Equivalent Fractions Calculator

Multiply the numerator and denominator by the same whole number and you get an equivalent fraction: the value stays identical, only the numbers describing it change. 1/2 × 2/2 = 2/4. 1/2 × 3/3 = 3/6. 1/2 × 50/50 = 50/100. Every one of these equals 0.5.

The reverse works too. Divide both terms by their Greatest Common Divisor (GCD) and you land back on the simplest form. 50/100 has a GCD of 50, so it collapses straight to 1/2. The calculator above runs this process in both directions: type a fraction and it multiplies out ten equivalent forms, then shows you the simplified version it started from.

Equivalent fractions are the standard way to compare fractions that do not share a denominator. To compare 3/4 and 5/8, rewrite 3/4 as 6/8 (multiply by 2/2). Now both fractions share the denominator 8, and comparing 6/8 to 5/8 is just comparing 6 to 5: 3/4 is larger.

The same trick works on a tape measure. 3/4" written as sixteenths is 12/16", and 5/8" written as sixteenths is 10/16". Since 12 is greater than 10, a 3/4" mark sits farther from zero than a 5/8" mark. This is why cabinet makers and machinists convert everything to a common denominator, usually 16ths, 32nds, or 64ths, before comparing cut lengths.

Sheet material thickness is a everyday example of equivalent fractions stacking up. Nominal 3/4" plywood is the same thickness as 6/8", 12/16", 24/32", and 48/64", because 3/4 = 0.75 in every one of those forms. A supplier might list a panel as "24/32 inch" on a spec sheet simply because that matches the denominator their gauge uses, but it is the exact same 3/4" your tape measure shows.

Fasteners work the same way. A 5/8" bolt is stamped 5/8 on some packaging and 20/32 on others, and both describe a 0.625" shank. If you are cross-checking a part number against a drawing that uses a different denominator, converting both sides to a shared denominator, or to decimal with the decimal to fraction calculator, removes any ambiguity.

Picture a pizza cut into 4 slices next to an identical pizza cut into 8 slices. Two of the four-slice pieces cover exactly the same area as four of the eight-slice pieces, which is the entire point of equivalent fractions: 2/4 and 4/8 describe the same physical amount, just sliced differently.

A ruler works the same way. The 1/2" mark and the 8/16" mark fall on the exact same line, even though one tape measure might only print the 1/2" label and another prints every sixteenth. Manufacturers pick one denominator system for their tools, usually 16ths, purely for readability, not because the underlying math changes.

Start with 9/16 and find three equivalent fractions. Multiply numerator and denominator by 2: 9×2=18, 16×2=32, giving 18/32. Multiply the original by 3: 9×3=27, 16×3=48, giving 27/48. Multiply by 4: 9×4=36, 16×4=64, giving 36/64. Check each one by dividing: 9÷16=0.5625, 18÷32=0.5625, 27÷48=0.5625, and 36÷64=0.5625. All four match, which confirms the fractions are equivalent.

To go the other direction, take 36/64 and simplify it. The GCD of 36 and 64 is 4, so dividing both terms gives 9/16, the fraction we started with. This multiply-up, divide-down relationship is exactly what the calculator's "10 equivalent forms" list demonstrates for any fraction you enter.

Finding equivalent fractions scales a fraction up by multiplying both terms, while simplifying scales it down by dividing both terms. They are inverse operations that both preserve value. 5/8 scaled up by 4/4 becomes 20/32; 20/32 simplified by its GCD of 4 goes straight back to 5/8.

Use the fraction to decimal calculator when you need to confirm two fractions truly match, and the decimal equivalent chart when you want every common inch fraction and its decimal side by side on one page.

Every inch fraction on this site reduces to one canonical decimal, and equivalent fractions are the reason two people can write the same measurement differently and both be correct. If a drawing calls out 0.625" and a supplier's parts list says 5/8", they match exactly, and both also match 10/16", 20/32", and 40/64". Converting through decimal is often the fastest way to check equivalence when the denominators do not line up: divide numerator by denominator and compare the results.

Try it on the decimal to inches calculator on the homepage, or use the mixed number calculator if your measurement includes a whole-number part, like 2 5/8". Both tools share the same GCD-based simplification logic used throughout this page.