All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 5 Test **are as per the latest syllabus guidelines.

## McGraw-Hill Math Grade 5 Chapter 5 Test Answer Key

**Follow the directions to simplify each expression.**

Question 1.

(15 – 5)^{3} – (20 × 5) × (8 – 4) + 10^{2} =

simplify inside parentheses: _____

____________________

Simplify exponents: ____________

Multiply: ___________

Add and subtract from left to right: ___________

Final answer: _____________

Answer:

simplify inside parentheses: (10)^{3} – (100) × (4) + 10^{2}

Simplify exponents: 1000 – 100 × 4 + 100

Multiply: 1000 – 400 + 100

Add and subtract from left to right: 1000 – 500

Final answer: 500.

Explanation:

Given the expression is(15 – 5)^{3} – (20 × 5) × (8 – 4) + 10^{2} . So first we will solve inside parentheses which is

(10)^{3} – (100) × (4) + 10^{2} , now we will solve the exponents which is

= (10)^{3} – (100) × (4) + 10^{2}

= 1000 – 100 × 4 + 100

= 1000 – 400 + 100

= 1000 – 500

= 500.

Question 2.

(30 × 5) × (6 – 2) + (10 – 5)^{2} – 10^{1} =

simplify inside parentheses: _____

____________________

Simplify exponents: ____________

Multiply: ___________

Add and subtract from left to right: ___________

Final answer: _____________

Answer:

simplify inside parentheses: (60) × (4) + (5)^{2} – 10

Simplify exponents: 60 × 4 + 25 – 10

Multiply: 240 + 25 – 10

Add and subtract from left to right: 240 + 15

Final answer: 255.

Explanation:

Given the expression is (30 × 5) × (6 – 2) + (10 – 5)^{2} – 10^{1} . So first we will solve inside parentheses which is

(60) × (4) + (5)^{2} – 10, now we will solve the exponents which is

= 60 × 4 + 25 – 10

= 240 + 15

= 255.

**Use the order of operations to simplify and solve. Show your work.**

Question 3.

(7 × 3) ÷ 3^{2}

Answer:

(7 × 3) ÷ 3^{2 }= 2\(\frac{1}{3}\).

Explanation:

Given that the expression is

(7 × 3) ÷ 3^{2}

= 21 ÷ 3^{2}

= 21 ÷ 9

= 7 ÷ 3

= 2\(\frac{1}{3}\).

Question 4.

5 + 2^{2} × (5 × 2) ÷ 5

Answer:

5 + 2^{2} × (5 × 2) ÷ 5 = 13.

Explanation:

Given that the expression is 5 + 2^{2} × (5 × 2) ÷ 5

= 5 + 4 × 10 ÷ 5

= 5 + 4 × 2

= 5 + 8

= 13.

Question 5.

(52 + 9) – 14

Answer:

(52 + 9) – 14 = 47.

Explanation:

Given that the expression is (52 + 9) – 14

= 61 – 14

= 47.

Question 6.

(60 ÷ 10) + (12 – 8)^{2}

Answer:

(60 ÷ 10) + (12 – 8)^{2 }= 22.

Explanation:

Given that the expression is (60 ÷ 10) + (12 – 8)^{2}

= 6 + (4)^{2}

= 6 + 16

= 22.

Question 7.

12 + (4 × 5) × 8

Answer:

12 + (4 × 5) × 8 = 172.

Explanation:

Given that the expression is 12 + (4 × 5) × 8

= 12 + (20) × 8

= 12 + 160

= 172.

Question 8.

2^{2} × 3^{2} + 6 – (8 × 4)

Answer:

2^{2} × 3^{2} + 6 – (8 × 4) = 10.

Explanation:

Given that the expression is 2^{2} × 3^{2} + 6 – (8 × 4)

= 2^{2} × 3^{2} + 6 – 32

= 4 × 9 + 6 – 32

= 36 + 6 – 32

= 42 – 32

= 10.

**Simplify each expression.**

Question 9.

{[3(5 + 5) + 25] × 2}

Simplify inside the parentheses: ________________________

Simplify inside the brackets: _______________

Simplify inside the braces: _________

{[3(5 + 5) + 25] × 2) = _________

Answer:

Simplify inside the parentheses: [3(10) + 25] × 2

Simplify inside the brackets: [30 + 25] × 2

Simplify inside the braces: 55 × 2

{[3(5 + 5) + 25] × 2) = 110.

Explanation:

Given the expression is {[3(5 + 5) + 25] × 2} . So first we will solve inside parentheses which is

[3(10) + 25] × 2, now we will solve the exponents which is [30 + 25] × 2

= 55 × 2

= 110.

Question 2.

3{[2(4 + 5) + 8] – 20}

Simplify inside the parentheses: __________

Simplify inside the brackets: __________

Simplify inside the braces: _________

3{[2(4 + 5) + 8] – 20} = _________

Answer:

Simplify inside the parentheses: 3{[2(9) + 8] – 20}

Simplify inside the brackets: 3{[18 + 8] – 20}

Simplify inside the braces: 3{6}

3{[2(4 + 5) + 8] – 20} = 18.

Explanation:

Given the expression is 3{[2(4 + 5) + 8] – 20}. So first we will solve inside parentheses which is

3{[2(9) + 8] – 20}, now we will solve the exponents which is 3{[18 + 8] – 20}

= 3{[26] – 20}

= 3{26 – 20}

= 3{6}

= 18.

Question 11.

