Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 7 Lesson 7.3 The Order of Operations **regularly and improve your accuracy in solving questions.

## 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.

- Do all operations within parentheses.
- Do all multiplication and division in order, from left to right.
- 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}