What is an equivalent fraction?
Two fractions are equivalent when they name the same amount using different numbers. 3/4 and 6/8 are the same amount of pie. One pie is cut into four pieces and you take three; the other is cut into eight and you take six. The numbers changed. The quantity didn't.
You get from one to the other by multiplying the top and the bottom by the same number. 3/4 becomes 6/8 when you multiply both by 2. That works because 2/2 equals 1, and multiplying by 1 never changes a value. Run it backwards — divide both by the same number — and you are simplifying. Same relationship, read in the other direction.
Every fraction has infinitely many equivalents, which is why a worksheet asks for three of them rather than all of them. The idea shows up everywhere else in fraction work too. Adding 1/3 and 1/4 means rewriting them as 4/12 and 3/12 first. Comparing 5/8 against 7/12 means the same move. Reading 7/10 as a percentage means turning it into 70/100. Equivalent fractions are the step underneath most of it.
The Equivalent Fractions Calculator on this page does the listing for you. Type 3/4 and you get 6/8, 9/12, 12/16, 15/20, 18/24 and onward, each row labelled with the number that produced it.
How to use the Equivalent Fractions Calculator
- Type your fraction in the box. A plain fraction like 3/4, a mixed number like 1 1/2, or a whole number like 5 all read correctly. Extra spaces don't matter. The table appears as you type — there is no Calculate button and nothing to submit.
- Read the working lines above the table. Type 4/8 and a line reads 4/8 is 1/2 in lowest terms. Type 1 1/2 and a line reads 1 1/2 = 3/2. You also get the decimal, and the mixed-number form when the fraction is top-heavy.
- Read the equivalent fractions chart. Each row is one fraction equal to yours, with the multiplier beside it. Twenty rows show by default, ending at ×21. Show more runs the list out to ×100 when you need a denominator further down.
- Switch to Solve for missing when the worksheet hands you one term. Pick whether you know the numerator or the denominator, type the number you have, and the missing one comes back inside the completed equation.
- Copy what you need. The button on a row copies that fraction alone. Copy all takes the list as a chain — 3/4 = 6/8 = 9/12 = 12/16 — which is the shape that pastes straight into a homework answer.
Five steps is the whole manual, and most people use two of them. Nothing to install, no account, no cookie wall between you and four numbers.
The rule behind equivalent fractions
There is one rule for how to find equivalent fractions, and it fits on a line.
a/b = (a × n) / (b × n) — for any whole number n other than zero.
Multiply the numerator and the denominator by the same number and the value holds. Multiply only one of them and it doesn't. That is the entire mechanism, and it is why the multiplier sits beside every row on this page: the row isn't a fact to memorise, it's a step you could have done yourself.
Here it is worked all the way through on 3/4. Multiply top and bottom by 2 and you have 6/8. By 3, and you have 9/12. By 4, 12/16. By 5, 15/20. By 6, 18/24. Check any of them by division: 6 ÷ 8 is 0.75, and 3 ÷ 4 is 0.75. Same number, different spelling.
One detail changes the answer, so it is worth saying plainly. The list is built from your fraction in lowest terms, not from the fraction as you typed it. Enter 4/8 and the tool reduces to 1/2 first, then generates 2/4, 3/6, 4/8, 5/10. Your own fraction turns up in its own list, at ×4. That looks strange for a second and is the correct behaviour — 2/4 and 3/6 really are equivalent to 4/8, and a list generated from the unreduced version would skip them entirely, handing you 8/16 and 12/24 instead. Reducing first is what makes the list complete. Showing the reduction on its own line is what makes it teachable.
Equivalent fractions chart for common fractions
Most school problems use a small set of fractions. Here is what the Equivalent Fractions Calculator returns for the ones that come up most, multiplied by 2 through 5, with the decimal each one is equal to.
| Fraction | ×2 | ×3 | ×4 | ×5 | As a decimal |
|---|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 | 0.5 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 | ≈ 0.333333 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 | ≈ 0.666667 |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 | 0.25 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 | 0.75 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 | 0.4 |
| 5/8 | 10/16 | 15/24 | 20/32 | 25/40 | 0.625 |
| 1/8 | 2/16 | 3/24 | 4/32 | 5/40 | 0.125 |
| 7/10 | 14/20 | 21/30 | 28/40 | 35/50 | 0.7 |
Two things fall out of the table. The decimal column never changes across a row, because nothing about the amount changed — only the notation did. And the denominators in each row are the multiples of the starting denominator: the 1/8 row lands on 16, 24, 32, 40, which is exactly the list of bottoms that 1/8 can reach.
That second point answers a lot of homework questions before you ask them. If a problem wants 3/4 rewritten with 20 on the bottom, 20 is a multiple of 4, so it works. If it wants 10 on the bottom, 10 is not a multiple of 4, and no equivalent exists. The pattern in the chart is the test.
How to find the missing number in 3/4 = ?/20
Half the time the worksheet doesn't want a list. It wants one number: 3/4 = ?/20. Ask what turned 4 into 20. It's 5. So multiply the top by 5 as well, and 3 × 5 = 15. The answer is 15/20.
