# 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”.)

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right

### Example 1:

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

Solution:

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

### Example 2:

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

Solution:

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

### Example 3:

Solve. $$(5+7)÷(3^2÷3)=$$

Solution:

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

### Example 4:

Solve. $$(11×5)-(12-7)=$$

Solution:

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

## Exercises

### 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. $$\color{blue}{50}$$