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Fraction Calculator

Fractions hide in recipes, test marks, discounts and every proportion written as one number over another, and the awkward part is rarely the concept — it is the arithmetic. This calculator takes two fractions, applies the operation you choose, and hands back the answer already reduced to lowest terms, with its decimal and percentage forms beside it.

Enter values

Top number of the first fraction a/b

Bottom number of the first fraction — must not be 0

Top number of the second fraction c/d

Bottom number of the second fraction — must not be 0

Results update as you type.

Results

Result (simplified)
5/6
As a decimal
0.8333
As a percentage
83.33%

How is the Fraction calculated?

Four number fields describe the two fractions: a over b, and c over d. Whole numbers only, because decimals need scaling first rather than a fraction engine. Choose add, subtract, multiply or divide from the operation list. The calculator combines numerators and denominators by that rule, divides top and bottom by their greatest common divisor, and prints three views of the same value: the simplified fraction, the decimal to four places, and the percentage.

Formula

a/b + c/d = (a·d + c·b) ÷ (b·d) and a/b − c/d = (a·d − c·b) ÷ (b·d), over the common denominator b·d. Multiplication is (a·c) ÷ (b·d); division flips the second fraction to (a·d) ÷ (b·c). a, b, c and d are the four whole numbers you enter, and every answer is reduced by the GCD of its top and bottom.

Example

Half a pizza plus a third of it: 1/2 + 1/3 = (1×3 + 1×2) ÷ (2×3) = 5/6, which is 0.8333 as a decimal and 83.33% of a whole. The same pair subtracted gives (1×3 − 1×2) ÷ 6 = 1/6. Switch to divide and the second fraction flips: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8, an improper fraction worth 1.125.

Things to remember

Reduced fractions compare cleanly: 5/6 and 10/12 are the same amount, but only one reads clearly in a mark book. An improper answer such as 9/8 simply means the value is a little more than one whole, which is perfectly normal. Keep this page beside the ratio calculator whenever a comparison is written as a : b instead.

Frequently Asked Questions

How do you add two fractions with different bottoms?

Find a common denominator — multiplying the two denominators always works — then cross-multiply the numerators and add. So 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Using the smallest common denominator, here 6, gives the same reduced answer with less cancelling afterwards.

How do you simplify a fraction to its lowest terms?

Divide the numerator and the denominator by their greatest common divisor. For 12/18 the GCD of 12 and 18 is 6, so both sides divide down to 2/3. The calculator performs this on every answer, keeping the sign on the numerator whenever the result comes out negative.

What is 3/4 as a decimal and a percent?

0.75 and 75%. Divide the top by the bottom — 3 ÷ 4 = 0.75 — then multiply by 100 for the percentage. The calculator shows both alongside the fraction, which helps when a recipe, a mark sheet and a discount are all describing the same quantity in different clothes.

Why can't the denominator be zero?

Division by zero has no answer, so a fraction with 0 underneath does not exist. Enter 0 as either denominator, or try to divide by 0/d, and the calculator returns dashes rather than an error — the calculation is undefined, not wrong, and no amount of rounding will fix it.

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