➕ Algebra 1 · Equations
Order of Operations cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The ladder (top to bottom)
- 1. Grouping: ( ) [ ] { } | | and fraction bars, innermost first
- 2. Exponents
- 3. × and ÷, left to right
- 4. + and −, left to right
Ties
- × and ÷ share a level: left to right
- + and − share a level: left to right
- 48 ÷ 6 × 2 = 8 × 2 = 16
Awkward cases
- −52 = −25 but (−5)2 = 25
- A fraction bar groups the top and the bottom
- Substitute negative values in parentheses
- Dividing by a group that equals 0 is undefined
Worked example
- 9 + 4 × 6 − 8 ÷ 2
- = 9 + 24 − 4 (× and ÷ first)
- = 33 − 4 = 29 (+ and − left to right)
Formulas
- The ladder: Grouping, then exponents, then × and ÷ (left to right), then + and − (left to right)
- Minus sign and exponent: −a2 = −(a2), but (−a)2 = a2
- Fraction bar: A fraction bar with top a + b and bottom c + d means (a + b) ÷ (c + d), when c + d ≠ 0
Order of Operations cheat sheet from HighSchoolQ.com, for personal study use.