ 16 = ____________. Since s = ____________, ____________ students can sit at each table.

Check for Reasonableness ____________ ≈ ____________

Answer: The quotient of 144 ÷ 16 = 9. Since s = 9. So 9 students can sit at each table.

For Chech Reasonableness is 7 is approximately equal to 9.

Explanation: Given that, the values are 144, 16.

Now, we will find the quotient value.

First, estimate the given values to nearest tens and hundreds.

The values 144 and 16 rounded to 140 and 20.

Now, divide it. We get the estimate values.

140/20 = 70.

Next, we will find the actual quotient.

The value 32 is greater than 16. So, the estimate is too low.

Try another estimate digit. The digit is 8.

The value 16 = 16. So, the estimated digit is too low.

Next, the another estimated digit is 9.

So, 144 is divided by 16, to get the quotient is 9.

Check reasonableness, 7 is approximately to 9.

**Example 2**

Find 1,252 ÷ 32.

1. Estimate by using compatible numbers

2. Try the estimate

Since 128 > 125, the estimated digit is too high.

3. Adjust. Try 3.

29 < 32 Continue dividing.

4. Bring down the 2 ones. Try 9.

4 < 32

So, 1,252 ÷ 32 = _____________ R _____________.

Check for Reasonableness ____________ R _____________ ≈ ____________

Answer: The quotient is 39 R 4.

For Chech Reasonableness is 39 R 4 is approximately equal to 40.

Explanation: Given that, the values are 1252, 35.

Now, we will find the quotient value.

First, estimate the given values to nearest tens and hundreds.

The values 1252 and 35 rounded to 1200 and 30.

Now, divide it. We get the estimate values.

1200/30 = 40.

Next, we will find the actual quotient.

Since, 128> 125. So, the estimated digit is too high.

Try with 3.

The 29 is less than 32. So, we can continue the division.

So, 1252 divided by 32, to get the quotient is 39 R 4.

Check reasonableness, 39 R 4 is approximately to 40.

**Talk Math**

Explain how know when a digit you try in the quotient is too small.

Answer: Using multiplication we can check whether we trying digit in the quotient is too small or big.

**Guided Practice**

Question 1.

Sara divided 306 by 34 and got a quotient of 8 R34. Explain and correct her error.

Answer: Sara did not adjust the quotient. The remainder must be less than the divisor. The correct quotient is 9.

**Independent Practice**

**Divide. Check each answer.**

Question 2.

1,272 ÷ 53 = ____________

Answer: The quotient value is 24.

Explanation: Given that, the values are

Now, we have to find the value of quotient.

So, the division process is,

After division, the quotient value is 24.

Question 3.

548 ÷ 62 = ______________

Answer: The quotient value is 8 R 52.

Explanation: As given that, the values are 548 and 62.

Now, we have to find the value of quotient.

So, the division process

By dividing 548 and 62, to get the value is 8(52/62) i.e., 8 R 52.

Question 4.

5,243 ÷ 71 = _______________

Answer: The quotient of the given values are 73 R 60.

Explanation: Given that, the values are 5243, 71.

Now, we will find the value of quotient.

Hence, the division process

The quotient of the given values is 73(60/71) i.e., 73 R 60.

Question 5.

115 ÷ 23 = ______________

Answer: The quotient value is 5.

Explanation: Given that, the values are 115, 23.

Now, we have to find the quotient value.

So, the division process

After division, the quotient value is 5.

Question 6.

1,728 ÷ 72 = ________________

Answer: The final value is 24.

Explanation: Given that, the values are 1728, 72.

Now, we need to find the value of quotient.

So, the division process

By dividing 1728 and 72. To get the quotient value is 24.

Question 7.

183 ÷ 19 = _____________

Answer: The quotient value is 9 R 12.

Explanation: Given that, the values are 183 and 19.

Now, we have to find the value of quotient,

So, the division process is

After the division, the quotient is 9(12/19) i.e., 9 R 12.

Question 8.

Answer: The final quotient value is 7 R 14.

