Order of Operation
Teacher
Order of Operation
Number and Operations: Understand numbers, ways of representing numbers,
relationships among numbers, and number systems.
7.N.1.5 Simplify numerical expressions using order of operations
7.N.2.1 Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions,
terminating decimals) and take positive rational numbers to whole-number powers.
When teaching order of operations, make sure the students understand that mathematic
problems must be completed in a specific order of sequence. If they are not, the problem
will be incorrect. Remind students that expressions do not have an equal sign.
ERROR: The most common error students make is to solve multiplication before division
and addition before subtraction regardless of where it fits in the equation. These are
inverse operations and are to be performed at the same step whichever one comes first
from left to right in the equation.
This is the order or “steps” to solve these problems:
First: do whatever is in parenthesis
Second: solve all exponents
Third: multiplication or division, whichever comes first reading from left to right
Fourth: addition or subtraction, whichever comes first reading from left to right
PEMDAS is a helpful acronym to remind students of the order of operation, but be sure
to remind them to be careful when it comes to the inverse operations.
Teacher Sample:
4 + 2(13-4) ÷ 3²
First: Do any part of the problem in parenthesis
4 + 2(13-4) ÷ 3² …… 4 + 2(9) ÷ 3²
Second: Exponents
4 + 2(9) ÷ 3² ……. 4 + 2(9) ÷ 9 (remind students 3² is 3x3 NOT 3x2)
Third: Multiply or divide from left to right
4 + 2(9) ÷ 9 …… 2 x 9 comes before 9 ÷ 9 …… 4 + 18 ÷ 9
4 + 18 ÷ 9 …… 4 + 2
Fourth: Add or subtract from left to right
4+2=6
Teacher
Samples:
1. 10 + 7 · 8² ÷ 2
2. 8 · 9 – (2 +3)²
3. 50 ÷ 5² · 13
4. (7-4) ²
Teacher
Samples: Answers
5. 10 + 7 · 8² ÷ 2 = 234
6. 8 · 9 – (2 +3)² = 47
7. 50 ÷ 5² · 13 = 26
8. (7-4) ² = 9
Student Practice
1. Choose the correct order of operations needed to evaluate the following
expression:
22 – 6 · (4+7)
A.
B.
C.
D.
Multiply 6 by 4. Add the product to 7. Subtract the sum from 22.
Add 4 and 7. Subtract 6 from 22. Multiply the difference by 6.
Subtract 6 from 22. Add 4 and 7. Multiply the difference by the sum.
Add 4 and 7. Multiply the sum by 6. Subtract the product from 22.
2. Simplify the expression below:
6 + 2(11-2) ÷ 3²
E.
F.
G.
H.
7
6
2
8
Simplify the following expressions:
3. (-3)³
4. (5-4)² + 7
5. 2(0.3 + 0.7) + 3(0.02 + 0.18)
6. What is the value of the expression
below when n = -5
A.
B.
C.
D.
-8
-2
2
8
7. Use the expression below to answer Parts A and B.
30 - 20 ÷ 4 · 3
A. Which operation should be performed first when simplifying the expression? Use
words, numbers or diagrams to justify your answer.
B. What is the value of the expression? Use words, numbers, or diagrams to justify
your answer.
C. Create an expression that includes the following:


Uses all 4 basic operations ( +, -, ·, ÷) only once and in any order
Contains only one exponent

Contains only single-digit numbers without having a number repeated
Be sure to give the value of your expression.
Student Practice Answers
1. Choose the correct order of operations needed to evaluate the following
expression:
22 – 6 · (4+7)
a.
b.
c.
d.
Multiply 6 by 4. Add the product to 7. Subtract the sum from 22.
Add 4 and 7. Subtract 6 from 22. Multiply the difference by 6.
Subtract 6 from 22. Add 4 and 7. Multiply the difference by the sum.
Add 4 and 7. Multiply the sum by 6. Subtract the product from 22.
The answer is D. Parenthesis, multiplication, then subtraction.
2. Simplify the expression below:
6 + 2(11-2) ÷ 3²
a.
b.
c.
d.
7
6
2
8
The answer is D. 8
Simplify the following expressions:
3. (-3)³
4. (5-4)² + 7
5. 2(0.3 + 0.7) + 3(0.02 + 0.18)
6. What is the value of the expression
below when n = -5
-(n + 3)
E. -8
F. -2
G. 2
H. 8
- (-5 + 3)
- (-2)
2 G is the correct answer
7. Use the expression below to answer Parts A and B.
30 - 20 ÷ 4 · 3
A. Which operation should be performed first when simplifying the expression? Use
words, numbers or diagrams to justify your answer.
Order of operation states we do multiply and divide first from left to right, so we
would start with 20 divided by 4
B. What is the value of the expression? Use words, numbers, or diagrams to justify
your answer.
30 – 20 / 4 · 3
30 – 5 · 3
30 – 15
15
C. Create an expression that includes the following:


Uses all 4 basic operations ( +, -, ·, ÷) only once and in any order
Contains only one exponent

Contains only single-digit numbers without having a number repeated
Be sure to give the value of your expression.
An example would be:
5 + 10/2 · 3² - 7
43