Order of Operations - Integers
Please Excuse My Dear Aunt Sally:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
When you have a problem with parentheses, multiplication, addition, etc. It is often difficult to decide what part to calculate first.
PEMDAS stands for Please Excuse My Dear Aunt Sally (as seen above). It is an acronym used to remind us of the order of operations.
Parentheses first, for example:
5 + (7 + 8)
= 5 + (15)
= 20
Hint: Absolute value bars are treated like parentheses considering they are evaluated first.
Exponents, including powers and roots, first. Then multiply, divide, add or subtract:
10 x 8²
=10 x 64
= 640
Multiplication/division is completed before addition or subtraction:
7 x 4 - 5
= 28 - 5
= 23
Hint: Multiplication and division rank equally so you would just go from left to right if you had a problem with both:
Problem 1
49 / 7 x 2 / 2
Step 1
Right to left:
49 / 7
= 7
Step 2
7 x 2 / 2
Right to left:
7 x 2
= 14
Step 3
14 / 2
= 7
Answer: 7
Problem 2
(-5 + 8) x 7 + 3 x 2²
Step 1
Complete operations inside the parentheses first:
(-5 + 8)
= 8 - 5
= 3
Step 2
Use exponents:
2²
= 4
Now we have:
3 x 7 + 3 x 4
Step 3
Multiply:
3 x 7
= 21
3 x 4
= 12
Step 4
Add:
21 + 12
= 33
Answer: 33
