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

Follow the directions to simplify each expression.

Question 1.
(15 – 5)3 – (20 × 5) × (8 – 4) + 102 =
simplify inside parentheses: _____
____________________
Simplify exponents: ____________
Multiply: ___________
Add and subtract from left to right: ___________
simplify inside parentheses: (10)3 – (100) × (4) + 102
Simplify exponents: 1000 – 100 × 4 + 100
Multiply: 1000 – 400 + 100
Add and subtract from left to right: 1000 – 500

Explanation:
Given the expression is(15 – 5)3 – (20 × 5) × (8 – 4) + 102 . So first we will solve inside parentheses which is
(10)3 – (100) × (4) + 102 , now we will solve the exponents which is
= (10)3 – (100) × (4) + 102
= 1000 – 100 × 4 + 100
= 1000 – 400 + 100
= 1000 – 500
= 500.

Question 2.
(30 × 5) × (6 – 2) + (10 – 5)2 – 101 =
simplify inside parentheses: _____
____________________
Simplify exponents: ____________
Multiply: ___________
Add and subtract from left to right: ___________
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

Explanation:
Given the expression is (30 × 5) × (6 – 2) + (10 – 5)2 – 101  . 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) ÷ 32
(7 × 3) ÷ 32 = 2$$\frac{1}{3}$$.

Explanation:
Given that the expression is
(7 × 3) ÷ 32
= 21 ÷ 32
= 21 ÷ 9
= 7 ÷ 3
= 2$$\frac{1}{3}$$.

Question 4.
5 + 22 × (5 × 2) ÷ 5
5 + 22 × (5 × 2) ÷ 5 = 13.

Explanation:
Given that the expression is 5 + 22 × (5 × 2) ÷ 5
= 5 + 4 × 10 ÷ 5
= 5 + 4 × 2
= 5 + 8
= 13.

Question 5.
(52 + 9) – 14
(52 + 9) – 14 = 47.

Explanation:
Given that the expression is (52 + 9) – 14
= 61 – 14
= 47.

Question 6.
(60 ÷ 10) + (12 – 8)2
(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
12 + (4 × 5) × 8 = 172.

Explanation:
Given that the expression is 12 + (4 × 5) × 8
= 12 + (20) × 8
= 12 + 160
= 172.

Question 8.
22 × 32 + 6 – (8 × 4)
22 × 32 + 6 – (8 × 4) = 10.

Explanation:
Given that the expression is 22 × 32 + 6 – (8 × 4)
= 22 × 32 + 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) = _________
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} = _________
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{ – 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 = _________
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
= 4.

Write an expression for each description.

Question 12.
Multiply 4 times 2 squared, and then subtract the product from 15.
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.
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.
(8-6) × 72 = 98.

Explanation:
Here, we need to multiply 7 squared by the difference between 8 and 6 which is (8-6) × 72 =which is 2 × 49 = 98.

Question 15.
Find the product of 12 and 15, and then add 3
(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
(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
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 – 32 × 22
48 – 32 × 22 = 12.

Explanation:
Given the expression is 48 – 32 × 22 which is
= 48 – 32 × 22)
= 48 – 9 × 4
= 48 – 36
= 12.

Question 19.
7 × (9 × 2) – 22
7 × (9 × 2) – 22 = 122.

Explanation:
Given the expression is 7 × (9 × 2) – 22 which is
= 7 × (18) – 4
= 126 – 4
= 122.

Solve.

Question 20.
(150 – 25) – (25 – 52)
(150 – 25) – (25 – 52) = 125.

Explanation:
Given that the expression is (150 – 25) – (25 – 52) which is
= (125) – (25 – 25)
= 125 – 0
= 125.

Question 21.
{[4 × (17 × 8) + 27] × 4}
{[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?
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.
(6+2)2 – 30 = 34.

Explanation:
Given that Dan Squares the sum of 6 plus 2 which is (6+2)2
= 82
= 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?