[(10 × 3 + 4) ÷ 17]^{2}

Simplify inside the parentheses: __________

Simplify inside the brackets: __________

[(10 × 3 + 4) ÷ 17]^{2} = _________

Answer:

Simplify inside the parentheses: [(30 + 4) ÷ 17]^{2}

Simplify inside the brackets: [(34) ÷ 17]^{2}

[(10 × 3 + 4) ÷ 17]^{2} = 4

Explanation:

Given the expression is [(10 × 3 + 4) ÷ 17]^{2}. So first we will solve inside parentheses which is

[(30 + 4) ÷ 17]^{2},now we will solve the exponents which is [(34) ÷ 17]^{2} =

= [2]^{2}

= 4.

**Write an expression for each description.**

Question 12.

Multiply 4 times 2 squared, and then subtract the product from 15.

Answer:

15 – (4×4) = 1.

Explanation:

Here, we need to multiply 4 times 2 squared which is 4×4 = 16. And then we need to subtract the product from 15 which is 15-16 = -1.

Question 13.

Divide 36 by 6, and then subtract the quotient from 54.

Answer:

54 – (36÷6) = 48.

Explanation:

Here, we need to divide 36 by 6 which is 36÷6 = 6. And then subtract the quotient from 54 which is 54-6 = 48.

Question 14.

Multiply 7 squared by the difference between 8 and 6.

Answer:

(8-6) × 7^{2} = 98.

Explanation:

Here, we need to multiply 7 squared by the difference between 8 and 6 which is (8-6) × 7^{2} =which is 2 × 49 = 98.

Question 15.

Find the product of 12 and 15, and then add 3

Answer:

(12×15) + 3 = 183.

Explanation:

The product of 12 and 15 is 12×15 = 180 and then add 3 which is 180 + 3 = 183.

**Write a description for each expression.**

Question 16.

(4 + 2)^{2} – 16

Answer:

(4 + 2)^{2} – 16 = 20.

Explanation:

Given the expression is (4 + 2)^{2} – 16 which is (6)^{2} – 16

= 36 – 16

= 20.

Question 17.

8 × (6 × 7) – 50

Answer:

8 × (6 × 7) – 50 = 286.

Explanation:

Given the expression is 8 × (6 × 7) – 50 which is

= 8 × (42) – 50

= 336 – 50

= 286.

Question 18.

48 – 3^{2} × 2^{2}

Answer:

48 – 3^{2} × 2^{2} = 12.

Explanation:

Given the expression is 48 – 3^{2} × 2^{2} which is

= 48 – 3^{2} × 2^{2})

= 48 – 9 × 4

= 48 – 36

= 12.

Question 19.

7 × (9 × 2) – 2^{2}

Answer:

7 × (9 × 2) – 2^{2} = 122.

Explanation:

Given the expression is 7 × (9 × 2) – 2^{2 }which is

= 7 × (18) – 4

= 126 – 4

= 122.

**Solve.**

Question 20.

(150 – 25) – (25 – 5^{2})

Answer:

(150 – 25) – (25 – 5^{2}) = 125.

Explanation:

Given that the expression is (150 – 25) – (25 – 5^{2}) which is

= (125) – (25 – 25)

= 125 – 0

= 125.

Question 21.

{[4 × (17 × 8) + 27] × 4}

Answer:

{[4 × (17 × 8) + 27] × 4} = 2,284.

Explanation:

Given that the expression is {[4 × (17 × 8) + 27] × 4} which is

= {[4 × (136) + 27] × 4}

= {[544 + 27] × 4}

= 571 × 4

= 2,284.

**Solve.**

Question 22.

Elizbeth needs to find the missing number in the following series.

0.459, 0.859, ____, 1.659, 2.059

What is the missing number?

Answer:

0.459, 0.859, 1.259, 1.659, 2.059.

Explanation:

Given that the series is 0.459, 0.859, ____, 1.659, 2.059. As the series follows by adding 0.4 to the numbers. So the missing digit is 0.859+0.4 which is 1.259. So the series is 0.459, 0.859, 1.259, 1.659, 2.059.

Question 23.

Twins Don and Dan are working together to solve a math problem. Don finds the answer and tells

Dan: “Square the sum of 6 plus 2, and then subtract 30.” Write the numerical expression that matches Don’s directions.

Answer:

(6+2)^{2 }– 30 = 34.

Explanation:

Given that Dan Squares the sum of 6 plus 2 which is (6+2)^{2}

= 8^{2}

= 64, and then subtract 30 which is

= 64 – 30

= 34.

Question 24.

A gallon of fat-free milk costs $3.99. A year ago, the gallon of milk cost 3 percent (0.03) less. How much did a gallon of milk cost a year ago?

Answer:

The cost of a gallon of milk a year ago is $3.87.

Explanation:

Given that a gallon of fat-free milk costs $3.99. A year ago, the gallon of milk cost 3 percent (0.03) less. So the cost of a gallon of milk a year ago is 3.99×3 which is = 11.97 ÷ 100 = 0.12. So 3.99-0.12 = $3.87.

Question 25.

Devon works a total of 21 hours on Friday, Saturday, and Sunday. He works twice as many hours on Sunday as he does on Saturday. He works 6 hours on Friday. How many hours does he work on Saturday?

Answer:

The number of hours he works on Saturday is 5 hours.

Explanation:

Given that Devon works a total of 21 hours on Friday, Saturday, and Sunday, he works twice as many hours on Sunday as he does on Saturday. As he works 6 hours on Friday, so the number of hours does he work on Saturday is. Let the Saturday hours be X and the Sunday hours will be 2X. So 2X+X+6 = 21 which is

3X+6 = 21

3X = 21 – 6

3X = 15

X = 15÷3

= 5.

So the number of hours he works on Saturday is 5 hours.