Equivalent Fractions Calculator
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Enter any fraction, such as 3 over 4, to see ten
equivalent forms and its simplest form.
Simplest form
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- Decimal value
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- Fraction type
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| Multiplier | Equivalent fraction |
|---|---|
| Enter a fraction above to see its equivalents. | |
To find an equivalent fraction, multiply the numerator and denominator by the same nonzero whole number. 3/4 multiplied by 2 becomes 6/8 — a different-looking fraction with the exact same value.
Same Value, Different Numbers
Equivalent fractions are different ways of writing the exact same quantity — think of slicing one pizza into 4 pieces versus slicing an identical pizza into 8 pieces and taking twice as many slices. 3/4 and 6/8 are the same amount of pizza.
The rule that makes this work is simple: multiplying (or dividing) both the numerator and the denominator by the same nonzero number never changes the fraction's value, because you're really just multiplying by a form of 1 — 2/2, 3/3, 10/10 — and multiplying by 1 leaves any number unchanged.
The Equivalent Fraction Formula
One rule generates every equivalent form of a fraction.
For any nonzero whole number k, N/D and (N×k)/(D×k) are the same value.
- NThe original numerator, such as 3 in 3/4.
- DThe original denominator, such as 4 in 3/4.
- kAny nonzero whole-number multiplier — 2, 3, 4, and so on.
Worked calculation — 3/4 at k = 5
- N × k = 3 × 5 = 15Multiply the numerator by k
- D × k = 4 × 5 = 20Multiply the denominator by the same k
3/4 = 15/20
Equivalents of 3/4
A worked example showing how far this chain of equivalent fractions extends.
| Multiplier | Equivalent fraction |
|---|---|
| × 2 | 6/8 |
| × 3 | 9/12 |
| × 4 | 12/16 |
| × 5 | 15/20 |
| × 6 | 18/24 |
| × 7 | 21/28 |
| × 8 | 24/32 |
| × 9 | 27/36 |
Checking Equivalence Without a Calculator
- Cross-multiply the two fractions. For 3/4 and 15/20: 3 × 20 = 60, and 4 × 15 = 60.
- Compare the two products. If they match, the fractions are equivalent.
- If they don't match, the fractions represent different values — no amount of simplifying will make them equal.
Frequently Asked Questions
What makes two fractions equivalent?
Two fractions are equivalent when they represent the same value, even though the numbers look different. Multiplying or dividing both the numerator and denominator by the same nonzero number never changes a fraction's value — only its appearance — so 1/2, 2/4 and 50/100 are all equivalent.
How do you find an equivalent fraction with a specific denominator?
Divide the target denominator by the original denominator to get the multiplier, then multiply the numerator by that same number. To rewrite 3/4 with a denominator of 20: 20 ÷ 4 = 5, so multiply the numerator by 5 as well — 3 × 5 = 15, giving 15/20.
What is the simplest form of a fraction?
The simplest form, also called lowest terms, is the equivalent fraction where the numerator and denominator share no common factor besides 1. It's found by dividing both numbers by their greatest common divisor: 8/12 has a GCD of 4, so its simplest form is 2/3.
How do you check if two fractions are equivalent without simplifying?
Cross-multiply: for a/b and c/d, the fractions are equivalent exactly when a × d equals b × c. Checking 3/4 against 15/20: 3 × 20 = 60 and 4 × 15 = 60 — the products match, so the fractions are equivalent.
Can a fraction have infinitely many equivalent forms?
Yes. Multiplying the numerator and denominator by 1, 2, 3, 4 and so on forever produces an unbroken, infinite chain of equivalent fractions — one for every positive whole-number multiplier, with the simplified form sitting at the start of that chain.
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