# Spectrum Math Grade 5 Chapter 7 Lesson 3 Answer Key The Order of Operations

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## Spectrum Math Grade 5 Chapter 7 Lesson 7.3 The Order of Operations Answers Key

The order of operations is used to find the value of an expression with more than one operation.

1. Do all operations within parentheses.
2. Do all multiplication and division in order, from left to right.
3. Do all addition and subtraction in order, from left to right.

3 × (4 + 5) + 6 ÷ 3       Do the operation inside the parentheses.
3 × 9 + 6 ÷ 3          Multiply and divide from left to right.
29

Name the operation that should be done first.

Question 1.
a. 7 × 3 + 2 ____________
multiply.

Explanation:
In the above given equation, 7 × 3 + 2
the first operation is multiplication.
7 x 3 = 21
then add, 21 + 2 = 23
So, 7 x 3 + 2 = 23

b. 2 + 3 × 5 _____________
multiply.

Explanation:
In the above given equation, 2 + 3 × 5
the first operation is multiplication.
3 x 5 = 15
then add, 2 + 15 = 17
So, 2 + 3 x 5 = 17

c. 4 + 3 – 5 _______________

Explanation:
In the above given equation, 4 + 3 – 5
4 + 3 = 7
then subtract, 7 – 5 = 2
So, 4 + 3 – 5 = 2

Question 2.
a. 8 – 6 + 4 _______________
subtract.

Explanation:
In the above given equation, 8 – 6 + 4
the first operation is subtraction.
8 – 6 = 2
then add, 2 + 4 = 6
So, 8 – 6 + 4 = 6

b. 7 + 9 ÷ 3 _______________
divide.

Explanation:
In the above given equation, 7 + 9 ÷ 3
the first operation is division.
9 ÷ 3 = 3
then add, 7 + 3 = 10
So, 7 + 9 ÷ 3 = 10

c. 12 ÷ 3 × 5 ______________
divide.

Explanation:
In the above given equation, 12 ÷ 3 x 5
the first operation is division.
12 ÷ 3 = 4
then multiply, 4 x 5 = 20
So, 12 ÷ 3 x 5 = 20

Question 3.
a. (3 + 5) × (3 + 1) ______________

Explanation:
In the above given equation, (3 + 5) × (3 + 1)
(3 + 5) = 8
(3 + 1) = 4
then multiply, 8 x 4 = 32
So, (3 + 5) × (3 + 1) = 32

b. (5 – 3) ÷ 2 ______________
subtract.

Explanation:
In the above given equation, (5 – 3) ÷ 2
the first operation is subtraction.
(5 – 3) = 2
(3 + 1) = 4
then divide, 2 ÷ 2 = 1
So, (5 – 3) ÷ 2 = 1

c. (2 + 5) × 3 _______________

Explanation:
In the above given equation, (2 + 5) × 3
(2 + 5) = 7
then multiply, 7 x 3 = 21
So, (2 + 5) × 3 = 21

Find the value of each expression.

Question 4.
a. 5 × (5 – 3) _____________
10

Explanation:
Given,
5 × (5 – 3)
As, we know that Parentheses, brackets, and braces can be used to show that one part of a mathematical expression should be solved before the rest of the equation.
Calculate the numbers in parentheses first.
(5 – 3) = 2
Then calculate the next terms in the equation.
5 x 2 = 100

b. 5 + 4 × 3 ÷ 6 _______________
7

Explanation:
In the above given equation, 5 + 4 × 3 ÷ 6
the first operation is multiplication.
4 x 3 = 12
then divide, 12 ÷ 6 = 2
then add, 5 + 2 = 7
So, 5 + 4 × 3 ÷ 6 = 7

Question 5.
a. 20 – 4 × 3 ______________
8

Explanation:
In the above given equation, 20 – 4 × 3
the first operation is multiplication.
4 x 3 = 12
then subtract, 20 – 12 = 8
So, 20 – 4 × 3 = 8

b. (32 ÷ 8) × 2 ______________
8

Explanation:
In the above given equation, (2 + 5) × 3
(2 + 5) = 7
then multiply, 7 x 3 = 21
So, (2 + 5) × 3 = 21