Explanation: As given that, the values are 413, 57.

Now, we will find the value of quotient.

So, the division process is,

Therefore, by dividing 413 and 57. To get the quotient value is 7 (14/57) i.e., 7 R 14.

Question 9.

Answer: The quotient value is 7R4.

Explanation: Given that, the values are 242, 34.

Now, we need to find the quotient value.

So, the process of division is,

After division, the quotient is 7(4/34) i.e., 7 R 4.

Question 10.

Answer: The quotient value is 42 R 24

Explanation: Explanation: Given that, the values are 2712, 64.

Now, we have to find the quotient value.

So, the division process is,

After dividing 2712 by 64. To get the quotient is 42(24/64) = 42 R 24.

**Mathematical PRACTICE** Use Algebra Divide to find the variable in each equation.

Question 11.

328 ÷ 41 = m

m = _____________

Answer: m = 8

Explanation: Given that, the values are 328, 41.

Now, we have to find the value of ‘m’ using the division method.

So, the division process is,

Therefore, by dividing 328 and 41. To get the quotient value is 8 i.e., m = 8.

Question 12.

4,536 ÷ 81 = w

w = _____________

Answer: w = 56

Explanation: Given that, the values are 4536, 81.

Now, we have to find the value of ‘w’ using the division method.

So, the division process is,

By dividing 4536 by 81, to get the quotient value is 56 i.e., w = 56.

Question 13.

735 ÷ 15 = x

x = _______________

Answer: x = 49

Explanation: Given that, the values are 735, 15.

Now, we have to find the value of ‘x’ using the division method.

So, the division process is,

By dividing 735 by 15, to get the quotient value is 49 i.e., x = 49.

**Problem Solving**

Question 14.

Sheila arranged a total of 680 chairs for a school assembly. If she placed an equal amount of chairs in 20 rows, how many chairs are in each row?

Answer: 34 chairs are in each row.

Explanation: Given that,

Sheila arranged a total of 680 chairs for a school assembly.

If she placed an equal amount of chairs in 20 rows, then how many chairs are in each row.

Now, we will find the number of chairs are in each row.

Uisng the division method,

i.e., 680/20 = 34.

Therefore, 34 chairs are in each row.

Question 15.

Given the area of a rectangle is 208 square inches, and the length is 26 inches, find the width.

Answer: The width of the rectangle is 8 inches.

Explanation: As given in the question,

The area of a rectangle is 208 square inches.

The length of the rectangle is 26 inches.

Now, we will find the width of the rectangle.

We know that, the Area of the rectangle formula.

The formula is, A = l x w.

208 = 26 x w

208/26 = w

i.e., 8 = w

So, the width of the rectangle is 8 inches.

Question 16.

A crew went net fishing to catch shrimp. They caught 486 shrimp in 54 minutes. How many shrimp did they catch per minute? Find the unknown number in the equation 486 ÷ 54 = s.

Answer: S=9. So, 9 shrimp they caught per minute.

Explanation: Given that,

A crew went net fishing to catch shrimp.

They caught 486 shrimp in 54 minutes.

Now, we will find out how many shrimp did they catch per minute.

The given values are 486 , 54. We will find the value of ‘s’ using the division method.

So, the division is

i.e., 486/54 = 9

So, s = 9. Therefore, 9 shrimp needs per minute.

**HOT Problems**

Question 17.

**Mathematical PRACTICE** Find the Error Emma estimated the first digit in the quotient of 2,183 ÷ 42 as 4. She adjusted the quotient to 3. What did she do wrong? Exp lain.

Answer: Her estimate is too low. She can use compatible numbers to estimate and then check by multiplying the rounded quotient and divisor.

Question 18.

**Building on the Essential Question** How can I adjust a quotient to solve a division problem?

Answer: Estimate a quotient by rounding. Try the quotient and if it is too high or low, then try another number. First, find the estimate quotient then find the actual quotient.

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

**Practice**

**Divide. Check each answer.**

Question 1.

Answer: The final quotient value is 26.

Explanation: Given that, the values are 1261 and 48.

