How to Use Order of Operations? (+FREE Worksheet!)

The order of operations rules shows which operation to perform first to evaluate a given mathematical expression. One of the most confusing tasks in the world is solving math exercises for someone who does not know the order of operations. You may have experienced situations where you do not know how to solve multiplication or addition in a simple mathematical expression. You may think to yourself that it makes no difference, But you are mistaken. For this reason, in this article, we intend to teach you how to solve mathematical expressions using the order of operation.

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Related Topics

• How to Add and Subtract Integers
• How to Multiply and Divide Integers
• How to Order Integers and Numbers
• How to Solve Integers and Absolute Value Problems

Step-by-step guide to using order of operations

• Step 1: In any equation, the numbers in parentheses must be calculated first. Whatever the operation, it is first simplified in parentheses.
• Step 2: The exponents are in second place. In any equation where there are exponential numbers, if there are no parentheses, you count them first.
• Step 3: The third priority in the equation is multiplication and division (from left to right).
• Step 4: The fourth priority is addition and subtraction (from left to right).

You also can use PEMDAS to memorize better the order of operations: (to memorize this rule, remember the phrase “Please Excuse My Dear Aunt Sally”.)

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Order of Operations For education statistics and research, visit the National Center for Education Statistics.

Order of Operations – Example 1:

Solve. \((2 \ + \ 4) \ \div \ (2^{2} \ \div \ 4)=\) For additional educational resources, visit the U.S. Department of Education website.

Solution: For additional educational resources, visit the U.S. Department of Education website.

First simplify inside parentheses: \((2+4=6\)), \((2^{2} \ \div \ 4=4 \ \div\ 4=1\)),
Then: \( (6) \ \div \ (1) =6\) For additional educational resources, visit the U.S. Department of Education website.

Order of Operations – Example 2:

Solve. \((9 \ \times \ 6) \ – \ (10 \ – \ 6)=\) For additional educational resources, visit the U.S. Department of Education website.

Solution: For additional educational resources, visit the U.S. Department of Education website.

First simplify inside parentheses: \((9 \ \times \ 6=54), (10 \ – \ 6=4\)),
Then: \( (54) \ – \ (4) =50\) For additional educational resources, visit the U.S. Department of Education website.

Order of Operations – Example 3:

Solve. \((5+7)÷(3^2÷3)=\) For additional educational resources, visit the U.S. Department of Education website.

Solution: For additional educational resources, visit the U.S. Department of Education website.

First simplify inside parentheses: \((5+7=12\)), \((3^2 ÷ 3= 9 ÷ 3=3\)),
Then: \((12)÷(3)=4\) For additional educational resources, visit the U.S. Department of Education website.

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Order of Operations – Example 4:

Solve. \((11×5)-(12-7)=\)

Solution:

First simplify inside parentheses: \((11×5=55), (12-7=5)\),
Then: \((55)-(5)=50\)

Exercises for Using Order of Operations

Order of Operations

Evaluate each expression.

1. \(\color{blue}{(2 × 2) + 5}\)
2. \(\color{blue}{(12 + 2 – 5) × 7 – 1}\)
3. \(\color{blue}{(\frac{7}{5 – 1}) × (2 + 6) × 2}\)
4. \(\color{blue}{(7 + 11) ÷ (– 2)}\)
5. \(\color{blue}{(5 + 8) × \frac{3}{5} + 2}\)
6. \(\color{blue}{\frac{50}{4 (5 – 4) – 3}}\)

Download Order of Operations Worksheet

Answers

1. \(\color{blue}{9}\)
2. \(\color{blue}{62}\)
3. \(\color{blue}{28}\)
4. \(\color{blue}{-9}\)
5. \(\color{blue}{9.8}\)
6. \(\color{blue}{50}\)

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