How to Use Order of Operations

How to Use Order of Operations

The order of operations rules shows which operation to perform first to evaluate a given mathematical expression.

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Step by step guide to using order of operations

When there is more than one math operation in an expression, use PEMDAS: (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 – Example 1:

Solve. \((2 \ + \ 4) \ \div \ (2^{2} \ \div \ 4)=\)

Solution:

First simplify inside parentheses: \((6) \ \div \ (4 \ \div \ 4)=(6) \ \div \ (1) =\)
Then: \( (6) \ \div \ (1) =6\)

Order of Operations – Example 2:

Solve. \((9 \ \times \ 6) \ – \ (10 \ – \ 6)=\)

Solution:

First simplify inside parentheses: \((9 \ \times \ 6) \ – \ (10 \ – \ 6)=(54) \ – \ (4)\)
\( (54) \ – \ (4) =50\)

Order of Operations – Example 3:

Solve. \((5+7)÷(3^2÷3)=\)

Solution:

First simplify inside parentheses: \((12)÷(9÷3)=(12)÷(3)=\)
Then: \((12)÷(3)=4\)

Order of Operations – Example 4:

Solve. \((11×5)-(12-7)=\)

Solution:

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

Exercises for Using 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

This image has an empty alt attribute; its file name is answer-3.png

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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