Equivalent fractions look different but represent the same amount — 1/2, 2/4, and 50/100 all mean exactly half of something. This calculator generates one equivalent fraction at a time by scaling the numerator and denominator together, which is the same technique you’d use to rewrite a fraction over a common denominator before adding or subtracting.
How to Find an Equivalent Fraction (step by step)
Step One: Choose a scale factor
Any nonzero whole number works as a scale factor. It represents how many equal pieces you’re splitting each existing piece into.
scale factor = 4
Step Two: Multiply the numerator and denominator by that same number
new numerator = numerator × scale factor
new denominator = denominator × scale factor
Step Three: Apply it to the calculator’s defaults
Starting fraction 2/3, scaled by 4:
new numerator = 2 × 4 = 8
new denominator = 3 × 4 = 12
2/3 = 8/12
Both fractions equal the same decimal, 0.6667, confirming the value never changed — only the numbers describing it did.
What your results mean
The equivalent numerator and equivalent denominator together form a new fraction with a larger numerator and denominator than you started with, but the exact same value. The value (unchanged by scaling) field shows that decimal explicitly, so you can confirm the original and scaled fractions really do match.
This is the same operation used behind the scenes whenever two fractions need a common denominator before they can be added or subtracted — each fraction gets scaled up to a shared denominator without changing what it represents.
A short table of equivalents
| Starting fraction | ×2 | ×3 | ×5 |
|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 5/10 |
| 2/3 | 4/6 | 6/9 | 10/15 |
| 3/4 | 6/8 | 9/12 | 15/20 |
| 1/5 | 2/10 | 3/15 | 5/25 |
Every fraction in a row has the same decimal value as the one to its left — only the pieces got smaller and more numerous.
Where this comes up
Finding equivalent fractions is the first real step in adding or subtracting fractions with different denominators, comparing fractions at a glance, and simplifying a recipe or measurement into more convenient units. If you need to go the other way — reducing a fraction down to its simplest equivalent — use the fraction simplifier instead. To rewrite two fractions over their smallest shared denominator specifically, see the least common denominator calculator.