Fraction Calculator
Top number of the first fraction.
Bottom number of the first fraction — can't be zero.
Top number of the second fraction.
Bottom number of the second fraction — can't be zero.
Choose whether to add, subtract, multiply or divide the two fractions.
Simplified fraction
5/4
Decimal value
1.2500
3/4 + 1/2 = 5/4, which is 1.2500 as a decimal.
Quick answer
A fraction calculator adds, subtracts, multiplies or divides two fractions and reduces the result to its simplest form. Enter two fractions and pick an operation — for example 3/4 + 1/2 — and it returns the answer as a simplified fraction, like 5/4, and as a decimal, using the greatest common divisor to simplify automatically.
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Fraction Calculator is one of numbers, percentages and conversion tools on OneCalculate — see the full set for this category.
Browse MathsHow it works
A fraction has two parts: a numerator (the top number) and a denominator (the bottom number). This calculator takes two fractions and combines them using whichever operation you choose, then simplifies the result to its lowest terms.
Adding and subtracting fractions only works once both fractions share the same denominator, since you can only add or subtract like parts. Rather than hunting for the lowest common denominator by hand, this calculator uses the standard cross-multiplication method, which always works even when the denominators don’t divide neatly into each other:
a/b + c/d = (a×d + b×c) / (b×d)
a/b − c/d = (a×d − b×c) / (b×d)Multiplying each numerator by the other fraction’s denominator puts both fractions over the same common denominator (b×d), so the numerators can then be added or subtracted directly.
Multiplying fractions needs no common denominator at all — multiply straight across, numerator by numerator and denominator by denominator:
a/b × c/d = (a×c) / (b×d)Dividing fractions uses the “keep, change, flip” rule: keep the first fraction as it is, change division to multiplication, and flip (find the reciprocal of) the second fraction:
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)Simplifying happens last, on every operation. The calculator finds the greatest common divisor (GCD) of the resulting numerator and denominator — the largest whole number that divides evenly into both — using the Euclidean algorithm, then divides both numbers by it. A result like 10/8 has a GCD of 2, so dividing both parts by 2 reduces it to the equivalent, simpler fraction 5/4. The sign is always kept on the numerator, so the denominator shown is never negative.
Worked example
Dale is a carpenter finishing a hallway renovation in Brisbane and needs to fit new skirting board along one wall. Digging through his offcuts bin, he finds two leftover lengths from previous jobs: one piece measures 3/4 of a metre, the other measures 1/2 of a metre. Before driving to the hardware store for more stock, he wants to know the combined length the two offcuts give him if he joins them end to end.
That’s an addition of two fractions with different denominators (4 and 2), so Dale reaches for the cross-multiplication formula:
3/4 + 1/2 = (3×2 + 4×1) / (4×2) = (6 + 4) / 8 = 10/8The raw result, 10/8, isn’t in its simplest form — both numbers share a common factor. The greatest common divisor of 10 and 8 is 2, so dividing both the numerator and denominator by 2 simplifies the fraction:
10/8 ÷ 2/2 = 5/4As a decimal, 5/4 is 1.25, so Dale’s two offcuts give him exactly one and a quarter metres of skirting board joined together — enough to cover most of a standard doorway gap without opening a fresh length:
| Piece | Length (fraction) | Length (decimal) |
|---|---|---|
| Offcut A | 3/4 m | 0.75 m |
| Offcut B | 1/2 m | 0.50 m |
| Combined (A + B) | 5/4 m | 1.25 m |
Frequently asked questions
How do you add or subtract fractions with different denominators?
Cross-multiply so both fractions share a common denominator: a/b ± c/d = (ad ± bc) / bd. Multiply each numerator by the other fraction's denominator, add or subtract the results, and multiply the two denominators together. Then simplify the answer using the greatest common divisor to reach its lowest terms.
How do you multiply fractions?
Multiplying fractions is the simplest operation — no common denominator needed. Just multiply the two numerators together to get the new numerator, and multiply the two denominators together to get the new denominator: a/b × c/d = ac/bd. Simplify the result afterwards if the numerator and denominator share a common factor.
How do you divide fractions?
To divide by a fraction, multiply by its reciprocal instead. Flip the second fraction upside down (swap its numerator and denominator), then multiply as normal: a/b ÷ c/d = a/b × d/c = ad/bc. This calculator does that flip automatically, so you just enter both fractions as they are.
Why do you flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal — that's true for whole numbers and fractions alike. Flipping c/d to d/c and multiplying gives exactly the same answer as dividing by c/d directly, but multiplication of fractions is far easier to compute than division, so flipping turns a harder problem into an easier one.
How do you simplify a fraction?
Find the greatest common divisor (GCD) — the largest whole number that divides evenly into both the numerator and denominator — then divide both by it. For example, 10/8 has a GCD of 2, so dividing both numbers by 2 simplifies it to 5/4. This calculator finds that GCD and simplifies every result automatically.
What is the greatest common divisor and why does this calculator use it?
The greatest common divisor (GCD) of two numbers is the largest number that divides both exactly with no remainder. Raw fraction arithmetic often leaves a denominator that's larger than it needs to be, so dividing the numerator and denominator by their GCD reduces the fraction to its simplest, lowest-terms equivalent every time.
Can this fraction calculator handle negative numbers or improper fractions?
Yes. Enter a negative numerator or denominator and the calculator keeps the sign correct, always showing it on the numerator with a positive denominator. Improper fractions, where the numerator is bigger than the denominator, such as 5/4, are also handled and displayed exactly as calculated — they aren't converted into mixed numbers.
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Written and verified by Nirbhay Tripathi
Last updated 18 August 2026
All rates on this page are verified againstKhan Academy — Adding and subtracting fractionson 18 August 2026. See our methodology for the full update calendar.