Arithmetic
Fraction Calculator
Add, subtract, multiply, or divide two fractions — mixed numbers included. Every result is simplified to lowest terms and shown as a decimal, a percentage, and a mixed number, with the full working.
Enter two fractions
Live result= 1/2 = 0.5
Operation
= 1/3 = 0.333333
Result
56
Mixed number
—
Decimal
0.833333
Percentage
83.333333%
Reduced by
already lowest
Mixed numbers welcome
Try an example
The basics
What is a fraction?
A fraction represents a part of a whole. It is written as one number over another, and the two numbers play very different roles — getting them straight is most of the battle.
a / b
Numerator over denominator
The top number — the numerator — counts how many parts you have. The bottom number — the denominator — says how many equal parts the whole was split into.
3/4 → 3 of 4 equal parts
a / b = a ÷ b
A fraction is a division
Every fraction is really a division waiting to happen. Carry it out and you get the decimal value — which is why a over b equals a divided by b.
3/4 = 3 ÷ 4 = 0.75
Method
How to calculate by hand
Adding and subtracting need a common denominator first; multiplying and dividing don't. Whatever the operation, finish by simplifying.
- 1
Match denominators (for + and −)
To add or subtract, rewrite both fractions over a shared denominator — the product of the two denominators always works. Multiplying and dividing skip this step.
1/2 + 1/3 → 3/6 + 2/6 - 2
Combine the numerators
Add or subtract the new numerators, or — for × and ÷ — multiply straight across (flipping the second fraction first when dividing).
3/6 + 2/6 = 5/6 - 3
Evaluate the result
Carry out the arithmetic to land on a single fraction, the raw unsimplified answer.
(1·3 + 1·2) / 6 = 5/6 - 4
Simplify to lowest terms
Divide the numerator and denominator by their greatest common divisor. If the top is larger than the bottom, you can also write it as a mixed number.
8/12 = 2/3 · 5/4 = 1 1/4
Worked examples
See each operation worked out
The same four-step recipe, applied across addition, subtraction, multiplication, and division. Each tab computes the answer live from the numbers.
Given 1/2 + 1/3
Common denominator 2·3 = 6: (1·3 + 1·2) / 6
Evaluate: 5/6
1/2 + 1/3 = 5/6
Where it shows up
Why fractions matter
Fractions are how we describe parts of things in the real world — long before decimals get involved.
½ cup × 2
Cooking & baking
Recipes live in fractions. Doubling or halving a batch means multiplying every fractional measurement — the most common everyday fraction arithmetic there is.
3/8 in
Building & DIY
Tape measures and drill bits are marked in halves, quarters, eighths, and sixteenths. Fitting parts together is constant fraction addition and subtraction.
1/4 of total
Money & shares
Splitting a bill, dividing an inheritance, or holding a fraction of a company all reduce to the same operations on a numerator and denominator.
Mixed numbers
Improper fractions and mixed numbers
The same value can wear two outfits. Converting between them is a quick multiply-and-add (or divide-with-remainder) — and this calculator does it both ways automatically.
w b/c → (w·c + b) / c
Mixed → improper
Multiply the whole number by the denominator, add the numerator, and keep the same bottom. This is the form you compute with, so do it before any arithmetic.
1 1/2 = (1·2 + 1) / 2 = 3/2
a/b → w r/b
Improper → mixed
Divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the new numerator over the same denominator.
7/4 = 1 3/4 (7 ÷ 4 = 1 r 3)
Worth knowing
Rules worth remembering
A handful of facts that make fraction work faster and catch most mistakes before they happen.
a/b ÷ c/d = a/b × d/c
Dividing is flipping
Division by a fraction is multiplication by its reciprocal. Flip the second fraction, switch the sign to ×, and proceed as a normal multiplication.
a/b = (a·k)/(b·k)
Equivalent fractions
Multiplying top and bottom by the same number leaves the value unchanged. That is exactly how you build common denominators.
cross-multiply
Comparing fractions
To compare a/b and c/d, compare the cross products a·d against c·b. The larger cross product sits over the larger fraction.
a/0 undefined
Never divide by zero
A denominator of zero has no meaning — there is no "number of parts" equal to zero. Any fraction with a zero on the bottom is undefined.
