Equivalent fractions name the same amount with different numbers: 2/3, 4/6, 6/9 and 20/30 all sit at the same point on the number line. You make them by multiplying (or dividing) the top and bottom of a fraction by the same number, which is the same as multiplying by 1. This calculator lists as many equivalents as you want, reduces the fraction to simplest form, and solves for the numerator that matches a denominator you choose.
How to use the calculator
- Enter a fraction or mixed number (mixed numbers become improper fractions first).
- Choose how many equivalent fractions to list.
- Optionally enter a target denominator to find the matching numerator.
- The tape shows the simplest form and decimal value; the table lists each equivalent with its multiplier. If your fraction was not in lowest terms, the tape also lists the fractions between yours and the simplest form.
The rule
Multiplying by k/k is multiplying by 1, so the value does not change — only the size and number of the pieces do. Dividing both parts by a common factor runs the rule backwards, which is how you simplify a fraction.
Worked example: 2/3
| Multiply by | Equivalent fraction |
|---|---|
| 2/2 | 4/6 |
| 3/3 | 6/9 |
| 4/4 | 8/12 |
| 5/5 | 10/15 |
| 8/8 | 16/24 |
Target denominator 24: 24 ÷ 3 = 8, so multiply the numerator by 8 too: 2 × 8 = 16, and 2/3 = 16/24.
Target denominator 10: 10 is not a multiple of 3, so no fraction with a whole-number numerator over 10 equals 2/3. The numerator would have to be 6.666…, which is why 2/3 has no exact two-decimal-place form.
Where equivalent fractions are used
- Adding and subtracting fractions requires rewriting each one with a common denominator — 1/2 + 1/3 becomes 3/6 + 2/6. The LCD calculator finds the best denominator.
- Comparing fractions is easy once they share a denominator: 3/5 = 24/40 and 5/8 = 25/40, so 5/8 is larger.
- Converting to percents and decimals: 3/4 = 75/100 = 75% = 0.75.
- Scaling recipes and measurements: 3/8 inch = 6/16 inch on a ruler marked in sixteenths.
Checking equivalence
Two fractions a/b and c/d are equivalent exactly when their cross products match, a × d = b × c. Another check is to simplify both: equivalent fractions always reduce to the same simplest form. Solving for one unknown entry in a pair of equivalent fractions is a proportion — the solve for x in fractions calculator handles the unknown in any position.
Frequently asked questions
How do you find equivalent fractions?
Multiply or divide the numerator and denominator by the same nonzero whole number. 2/3 × 2/2 = 4/6 and 2/3 × 5/5 = 10/15, so 4/6 and 10/15 are equivalent to 2/3.
How do I find an equivalent fraction with a specific denominator?
Divide the new denominator by the old one to find the multiplier, then multiply the numerator by the same number. For 3/4 = ?/24: 24 ÷ 4 = 6, so the numerator is 3 × 6 = 18, giving 18/24.
Why is there sometimes no equivalent fraction with my denominator?
The new denominator must be a multiple of the denominator in lowest terms. 2/3 cannot be written over 10 with a whole-number numerator, because 10 is not a multiple of 3; the numerator would be 6.666….
How can I check whether two fractions are equivalent?
Cross-multiply. If a × d equals b × c, then a/b and c/d are equivalent. 4/6 and 10/15 give 4 × 15 = 60 and 6 × 10 = 60, so they are equal.