Comparing Fractions – Which Is Bigger?
Comparing fractions means deciding which of two fractions is larger, smaller, or whether they are equal. With like fractions it is immediate; with unlike fractions you need one of the four methods below.
Case 1 – Same Denominator (Like Fractions)
Compare the numerators directly. The larger numerator gives the larger fraction.
3/8 vs 5/8 — same denominator: 5 > 3, so 5/8 > 3/8
Case 2 – Same Numerator
The fraction with the smaller denominator is larger (larger pieces).
3/5 vs 3/8 — same numerator: 5 < 8, so 3/5 > 3/8
Method 1 – Common Denominator
Convert both fractions to like fractions using the LCM, then compare numerators.
Compare 3/4 and 5/6
LCM(4,6) = 12. 3/4 = 9/12. 5/6 = 10/12. 10 > 9, so 5/6 > 3/4.
Method 2 – Cross-Multiplication
Multiply diagonally. Compare the two products.
Compare 2/3 and 3/5
2 × 5 = 10. 3 × 3 = 9. 10 > 9 → 2/3 is on the left → 2/3 > 3/5.
Method 3 – Convert to Decimals
Compare 5/8 and 3/5
5/8 = 0.625. 3/5 = 0.6. 0.625 > 0.6 → 5/8 > 3/5.
Method 4 – Benchmark Fractions
Compare each fraction to 1/2 (or 0 or 1) as a reference point.
7/15 vs 5/9: 7/15 < 1/2 (since 7 < 7.5). 5/9 > 1/2 (since 5 > 4.5). So 5/9 > 7/15.
Symbols Reminder
| Symbol | Meaning | Example |
|---|---|---|
| > | Greater than | 3/4 > 1/2 |
| < | Less than | 1/3 < 1/2 |
| = | Equal to | 2/4 = 1/2 |
Key Takeaways
- Like fractions: compare numerators. Same numerator: smaller denominator wins.
- Common denominator: convert then compare.
- Cross-multiplication is fast and reliable for any two fractions.
- Benchmark fractions (using 0, 1/2, 1) give quick estimates.
Practice Questions
- Compare 5/9 and 7/9. Which is larger?
- Compare 2/3 and 5/8 using cross-multiplication.
- Compare 7/12 and 3/5 using a common denominator.
- Which is closer to 1: 7/8 or 5/6?
- Insert <, >, or = : 4/7 __ 8/14.