Lesson 5: Order of Operations, Part 1

Definition

A set of rules determining the sequence for solving expressions. Operations are performed left-to-right, but parentheses indicate which part to solve first.

What’s next

This lesson introduces the foundational rules for sequencing. You'll apply these principles in worked examples with addition, subtraction, multiplication, and division.

Property

When there is more than one addition or subtraction step within a problem, we take the steps in order from left to right.

Examples

$20 - 8 - 2 = 12 - 2 = 10$

$15 + 5 - 10 = 20 - 10 = 10$

Property

When there is more than one multiplication or division step within a problem, we take the steps in order from left to right.

Examples

$24 \div 6 \times 2 = 4 \times 2 = 8$

$100 \div 10 \div 2 = 10 \div 2 = 5$

Property

If a different order of steps is desired, parentheses are used to show which step is taken first.

Examples

$20 - (8 - 2) = 20 - 6 = 14$

$100 \div (10 \div 2) = 100 \div 5 = 20$

Property

For addition: $(a + b) + c = a + (b + c)$
For multiplication: $(a \times b) \times c = a \times (b \times c)$

Examples

$(7 + 3) + 5 = 10 + 5 = 15$ is the same as $7 + (3 + 5) = 7 + 8 = 15$.

$(4 \times 5) \times 2 = 20 \times 2 = 40$ is the same as $4 \times (5 \times 2) = 4 \times 10 = 40$.