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.
27 + 2           Add.
29

Name the operation that should be done first.

Question 1.
a. 7 × 3 + 2 ____________
Answer:
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 _____________
Answer:
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 _______________
Answer:
add.

Explanation:
In the above given equation, 4 + 3 – 5
the first operation is addition.
4 + 3 = 7
then subtract, 7 – 5 = 2
So, 4 + 3 – 5 = 2

Question 2.
a. 8 – 6 + 4 _______________
Answer:
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 _______________
Answer:
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 ______________
Answer:
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) ______________
Answer:
add.

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

b. (5 – 3) ÷ 2 ______________
Answer:
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 _______________
Answer:
add.

Explanation:
In the above given equation, (2 + 5) × 3
the first operation is addition.
(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) _____________
Answer:
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 _______________
Answer:
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 ______________
Answer:
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 ______________
Answer:
8

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

Question 6.
a. 15 ÷ 3 + 16 ÷ 4 ________________
Answer:
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 _______________
Answer:
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 _______________
Answer:
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) ________________
Answer:
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 ________________
Answer:
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 _______________
Answer:
2

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

Question 9.
a. (7 – 3) × 2 ______________
Answer:
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) ______________
Answer:
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 ______________
Answer:
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) _______________
Answer:
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) _______________
Answer:
1

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

b. (8 – 5) + 2 _______________
Answer:
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) _______________
Answer:
32

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

b. (4 × 3) + (4 × 3) _____________
Answer:
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) = _____________
Answer:
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 = ______________
Answer:
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) = _______________
Answer:
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 = _______________
Answer:
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 = ______________
Answer:
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) = ______________
Answer:
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 = ________________
Answer:
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) = ________________
Answer:
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] = _______________
Answer:
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 = ________________
Answer:
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 = ________________
Answer:
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) = ______________
Answer:
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 = ________________
Answer:
3

Explanation:
In the above given equation, 7 ÷ (10 + 3 – 6) + 2
the first operation is addition.
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} = _______________
Answer:
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.
the first operation is addition.
(2 + 7) = 9
then divide, 9 ÷ 3 = 3
then multiply, 3 x 12 = 36
finally subtract, 60 – 36 = 24
So, 60 – {[(2 + 7) ÷ 3] × 12}

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