Now, we will find the final value using the division method.

So, the division is,

After dividing, to get the value is 26(13/48). So, to estimate the quotient as 26.

Question 2.

Answer: The quotient value is 14.

Explanation: As given that, the values are 1204 and 86.

Now, we will find the quotient value. We can perform the division operation.

The below is the division operation,

Hence, by dividing 1204 by 86. To get the quotient value is 14.

Question 3.

428 ÷ 61 = _____________

Answer: The quotient value is 7.

Explanation: Given that, the values are 428 and 61.

Now, find the dividend value. Using the division method,

So, by dividing 428 by 61. We get the quotient value is 7.

**Algebra. Divide to find the variable in each equation.**

Question 4.

140 ÷ 28 = t

t = ____________

Answer: t =5

Explanation: As given in the question, the values are 140 and 28.

Now, we will find the value of ‘t’ using the division method.

The division is,

So, by dividing 140 and 28, to get the quotient is 5. Therefore, the value of t = 5.

Question 5.

2,075 ÷ 83 = c

c = _____________

Answer: c = 25

Explanation: Given that, the values are 2075 and 83.

Now, we will find the c value using the division method.

So, the division is

Therefore, by dividing 2075 by 83, to get the value is 25. So, the value of c is 25.

Question 6.

531 ÷ 59 = n

n = ______________

Answer: n =9

Explanation: Given that, the values are 531 and 59.

Now, we will find the n value using the division method.

So, the division is,

By dividing 531 by 59, to get the value is 9.

So, the value of n is 9.

**Problem Solving**

Question 7.

**Mathematical PRACTICE** Use Algebra Woodfern School has a raffle each year to raise money for the music program. The raffle needs to sell 1,500 tickets. How many raffle ticket sellers are needed if each seller sells 75 tickets? Find the unknown number in the equation 1,500 ÷ 75 t.

Answer: 20 Raffle ticket sellers are needed if each seller sells 75 tickets. So, the unknown number is 20.

Explanation: Given that, the data is

Woodfern School has a raffle each year to raise money for the music program.

The raffle needs to sell 1,500 tickets.

So, how many raffle ticket sellers are needed if each seller sells 75 tickets.

Now, we will find the value of ‘t’ using the division method.

The values are 1500 and 75. Now divide it.

1500/75 = 20

Therefore, 20 raffle ticket sellers are needed if each seller sells 75 tickets.

Question 8.

Given the area of a square is 225 square feet, what is the length of each side?

Answer: The length of each side is 56.25 feet.

Explanation: Given that,

The area of a square is 225 square feet.

Now, we will the length of each side.

We know the formula for area of a square.

A = 4 x s.

225 sq.ft = 4s

225/4 = s

56.25 =s

The length of the each square side is 56.25 ft.

Question 9.

The Rodriquez family is taking a 1,430-mile train ride. If the train travels 55 miles per hour, how many hours will the ride last?

Answer: 26 hours will the last ride.

Explanation: As given in the question, the data is

The Rodriquez family is taking a 1,430-mile train ride.

If the train travels 55 miles per hour, then how many hours will the ride last.

Now, we will find out the hours.

So, the values are 1430 miles and 55 miles per hour.

Divide the given values. we get the final value.

i.e., 1430/55 = 26 hours.

So, the total 26 hours will ride the last.

**Test Practice**

Question 10.

Alaska has the longest coastline in the United States. Traveling at 60 miles per hour, how many hours would it take to travel along the Pacific Coast?

(A) 18 hours

(B) 23 hours

(C) 93 hours

(D) 103 hours

Answer: C

Explanation: Given that,

Alaska has the longest coastline in the united states.

The Alaska coastline has 2 coastline one is pacific and the another one is Arctic.

Now, we will find out the value. If we travel 60 miles per hour then how many hours it take to travel the pacific coast.

The miles of pacific coast is 5580 and the traveling hour is 60 miles per hour.

Now, divide it.

5580/60 = 93 hours.

So, the total 93 hours is taken to travel the pacific coast.