Fraction Calculator

What is a fraction calculator?

A fraction calculator combines two fractions using addition, subtraction, multiplication or division, then reduces the answer to lowest terms. You enter two fractions such as 1/2 and 1/3, pick one of the four operations, and the tool returns the result three ways: as a simplified fraction, as a mixed number, and as a decimal. Every calculation runs entirely in your browser, so nothing is sent to a server.

The one rule to remember is that denominators cannot be 0 — a zero on the bottom of a fraction means dividing by zero, which has no value. As long as both denominators are non-zero numbers, the calculator handles the arithmetic and the simplifying for you in a single step.

How does the fraction calculator work?

The tool takes two fractions, a/b and c/d, applies the rule for your chosen operation, and then reduces by the greatest common divisor (GCD) — the largest whole number that divides both the top and the bottom exactly. Here is the exact method behind each button:

• Addition and subtraction put the fractions over a common denominator of b × d, combine the numerators, then reduce: a/b + c/d = (a×d + c×b) / (b×d).
• Multiplication multiplies straight across: a/b × c/d = (a×c) / (b×d).
• Division multiplies by the reciprocal of the second fraction: a/b ÷ c/d = (a×d) / (b×c).

In every case the final step is the same — divide the numerator and denominator by their GCD so the result is in lowest terms. The terms are simple: the numerator is the top number, the denominator is the bottom number, the mixed number writes any whole part separately (for example 1 1/2), and the decimal is the same value written with a decimal point.

Because the addition and subtraction method multiplies the denominators rather than hunting for the lowest common denominator, the common denominator (b × d) is not always the smallest possible — but the GCD reduction at the end produces the same simplified answer, so the extra step is unnecessary.

Examples

Each example below matches exactly what the calculator returns.

Example 1: adding fractions

1/2 + 1/3

• Common denominator 2 × 3 = 6: rewrite as 3/6 + 2/6
• Add the numerators: 5/6
• GCD(5, 6) = 1, so it stays 5/6
• Decimal: ≈ 0.8333 (a repeating value, shown rounded)

Example 2: multiplying fractions

1/2 × 1/3

• Multiply across: (1 × 1) / (2 × 3) = 1/6
• GCD(1, 6) = 1, so it stays 1/6

Example 3: dividing fractions

3/4 ÷ 1/2

• Multiply by the reciprocal: 3/4 × 2/1 = (3 × 2) / (4 × 1) = 6/4
• GCD(6, 4) = 2, so 6 ÷ 2 = 3 and 4 ÷ 2 = 2 → 3/2
• As a mixed number: 3 ÷ 2 = 1 remainder 1 → 1 1/2

Example 4: simplifying alone

A fraction like 2/4 reduces because GCD(2, 4) = 2: 2 ÷ 2 = 1 and 4 ÷ 2 = 2, giving 1/2. Any operation that lands on 2/4 is automatically shown in this reduced form.

All four operations on the same pair

Using 1/2 and 1/3, here is how each operation lands so you can see the rules side by side:

Operation	Working	Result (fraction)	Decimal
1/2 + 1/3	3/6 + 2/6	5/6	≈ 0.8333
1/2 − 1/3	3/6 − 2/6	1/6	≈ 0.1667
1/2 × 1/3	(1×1)/(2×3)	1/6	≈ 0.1667
1/2 ÷ 1/3	(1×3)/(2×1) = 3/2	3/2	1.5

Notice that addition gives a bigger result than multiplication here — a quick sanity check that you have selected the right operation.

Where are fraction calculations used?

Fraction arithmetic turns up far more often than the classroom suggests:

• Cooking and baking — combining 1/2 cup and 1/3 cup, or halving a recipe.
• Woodworking and DIY — adding tape-measure lengths written in fractions of an inch.
• Sewing and crafts — totalling fabric measured in fractions of a yard.
• Schoolwork and homework — checking add, subtract, multiply and divide answers.
• Probability and odds — multiplying fractions to combine independent chances.

Tips and common mistakes

• A common denominator is only needed for + and −. Multiplication and division do not need one — you multiply across or flip and multiply.
• In division, flip the second fraction, not the first. 3/4 ÷ 1/2 becomes 3/4 × 2/1, not 4/3 × 1/2.
• Always reduce. 6/4 and 3/2 are equal, but only 3/2 is in lowest terms; the calculator reduces by the GCD for you.
• Keep denominators non-zero. A zero denominator is undefined and the tool will not accept it.
• Decimals can repeat. A value such as 5/6 is shown as roughly 0.8333; the fraction form is the exact one.

Limitations and notes

The fraction and mixed-number results are mathematically exact because the arithmetic is done on whole-number numerators and denominators with no rounding. The decimal is a convenience conversion and may be rounded for repeating values like 0.8333, so treat the fraction as the precise answer. The calculator combines exactly two fractions at a time; for a longer chain, work through it in steps, feeding each result back in. Very large numerators or denominators can push intermediate products such as b × d beyond standard number precision, though everyday fractions never reach that point. This tool is provided for educational and general-purpose use — double-check any value that feeds into safety-critical or professional work.

For related math, try the percentage calculator, the square root calculator and the scientific notation calculator, or browse the full math tools category.