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}