Equivalent fractions represent the same value written with different numbers — 1/2, 2/4, and 5/10 are all exactly one-half, just split into a different number of equal pieces. This chart shows the first several equivalents for the fractions people look up most.
Halves, thirds, and quarters
| Fraction | ×2 | ×3 | ×4 | ×5 |
|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 |
Fifths and eighths
| Fraction | ×2 | ×3 | ×4 | ×5 |
|---|---|---|---|---|
| 1/5 | 2/10 | 3/15 | 4/20 | 5/25 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 |
| 1/8 | 2/16 | 3/24 | 4/32 | 5/40 |
| 3/8 | 6/16 | 9/24 | 12/32 | 15/40 |
Every fraction in a row shares the same decimal value — read across 1/4, 2/8, 3/12, 4/16, and 5/20, and each one equals exactly 0.25.
How to generate an equivalent fraction
Multiply the numerator and denominator by the same nonzero number. Because that’s the same as multiplying by n/n — which always equals 1 — the fraction’s value never changes, only how it’s written.
1/4 scaled by 3:
numerator: 1 × 3 = 3
denominator: 4 × 3 = 12
1/4 = 3/12
Finding an equivalent fraction with a specific denominator
Divide your target denominator by the current one to find the scale factor, then apply it to the numerator. To rewrite 2/3 with a denominator of 15:
scale factor = 15 ÷ 3 = 5
new numerator = 2 × 5 = 10
2/3 = 10/15
This is exactly the technique used to give two fractions a common denominator before adding or subtracting them.
Try it with your own numbers
For any starting fraction and scale factor, use the equivalent fractions calculator to generate the result instantly. To go the other direction — reducing a fraction down to its simplest equivalent — use the fraction simplifier. And if you need the smallest denominator two specific fractions can share, see the least common denominator calculator.