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List equivalent fractions
On the default, 2/3 expands into 8 equivalents: 4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24, and 18/27. Enter your own fraction below.
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Equivalent Fractions Calculator
Multiply the top and bottom of any fraction by the same whole number and the value never changes — 2/3, 4/6, and 10/15 are all the same amount. Enter a fraction and list as many equivalents as you need, with the simplest form and a proof included.
How equivalent fractions work
Equivalent fractions are different names for the same amount. Multiplying the top and bottom of a fraction by the same whole number is really multiplying by 1 in disguise (2/2, 3/3, 4/4 all equal one), so the value stays exactly the same while the numbers get bigger: 2/3 × 2/2 = 4/6. Dividing top and bottom by their greatest common divisor does the reverse, taking you back to the simplest form.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Equivalent fraction | (n × k) / (d × k) for k = 2, 3, 4… | Multiply 2/3 by 2/2, 3/3, 4/4… to get 4/6, 6/9, 8/12 — same value, bigger numbers. |
| Simplest form | top and bottom divided by their GCD | 2/3 has a GCD of 1, so it is already in lowest terms. |
| Decimal | n ÷ d | 2 ÷ 3 = 0.666667 — every equivalent fraction shares this decimal. |
| Percent | decimal × 100 | 0.666667 × 100 = 66.67% — another shared identity for the whole family. |
| Cross-check | a/b = c/d exactly when a × d = b × c | 2/3 vs 18/27: 2 × 27 = 54 and 3 × 18 = 54 — proven equal. |
Worked example: 8 equivalents of 2/3
Multiply the top and bottom by 2: (2 × 2)/(3 × 2) = 4/6. By 3: 6/9. By 4: 8/12. By 5: 10/15. By 6: 12/18. By 7: 14/21. By 8: 16/24. By 9: 18/27. Eight equivalents, all equal to exactly two thirds. The proof: 2/3 against the largest, 18/27 — cross-multiply: 2 × 27 = 54 and 3 × 18 = 54. Equal products, equal fractions. The simplest form stays 2/3 because its greatest common divisor is 1.
Who uses this
- Students: fraction homework and tests, with the multiplication pattern shown so you can copy the steps.
- Cooks: scaling a recipe by thirds or quarters — 2/3 cup of flour is 4/6 cup when you need matching measures.
- Teachers & tutors: generating practice sets of equal fractions with the simplest form and proof on screen.
- Crafters & sewists: converting fractional measurements to matching rulers and patterns — 1/2 inch is 4/8 inch.
Accuracy & limitations
Everything here uses exact integer math — the equivalents are computed by multiplying whole numbers, never by floating-point division, so equality is perfect, not approximate. Inputs must be whole numbers; the denominator cannot be zero. The list always grows upward (multiplying by 2, 3, 4…); to shrink a fraction instead, run the result through the fraction simplifier.
Want these in another format? The fraction to decimal chart covers every equivalent's decimal, and the fraction to percent converter handles the percent side.
Cite this calculatorBright Side Kit. “Equivalent Fractions Calculator.” brightoolbox.com, 2026.
Bright Side Kit. "Equivalent Fractions Calculator." https://brightoolbox.com/equivalent-fractions-calculator/ Accessed October 22, 2026.Frequently asked questions
What are equivalent fractions?
Different fractions with the same value. 2/3, 4/6, and 10/15 all describe the same amount — two parts out of every three. They look different because the numbers are bigger or smaller, but the portion is identical.
Why must I multiply both the top and the bottom?
Because you are really multiplying by 1 in disguise. 2/2, 3/3, and 9/9 all equal one, so (2/3) × (9/9) = 18/27 changes the look without changing the value. Multiply only the top and you have changed the amount — a different fraction entirely.
How do I check that two fractions are equivalent?
Cross-multiply. Two fractions a/b and c/d are equal exactly when a × d = b × c. For 2/3 and 18/27: 2 × 27 = 54 and 3 × 18 = 54, so they are proven equivalent. The calculator runs this check on the first and last fractions in the list.
How do I find the simplest form of a fraction?
Divide the top and bottom by their greatest common divisor (GCD). For 18/27 the GCD is 9, so 18/27 ÷ 9 = 2/3. The fraction simplifier finds the GCD and the simplest form for any fraction.
Do equivalent fractions always have bigger denominators?
No. Multiplying by 2, 3, 4… makes bigger denominators, but the reverse — dividing by the GCD — makes them smaller. 18/27, 6/9, 4/6, and 2/3 are all equivalent; 2/3 is simply the smallest way to write it.
Do equivalent fractions have the same decimal and percent?
Yes, always. Every fraction equivalent to 2/3 equals 0.666667 and 66.67%, because they are the same number written differently. If two fractions give different decimals, they cannot be equivalent.
Show a simple example: 1/2 = 2/4 = 3/6.
Start with 1/2. Multiply top and bottom by 2: (1 × 2)/(2 × 2) = 2/4. Multiply by 3: (1 × 3)/(2 × 3) = 3/6. All three equal one half: 0.5, or 50%. The pattern continues forever — 4/8, 5/10, 6/12, and on.