# How to Use Order of Operations

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

## Step by step guide to use 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. $$\color{blue}{\frac{50}{4 (5 – 4) – 3}}$$

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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