#### Solved Examples and Worksheet for Evaluating Numerical Expressions

Q1Which operation should be performed first to evaluate 4 + 6 ÷ 8 - 3 ?

A. Subtraction
B. Division
D. None of the above

Step: 1
Among division, addition and subtraction, division has the highest priority.
Step: 2
Division should be performed first to evaluate the expression.
Q2Which operation would you perform first to evaluate 33 ÷ 5 × (6 + 7)?
B. Division
C. Multiplication
D. Subtraction

Step: 1
Operation within the parentheses should be done first.
Step: 2
Q3What is the value of the expression 17 - (2 × 6)?

A. 6
B. 8
C. 5
D. 7

Step: 1
The order of operation for the expression is, operation within grouping symbols first and then subtraction, from left to right.
Step: 2
17 - (2 × 6)
[Original expression.]
Step: 3
= 17 - 12
[Multiply 2 and 6.]
Step: 4
= 5
[Subtract 12 from 17.]
Step: 5
The value of the expression is 5.
Q4What is the value of the expression below?
20 - (5 × 4) + 4

A. 4
B. 2
C. 1
D. 3

Step: 1
The order of operation for the expression is, operation within grouping symbol first, addition next and then subtraction, from left to right.
Step: 2
20 - (5 × 4) + 4
[Original expression.]
Step: 3
= 20 - 20 + 4
[Do the operation within the grouping symbol.]
Step: 4
= 24 - 20
Step: 5
= 4
[Subtract 20 from 24.]
Step: 6
The value of the expression is 4.
Q5Which operation do you perform first in the expression?
3 × 2 - 9

A. Subtraction
C. none of these
D. Multiplication

Step: 1
The expression has two operations, multiplication and subtraction.
Step: 2
Of these two, multiplication has a higher priority.
Step: 3
Multiplication is performed first in the expression.
Q6Simplify the expression 49 ÷ (2 + 5) - (2 + 5).

A. 0
B. - 1
C. 1
D. 2

Step: 1
49 ÷ (2 + 5) - (2 + 5)
[Original Expression.]
Step: 2
= 49 ÷ 7 - 7
[Add within the parentheses from left to right.]
Step: 3
= 7 - 7
[Divide.]
Step: 4
= 0
[Subtract.]
Step: 5
The value of the expression is 0.
Q7Simplify:
3 × 5 - 12 ÷ 4 + 7

A. 21
B. 19
C. 17
D. 23

Step: 1
The order of operation for the expression is division first, multiplication next and then addition and subtraction, in the order from left to right.
Step: 2
3 × 5 - 12 ÷ 4 + 7
[Original expression.]
Step: 3
= (3 × 5) - (124) + 7
[Group the operations in order.]
Step: 4
= 15 - 3 + 7
[Work inside the grouping symbols.]
Step: 5
= 12 + 7
[Subtract 3 from 15.]
Step: 6
= 19
Q8Simplify:
905 + 36 × 30 ÷ 6 - 5

A. 1044
B. 1074
C. 1086
D. 1080

Step: 1
The order of operation for the expression is division first, multiplication next and then addition and subtraction, in the order from left to right.
Step: 2
905 + 36 × 30 ÷ 6 - 5
[Original expression.]
Step: 3
= 905 + 36 × (30 ÷ 6) - 5
[Group the operation in order.]
Step: 4
= 905 + 36 × 5 - 5
[Divide inside the grouping symbols.]
Step: 5
= 905 + (36 × 5) - 5
[Group the operation in order.]
Step: 6
= 905 + 180 - 5
[Multiply inside the grouping symbols.]
Step: 7
= 1085 - 5
Step: 8
= 1080
[Subtract.]
Q9Find the value of the expression 5 + 6 × 7.
A. 47
B. 77
C. 46
D. 78

Step: 1
The order of operation for the expression is, multiplication first and then addition.
Step: 2
5 + 6 × 7
[Original expression.]
Step: 3
= 5 + 42
[Multiply.]
Step: 4
= 47
Q10What is the value of the expression 41 - (4 × 8) ?
A. 13
B. 5
C. 9
D. None of the above

Step: 1
The order of operation for the expression is, operation within grouping symbol first and then subtraction, from left to right.
Step: 2
41 - (4 × 8)
[Original expression.]
Step: 3
= 41 - 32
[Multiply 4 and 8.]
Step: 4
= 9
[Simplify.]
Step: 5
The value of the expression is 9.
Q11Use the order of operations to find the values of the following expressions.
13 + 7 × 2 + 10 =

A. 50
B. 240
C. 136
D. 97
E. 37

Step: 1
13 + 7 × 2 + 10
[Original numerical expression.]
Step: 2
= 13 + (7 × 2) + 10
Step: 3
= 13 + 14 + 10
[Multiply 7 and 2.]
Step: 4
= 37