Fraction Simplifier
Reduce a fraction to lowest terms, add, subtract, multiply and divide fractions, and convert to and from decimals, including repeating ones like 0.1666…
2/3
0.(6)
2/3
66.(6)%
4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24, 18/27, 20/30
Working
- Greatest common divisor of 8 and 12, by Euclid's divisions:
- 12 = 1 × 8 + 4
- 8 = 2 × 4 + 0
- GCD = 4
- Divide both by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3
- So 8/12 = 2/3
Three things, on one page
Reduce a fraction to lowest terms; turn a decimal back into a fraction; or add, subtract, multiply and divide two fractions. Whichever you pick, the same four answers appear underneath — the fraction in lowest terms, the exact decimal, the mixed number and the percentage — each drawn as a fraction is written on paper, with its own copy button. An "Equivalent fractions" row lists the same value with bigger terms (2/3 gives 4/6, 6/9 and on). When the answer is an improper fraction — a numerator larger than its denominator, as in 7/4 — and not a whole number, a line under the mixed number names it as one and gives the mixed number it equals. Clear empties the boxes of the mode on screen, and Copy link hands over the fraction you typed without writing it into the address bar.
Repeating decimals, written the way you write them
0.1666… is a sixth; reading it as 1666/10000 would be wrong. Type it with dots (0.1666… or 0.1666...) or with brackets (0.1(6)) and it comes back as 1/6. The repeating part has to appear at least twice before it is treated as repeating — 0.3… could be a third or it could be 0.31, so the page does not guess. A decimal with no dots is still read literally, so 0.333 is 333/1000.
Exact, not rounded
The decimal it prints back is exact: a third shows as 0.(3), not 0.3333333333, and a seventh as 0.(142857). It comes from long division that watches for the first remainder to come round again, which is where the repeat begins. Every number is read exactly as typed and worked in big integers, so numerators, denominators and common denominators far larger than a calculator normally holds still give the right answer — and a number too long to take is refused with a sentence saying so, never rounded into a plausible wrong one.
How simplifying works
Reducing a fraction divides the top and bottom by their greatest common divisor, which changes how it is written and not what it is worth. The sign always sits on the numerator and the denominator stays positive, so -8/12 and 8/-12 both show as -2/3. A denominator of 0 has no value at all, so the page asks for a non-zero one rather than showing anything.
Frequently asked questions
Can it add or multiply two fractions?
Yes — that is the third mode. Put a fraction in each box, pick +, −, × or ÷, and the answer appears in lowest terms with its decimal, mixed number and percentage. 1/2 + 1/3 is 5/6, and 1/2 ÷ 3/4 is 2/3.
How do I enter a repeating decimal like 0.333…?
Either way you would write it: 0.333… (or 0.333...) with the repeating digits typed at least twice, or 0.(3) with the repeating part in brackets. Both give 1/3. For a repeat that starts later, 0.1(6) and 0.1666… both give 1/6.
Why does 8/12 become 2/3?
Dividing the top and the bottom by their greatest common divisor — 4 in this case — leaves the same value written with the smallest whole numbers. The tool does it the moment you type.
What is a mixed number?
The same value written as a whole number next to a proper fraction: the improper fraction 7/4 — its numerator larger than its denominator — is 1 3/4. The page draws it stacked rather than flat, because 1 3/4 on one line reads as thirteen quarters just as easily as one and three quarters.
Can I see how the fraction was simplified?
Yes. The working is listed step by step — the divisions that find the greatest common divisor, the division by it, and for an improper fraction the long division to a mixed number.
Can I send the fraction to someone, or see the equivalent fractions?
Yes. Copy link hands over the fraction and the mode you are in; the numbers travel only in that link and are taken out of the address when it is opened. An "Equivalent fractions" row lists the answer with bigger terms — 2/3 gives 4/6, 6/9 and on — with its own Copy button.
Does it say when a fraction is improper?
Yes. When the answer's numerator is larger than its denominator and it is not a whole number, a line under the mixed number says so — “7/4 is an improper fraction: its numerator is larger than its denominator” — and gives the mixed number it equals, 1 3/4. For a negative fraction the sign is set aside for the comparison, and a proper fraction gets no such line.