Question 6.
a. 15 ÷ 3 + 16 ÷ 4 ________________
9

Explanation:
In the above given equation, 15 ÷ 3 + 16 ÷ 4
the first operation is division.
15 ÷ 3 = 5
16 ÷ 4 = 4
then add, 5 + 4 = 9
So, 15 ÷ 3 + 16 ÷ 4 = 9

b. 4 × 3 ÷ 6 – 1 _______________
1

Explanation:
In the above given equation, 4 × 3 ÷ 6 – 1
the first operation is multiplication.
4 x 3 = 12
then divide, 12 ÷ 6 = 2
finally subtract, 2 – 2 = 1
So, 4 × 3 ÷ 6 – 1 = 1

Question 7.
a. 20 ÷ 5 × 2 _______________
8

Explanation:
In the above given equation, 20 ÷ 5 × 2
the first operation is division.
20 ÷ 5 = 4
then multiply, 4 x 2 = 8
So, 20 ÷ 5 × 2  = 8

b. (7 × 8) – (4 × 9) ________________
20

Explanation:
In the above given equation, (7 × 8) – (4 × 9)
the first operation is multiplication.
(7 × 8) = 56
(4 × 9) = 36
then subtract, 56 – 36 = 20
So, (7 × 8) – (4 × 9) = 20

Question 8.
a. 6 × 5 – 5 × 4 ________________
10

Explanation:
In the above given equation, 6 × 5 – 5 × 4
the first operation is multiplication.
6 × 5 = 30
5 × 4 = 20
then subtract, 30 – 20 = 10
So, 6 × 5 – 5 × 4  = 10

b. 84 ÷ (8 + 6) ÷ 3 _______________
2

Explanation:
In the above given equation, 84 ÷ (8 + 6) ÷ 3
8 + 6 = 14
then division, 84 ÷ 14 = 6
6 ÷ 3 = 2
So, 84 ÷ (8 + 6) ÷ 3 = 2

Question 9.
a. (7 – 3) × 2 ______________
8

Explanation:
In the above given equation, (7 – 3) × 2
the first operation is subtraction.
(7 – 3) = 4
then multiply, 4 x 2 = 8
So, (7 – 3) × 2 = 8

b. 16 ÷ (8 – 6) ______________
8

Explanation:
In the above given equation, 16 ÷ (8 – 6)
the first operation is subtraction.
(8 – 6) = 2
then divide, 16 ÷ 2 = 8
So, 16 ÷ (8 – 6) = 8

Question 10.
a. (2 × 5) × 4 ______________
40

Explanation:
In the above given equation, (2 x 5) × 4
the first operation is multiplication.
(2 x 5) = 10
then multiply, 10 x 4 = 40
So, (2 x 5) × 4 = 40

b. 2 × (5 × 4) _______________
40

Explanation:
In the above given equation, 2 × (5 × 4)
the first operation is multiplication.
(5 × 4) = 20
then multiply, 20 x 2 = 40
So, 2 × (5 × 4) = 40

Question 11.
a. 8 – (5 + 2) _______________
1

Explanation:
In the above given equation, 8 – (5 + 2)
(5 + 2) = 7
then subtract, 8 – 7 = 1
So, 8 – (5 + 2) = 1

b. (8 – 5) + 2 _______________
5

Explanation:
In the above given equation, (8 – 5) + 2
the first operation is subtraction.
(8 – 5) = 3
then add, 3 + 2 = 5
So, (8 – 5) + 2  = 5

Question 12.
a. 4 × (5 + 3) _______________
32

Explanation:
In the above given equation, 4 × (5 + 3)
(5 + 3) = 8
then multiply, 4 x 8 = 32
So, 4 × (5 + 3) = 32

b. (4 × 3) + (4 × 3) _____________
24

Explanation:
In the above given equation, (4 × 3) + (4 × 3)
the first operation is multiplication.
(4 × 3) = 12
(4 × 3) = 12
then add, 12 + 12 = 24
So, (4 × 3) + (4 × 3) = 24

Find the value of each expression.

