Lesson 3: Order of Operations

Property

The term expression means a “phrase that makes sense” made up of numbers, letters, and operations.
A numeric expression is made up of numbers and arithmetic operations.
Two numeric expressions are equivalent if they compute the same number.

Examples

• Evaluate $10 + 4 \cdot 2$. Multiplication comes first: $4 \cdot 2 = 8$. Then add: $10 + 8 = 18$.
• Evaluate $(10 + 4) \cdot 2$. Parentheses come first: $10 + 4 = 14$. Then multiply: $14 \cdot 2 = 28$.
• Show that $3 \cdot 6 + 3 \cdot 2$ is equivalent to $3 \cdot (6 + 2)$. The first expression is $18 + 6 = 24$. The second is $3 \cdot 8 = 24$. Since they both equal 24, they are equivalent.

Explanation

Think of a numeric expression as a recipe. The numbers are your ingredients and the operations $(+, -, \cdot, \div)$ are your cooking steps. Parentheses tell you which steps to do first to get the right delicious result!

Property

When evaluating numerical expressions with exponents, follow the order of operations: exponents are calculated before multiplication, division, addition, and subtraction (unless parentheses indicate otherwise).
For expressions with multiple operations, compute exponents first, then proceed with multiplication and division from left to right, followed by addition and subtraction from left to right.

Examples

Property

PEMDAS is the acronym for the order of operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Follow these steps systematically:
1) Evaluate expressions inside parentheses first;
2) Calculate exponents;
3) Perform multiplication and division from left to right;
4) Perform addition and subtraction from left to right.

Examples