0/b = 0
Zero on top is zero
If the numerator is zero, the whole fraction is zero, no matter the denominator. Zero parts of anything is nothing.
reduce early
Cancel before you multiply
When multiplying, you can cancel common factors across the fractions first. Smaller numbers mean less simplifying at the end and fewer arithmetic slips.
Reference
Common fractions as decimals and percentages
The conversions worth knowing by heart, ordered from smallest to largest. These are the ones that come up in measurements, test scores, and everyday math.
1/8
0.125
1/6
0.1667
1/5
0.2
1/4
0.25
1/3
0.3333
3/8
0.375
2/5
0.4
1/2
0.5
3/5
0.6
5/8
0.625
2/3
0.6667
3/4
0.75
4/5
0.8
7/8
0.875
Quick chart
What is X / Y as a decimal?
Pick a denominator and read off every numerator at once — the decimal and percentage for each, with the reduced form where it simplifies. The fast answer to "what is 5/8 as a decimal?" and its hundreds of cousins.
Denominator
1/8
0.125
2/8 = 1/4
0.25
3/8
0.375
4/8 = 1/2
0.5
5/8
0.625
6/8 = 3/4
0.75
7/8
0.875
Pitfalls
Common mistakes to avoid
Almost every fraction error is one of these four. Knowing them is the quickest way to check your own work.
1/2 + 1/3 ≠ 2/5
Adding the bottoms
You never add denominators. Give the fractions a common denominator first, then add only the numerators. The bottom number stays put.
flip the right one
Flipping the wrong fraction
When dividing, only the second fraction (the divisor) gets flipped. Reversing the first one instead gives a different, wrong answer.
forgot to reduce
Leaving it unsimplified
An answer of 8/12 is correct but unfinished. Most teachers and forms expect lowest terms — divide out the greatest common divisor to reach 2/3.
convert mixed first
Multiplying mixed numbers as-is
You can't multiply 1 1/2 by treating the whole and the fraction separately. Convert to the improper fraction 3/2 first, then multiply.
FAQ
Common questions
Give both fractions a common denominator, then add the numerators. For a/b + c/d the common denominator is b·d, so the sum is (a·d + c·b) / (b·d). Then divide the top and bottom by their greatest common divisor to simplify. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Multiply the numerators together and the denominators together — no common denominator needed: a/b × c/d = (a·c) / (b·d). Then reduce. Example: 2/3 × 3/5 = 6/15 = 2/5.
Keep the first fraction, flip the second (its reciprocal), and multiply: a/b ÷ c/d = a/b × d/c = (a·d) / (b·c). Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
Divide both the numerator and denominator by their greatest common divisor (GCD). For example 6/8 has a GCD of 2, so 6/8 = 3/4 in lowest terms. A fraction is fully simplified when the only number that divides both parts is 1.
Convert each mixed number to an improper fraction first: multiply the whole number by the denominator and add the numerator. So 1 1/2 = (1·2 + 1) / 2 = 3/2. Then add, subtract, multiply, or divide as usual. This calculator accepts mixed numbers directly — just type '1 1/2'.
In a proper fraction the numerator is smaller than the denominator (3/4), so its value is less than 1. In an improper fraction the numerator is equal to or larger than the denominator (5/4), so its value is 1 or more. Improper fractions can be rewritten as mixed numbers — 5/4 = 1 1/4.
Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. Some fractions give terminating decimals (1/8 = 0.125) and others repeat (1/3 = 0.333…). Use the lookup chart on this page to see common conversions at a glance.
Yes. Multiplying the two denominators always gives a valid common denominator, so 1/4 + 1/6 = 6/24 + 4/24 = 10/24 = 5/12. Using the least common denominator (12 here) just keeps the numbers smaller; the final simplified answer is identical either way.
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Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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