Question 1.
a. 9 ÷ 9 × (8 + 7) = _____________
15

Explanation:
In the above given equation, 9 ÷ 9 × (8 + 7)
the first operation is division.
9 ÷ 9 = 1
then add, 8 + 7 = 15
finally multiply, 1 x 15 = 15
So, 9 ÷ 9 × (8 + 7) = 15

b. 4 ÷ (8 – 6) ÷ 2 = ______________
1

Explanation:
In the above given equation, 4 ÷ (8 – 6) ÷ 2
the first operation is subtraction.
8 – 6 = 2
then divide, 4 ÷ 2 = 2
2 ÷ 2 = 1
So, 4 ÷ (8 – 6) ÷ 2 = 1

Question 2.
a. 10 ÷ 5 × (3 × 3) = _______________
18

Explanation:
In the above given equation, 10 ÷ 5 × (3 × 3)
the first operation is division.
10 ÷ 5 = 2
then multiply, 3 x 3 = 9
2 x 9 = 18
So, 10 ÷ 5 × (3 × 3) = 18

b. 10 + 8 ÷ 1 – 5 = _______________
13

Explanation:
In the above given equation, 10 + 8 ÷ 1 – 5
the first operation is division.
8 ÷ 1 = 8
then add, 10 + 8 = 18
finally subtract, 18 – 5 = 13
So, 10 + 8 ÷ 1 – 5 = 13

Question 3.
a. [4 + 1 + (2 × 2)] ÷ 3 = ______________
3

Explanation:
In the above given equation, [4 + 1 + (2 × 2)] ÷ 3
When a problem has a combination of parentheses, brackets, and braces, work the problem from the inside out.
So, the first operation is multiplication.
2 x 2 = 4
then add, 4 + 1 + 4 = 9
finally divide, 9 ÷ 3 = 3
So, [4 + 1 + (2 × 2)] ÷ 3 = 3

b. 1 × 2 × (4 – 2) = ______________
4

Explanation:
In the above given equation, 1 × 2 × (4 – 2)
the first operation is subtraction.
4 – 2 = 2
then multiply, 1 x 2 x 2 = 4
So, 1 × 2 × (4 – 2)  = 4

Question 4.
a. {10 – [(8 + 2) – 8]} × 2 = ________________
16

Explanation:
In the above given equation, {10 – [(8 + 2) – 8]} × 2
When a problem has a combination of parentheses, brackets, and braces, work the problem from the inside out.
So, the first operation is addition.
8 + 2 = 10
then subtraction, 10 – 8 = 2
10 – 2 = 8
finally multiply, 2 x 8 = 16
So, {10 – [(8 + 2) – 8]} × 2 = 16

b. 90 + 9 ÷ (3 × 3) = ________________
91
Explanation:
In the above given equation, 90 + 9 ÷ (3 × 3)
the first operation is multiplication.
3 x 3 = 9
then divide, 9 ÷ 9 = 1
finally add, 90 + 1 = 91
So, 90 + 9 ÷ (3 × 3) = 91

Question 5.
a. 10 ÷ [(1 + 5) ÷ 6] = _______________
10

Explanation:
In the above given equation, 10 ÷ [(1 + 5) ÷ 6]
When a problem has a combination of parentheses, brackets, and braces, work the problem from the inside out.
So, the first operation is addition.
(1 + 5) = 6
then divide, 6 ÷ 6 = 1
10 ÷ 1 = 10
So,10 ÷ [(1 + 5) ÷ 6] = 10

b. 5 + 4 – 3 + 9 = ________________
15

Explanation:
In the above given equation, 5 + 4 – 3 + 9
the first operation is subtraction.
4 – 3 = 1
then add, 5 + 1 + 9 = 15
So, 5 + 4 – 3 + 9 = 15

Question 6.
a. 4 + 1 + 6 – 4 = ________________
7

Explanation:
In the above given equation, 4 + 1 + 6 – 4
the first operation is subtraction.
6 – 4 = 2
then add, 4 + 1 + 2 = 7
So, 4 + 1 + 6 – 4 = 7

b. 2 × 2 ÷ (10 – 9) = ______________
4

Explanation:
In the above given equation, 2 × 2 ÷ (10 – 9)
the first operation multiplication.
2 x 2 = 4
then subtraction, 10 – 9 = 1
finally divide, 4 ÷ 1 = 4
So, 2 × 2 ÷ (10 – 9) = 4

Question 7.
a. 7 ÷ (10 + 3 – 6) + 2 = ________________
3

Explanation:
In the above given equation, 7 ÷ (10 + 3 – 6) + 2
10 + 3 = 13
then subtract, 13 – 6 = 7
then divide, 7 ÷ 7 = 1
finally add, 1 + 2 = 3
So, 7 ÷ (10 + 3 – 6) + 2 = 3

b. 60 – {[(2 + 7) ÷ 3] × 12} = _______________
24

Explanation:
In the above given equation, 60 – {[(2 + 7) ÷ 3] × 12}
When a problem has a combination of parentheses, brackets, and braces, work the problem from the inside out.