Lesson 3: Write and Evaluate Numerical Expressions

Property

Step 1. Parentheses and Other Grouping Symbols
Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
Step 2. Exponents
Simplify all expressions with exponents.
Step 3. Multiplication and Division
Perform all multiplication and division in order from left to right. These operations have equal priority.
Step 4. Addition and Subtraction
Perform all addition and subtraction in order from left to right. These operations have equal priority.

Examples

• To simplify $30 - 5 \cdot 4$, we perform multiplication first: $30 - 20 = 10$.
• In the expression $(3+2)^2 \div 5$, we start with parentheses $(5)^2 \div 5$, then the exponent $25 \div 5$, and finally division to get $5$.
• For $4 + 2[10 - 3(2)]$, we work inside the innermost parentheses first: $4 + 2[10 - 6]$, then inside the brackets $4 + 2[4]$, then multiply $4 + 8$, and finally add to get $12$.

Explanation

The order of operations (PEMDAS) is a set of rules everyone follows to solve math problems. This ensures that every expression has only one correct answer, preventing confusion and making sure our calculations are consistent.

Property

The standard order of operations (PEMDAS/GEMDAS) applies when evaluating numerical expressions that include fractions and decimals. The steps are followed in this order:

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

Examples