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Basic Operations

Basic Operations

At a Glance - Order of Operations

The order in which we complete a mathematical equation or expression is essential. Doing the steps of a problem out of order can lead to a totally different answer, even if you do the calculations correctly. So, for everyone to get the same answer, the order of operations was developed. You will be using these almost every day of your mathematical careers from now on.

All equations and expressions must be completed in the following order...


  • Parentheses - simplify everything inside the parentheses
  • Exponents - simplify any exponents (See Powers and Roots) 
  • Multiplication & Division - multiply and divide from left to right
  • Addition & Subtraction - add and subtract from left to right

PEMDAS will be your friend for life. If you have trouble remembering your new BFF's name, try out this memory trick... "Please Excuse My Dear Aunt Sally".

Look Out: even though M comes before D, multiplication and division are equals; you'll need to complete these operations from left to right. The same is true for addition and subtraction. Think of them as equal partners.

Order of Operations Example 1

5 - 3 + 6 ÷ 2

Since there are no parentheses or exponents, division is our first step.

Order of Operations Example 2

5(6 + 9 ÷ 3 - 1)^2

First, simplify the parentheses. Since there are many operations in the parentheses, follow the order of operations inside them, too. In this problem, division would come first.

Order of Operations Example 3

(12 + 3 x 2)/(4^2 - 7)

In this problem, treat the numerator and denominator like they are in separate parentheses, and the fraction bar as a division sign. You could rewrite this problem as: (12 + 3 x 2) / (4^2 - 7) . Now simplify each set of parentheses using the correct order of operations.

Order of Operations Example 4

[3(6 - 4)]^2

Here, we have two sets of parentheses, the regular ones and the brackets. Simplify the innermost set first.

Order of Operations Exercise 1

100 - 3(6 - 5 +1)^3

Order of Operations Exercise 2

7 + 4(28 - 5^2 - 3)

Order of Operations Exercise 3

(15 - 10 + 3) / (1 +1)^2

Order of Operations Exercise 4

[7(5 + 2) - (5 x 8)]^2

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