Comparing Fractions
Comparing fractions quickly is a core GRE skill, especially in Quantitative Comparison where the whole question is "which is bigger?". Three tools cover almost everything. (1) Cross-multiplication: for positive fractions, a/b vs c/d reduces to comparing a·d with b·c — bigger cross-product sits over the bigger fraction. (2) Common numerator: if the tops match, the fraction with the smaller denominator is larger (1/4 > 1/5). (3) Benchmarks: compare each to 1/2 or 1 to sort them at a glance — 5/9 is just over 1/2, 4/9 just under. Watch two traps: cross-multiplication's direction flips if a fraction is negative, and a fraction greater than 1 (like 7/6) beats any proper fraction outright. Reaching for the calculator to compare fractions is usually slower and can hide ties.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.
Formula Reference Sheet
Fraction operations
| Add / subtract | common denominator, then add numerators |
|---|---|
| Multiply | (a/b)(c/d) = ac/bd |
| Divide | (a/b) ÷ (c/d) = (a/b)(d/c) |
| Simplify | divide top and bottom by their GCD |
Conversions & benchmarks
| Fraction → decimal | divide numerator by denominator |
|---|---|
| Decimal → percent | multiply by 100 (shift 2 places right) |
| 1/8 = 0.125 | = 12.5% |
| 1/3 ≈ 0.333 | ≈ 33.3% |
| Cross-multiply to compare | a/b vs c/d ⇒ compare ad vs bc |