Fraction Calculator
Add, subtract, multiply or divide two fractions, simplify one, or convert a decimal to a fraction. Shows the mixed number and decimal equivalent throughout.
How to use this calculator
- 1Enter the numerator and denominator of each fraction — add a whole number too if you have a mixed number like 1¾.
- 2Pick the operation, choose "Simplify only" to reduce a single fraction to lowest terms, or "Decimal to fraction" to convert a decimal instead.
- 3The answer appears simplified, as a mixed number, and as a decimal.
How the calculation works
a/b + c/d = (ad + cb)/bd a/b × c/d = ac/bd a/b ÷ c/d = ad/bc- a, c
- Numerators — the numbers on top
- b, d
- Denominators — the numbers underneath
Addition and subtraction need a common denominator; multiplication and division do not.
The result is simplified by dividing both parts by their greatest common divisor, found with the Euclidean algorithm.
Worked example
3/4 + 5/6
- 1.Common denominator: 4 × 6 = 24.
- 2.3/4 = 18/24 and 5/6 = 20/24.
- 3.18 + 20 = 38, giving 38/24.
- 4.Both divide by 2, so the answer simplifies to 19/12, or 1 7/12.
Result: 19/12 (1 7/12, or 1.5833…)
0.625 as a fraction
- 1.0.625 has three decimal digits, so it is 625/1000 before simplifying.
- 2.The greatest common divisor of 625 and 1000 is 125.
- 3.625 ÷ 125 = 5, and 1000 ÷ 125 = 8.
Result: 5/8
What a fraction represents
A fraction describes a part of a whole, split into equal pieces. The bottom number, the denominator, says how many equal pieces the whole has been divided into; the top number, the numerator, says how many of those pieces you actually have. Three-quarters, written 3/4, means the whole has been cut into 4 equal pieces and you are counting 3 of them.
Every fraction can also be read as a division: 3/4 is exactly the instruction "3 divided by 4," which is why it equals 0.75 as a decimal. Fractions, decimals and percentages are three different ways of writing the same underlying value.
Equivalent fractions and lowest terms
Multiplying or dividing both the numerator and denominator of a fraction by the same number never changes its value — 1/2, 2/4 and 50/100 all represent exactly the same amount, just cut into a different number of pieces. These are called equivalent fractions.
A fraction is in "lowest terms" (or "simplest form") when the numerator and denominator share no common factor other than 1. Finding the greatest common divisor of the two numbers and dividing both by it always gets you there in one step, which is faster than dividing repeatedly by small numbers and checking.
Where fractions show up outside the classroom
Fractions are one of the few pieces of school math most people keep using for the rest of their lives, often without noticing.
- Cooking and baking — recipes are written in fractions of a cup, teaspoon or ounce, and scaling a recipe up or down means multiplying every fraction by the same factor.
- Construction and carpentry — tape measures and drill bits are marked in fractions of an inch — 3/8, 5/16, 1/4 — rather than decimals.
- Music — time signatures like 3/4 or 6/8 describe how a bar of music is divided into beats.
- Finance — stock prices were historically quoted in fractions of a dollar, like 1/8, before decimalization, and ownership stakes are still routinely described as fractions.
- Probability — the chance of an event is often most naturally expressed as a fraction — a 1-in-4 chance is 1/4.
Why some operations need a common denominator and others do not
Adding or subtracting fractions only works directly when the pieces are the same size — you cannot add 1/2 and 1/3 by adding numerators, because halves and thirds are different-sized pieces. Converting both fractions to a shared denominator first, sixths in this case, makes the pieces comparable, after which the numerators add normally.
Multiplication and division do not have this restriction, which surprises people the first time they see it: multiplying straight across the numerators and then the denominators is always valid, whatever the two denominators are. Dividing by a fraction works by flipping it and multiplying instead, because dividing by 1/2 asks "how many halves fit in here," which is the same question as multiplying by 2.
Common mistakes with fractions
A few habits explain most fraction errors.
- Adding straight across — treating 1/2 + 1/3 as 2/5 by adding numerators and denominators separately. This never gives the right answer — a common denominator is required first.
- Forgetting to simplify — an answer like 12/16 is not wrong, exactly, but it is not fully reduced. Most contexts expect the lowest-terms form, 3/4.
- Mixing up numerator and denominator when reading "of" — "3 out of 4" is the fraction 3/4, with the part on top and the whole on the bottom — reversing them is a common slip under time pressure.
Fractions, decimals and percentages together
Because a fraction is just a division, converting one to a decimal is always a matter of dividing the numerator by the denominator. Going the other way — turning a decimal into a fraction — uses the place value of the last digit: 0.625 has three decimal places, so it starts life as 625/1000, which then simplifies down to 5/8. Multiplying a decimal by 100 converts it to a percentage, so all three forms are really the same information, chosen for whichever context reads most naturally.
What this assumes, and where it stops
Assumptions
- Numerators and denominators are whole numbers.
Limitations
- Handles two fractions at a time. For longer expressions, work left to right in stages.
- Very large numerators and denominators may exceed exact integer precision in JavaScript beyond about 9 quadrillion.
- Decimal-to-fraction rounds to 9 decimal places first, which discards floating-point noise but also means a repeating decimal is converted from its truncated value, not the exact repeating fraction.
Common questions
How do I add fractions with different denominators?
Convert both to the same denominator first. Multiplying the two denominators always works, though the least common multiple keeps the numbers smaller. Then add the numerators and simplify.
Why does dividing by a fraction make the answer bigger?
Because dividing by a number less than one asks "how many of these fit inside?" — and small things fit many times. 1 ÷ ½ = 2, because two halves fit into one whole.
How do I convert a decimal like 0.625 to a fraction?
Choose "Decimal to fraction" and enter it directly. Behind the scenes, the digits after the decimal point become the numerator over a power of ten — 0.625 has three decimal digits, so it starts as 625/1000, which simplifies to 5/8 once you divide both by their greatest common divisor, 125.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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