Switch the Equivalent Fractions Calculator to Solve for missing and it does that, returning 3/4 = 15/20 with ×5 shown beside it so you can check the step instead of copying a number you didn't follow. It works from the top too: give it 3/4 with 9 as the numerator and it finds 12, because 3 × 3 = 9 means the bottom gets multiplied by 3. Ask for 2/5 with 100 on the bottom and you get 40/100, at ×20 — which is also how you'd read 2/5 as 40%.
The interesting case is the one with no answer. 3/4 with 10 on the bottom has no equivalent, because 10 isn't a multiple of 4. Rather than an error, or the 7.5 you'd get by dividing anyway, the tool says so in words and names the denominators that do work: 8, 12, 16, 20, 24. Same for 1/8 with 100 on the bottom — it points you at 16, 24, 32, 40, 48 instead. A number that isn't a numerator is a worse answer than a sentence that is true.
This is the part most calculators that rank for equivalent fractions don't do on the page you landed on. The common pattern is a list-only result, with a link sending you somewhere else to solve for the missing term — which is a strange split, given it's the same question with one term already filled in. Both modes live here, in the same box.
Edge cases and limitations
If the Equivalent Fractions Calculator isn't showing what you expect, here's what to try first.
You typed a decimal. 0.75 isn't read as a fraction, because turning a decimal into one is a separate job with its own rules for repeating digits. The decimal to fraction converter does that part, and the tool links you there when it sees a dot.
You typed a zero denominator. 3/0 isn't a fraction, so the table stays hidden and a line says so. Zero on top is fine, though: 0/5 reduces to 0/1 and lists 0/2, 0/3, 0/4, which is correct rather than a bug.
Your fraction is negative. The minus sign lives on the numerator and stays there. -3/4 gives -6/8, -9/12, -12/16. Type 3/-4 and it is normalised to -3/4 before anything is generated, so both spellings give the same chart. You will never see 6/-8 here, which is legal arithmetic and terrible notation.
Your numbers are very large. Both terms have to stay under 1,000,000. That cap exists so every digit printed is exact — the largest row the tool can build is well inside the range where whole-number arithmetic can't drift.
Two honest limits. The list starts at ×2, because ×1 is the fraction you typed and a row repeating your own input teaches nothing; it appears on the lowest-terms line above the table instead. And Show more stops at ×100, ending at 300/400 for 3/4. Past that, the pattern is the answer: multiply both numbers by whatever you need.
Related fraction tools
Equivalent fractions sit in the middle of a chain of other jobs, and each one has its own page here.
Going the other way — many fractions down to one — is the fraction simplifier, which reduces any fraction to lowest terms. If you want the decimal rather than another fraction, fraction to decimal handles that, and percent to fraction covers the percentage direction. For adding, subtracting, multiplying or dividing two fractions once you have a common denominator, use the fraction calculator.
The two tools that pair most closely with this one are the greatest common factor calculator — the GCF is the number you divide by to reach lowest terms — and the least common multiple calculator, which finds the shared denominator when you're rewriting two fractions to add them.
Frequently asked questions
What are the equivalent fractions of 1/2?
2/4, 3/6, 4/8, 5/10, 6/12, 7/14 and so on forever — multiply the top and the bottom by the same number and you have another one. The pattern is easy to see here: the top counts 1, 2, 3, 4 and the bottom counts 2, 4, 6, 8. Every fraction whose denominator is exactly double its numerator is equal to 1/2.
How do I check whether two fractions are equivalent?
Cross-multiply. For 3/4 and 9/12, multiply 3 × 12 and 4 × 9. Both give 36, so the fractions are equal. If the two products differ, they aren't. Dividing each fraction out also works — 3 ÷ 4 and 9 ÷ 12 both give 0.75 — though cross-multiplying avoids rounding on fractions like 1/3, whose decimal never finishes.
Is 3/4 equivalent to 75/100?
Yes. 3/4 multiplied top and bottom by 25 gives 75/100, which is where "3/4 is 75%" comes from. It shows up in the full list on this page at ×25. Reduced the other way, 75/100 divided by 25 returns to 3/4.
What's the difference between equivalent fractions and simplifying?
Direction. Simplifying divides the top and the bottom by a shared factor to reach the smallest version — 8/12 becomes 2/3. Finding equivalents multiplies instead, producing bigger versions of the same amount. Both produce fractions equal to the one you started with, so a simplified fraction is an equivalent fraction. This page multiplies; the fraction simplifier divides.
Do equivalent fractions always have the same decimal value?
Always. That is what makes them equivalent. 1/3, 2/6 and 4/12 all read as 0.333333… with the digits repeating forever, which is why this tool prints a ≈ sign in front of a decimal it had to cut short. The approximation is in the decimal, never in the fractions.
Does this calculator cost anything, or need an account?
No, and no. There is no signup, no trial, no download prompt, and nothing to dismiss before you can read the answer. The arithmetic runs in your browser, so nothing you type is uploaded or stored, and closing the tab clears it. Microapp gives 10% of its revenue to charity, off the top and audited quarterly.