Fraction Calculator

What this calculator does

Adds, subtracts, multiplies, or divides two fractions and returns the answer in simplest form. Enter the numerator and denominator for each fraction, choose the operation, and it handles finding a common denominator, the arithmetic itself, and reducing the result: all the steps that make fraction math error-prone when done by hand.

Who this is for

Students checking homework or studying for a math test, parents helping with schoolwork, anyone working with recipes or measurements given in fractional form (cups, inches on a tape measure), and anyone who wants to double-check a manual fraction calculation before relying on it.

Methodology

Addition/Subtraction: convert both fractions to a common denominator (the product or least common multiple of the two denominators), then add or subtract the numerators. Multiplication: multiply numerators together and denominators together directly. Division: multiply the first fraction by the reciprocal (flipped version) of the second. Every result is automatically simplified by dividing both parts by their greatest common divisor (GCD).

Worked examples

Addition: 1/2 + 1/3. Common denominator is 6, so this becomes 3/6 + 2/6 = 5/6.

Multiplication: 2/3 × 3/4 = (2×3)/(3×4) = 6/12, which simplifies to 1/2.

Division: 1/2 ÷ 1/4 means multiplying by the reciprocal: 1/2 × 4/1 = 4/2 = 2.

Converting Fractions to Decimals and Percentages

To convert any fraction to a decimal, divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. To convert that decimal to a percentage, multiply by 100: 0.75 × 100 = 75%. A few fractions come up often enough to be worth memorizing directly: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/3 = 0.333... = 33.3%, 3/4 = 0.75 = 75%.

Working with Mixed Numbers

A mixed number like 2½ combines a whole number and a fraction. To use it in fraction arithmetic, convert it to an improper fraction first: multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 2½: (2 × 2) + 1 = 5, giving 5/2. This calculator works with straightforward numerator/denominator pairs — for a mixed number, convert to an improper fraction like this before entering it.

Common mistakes

• Adding numerators and denominators directly. 1/2 + 1/3 is not 2/5; you must find a common denominator first, giving 3/6 + 2/6 = 5/6.
• Forgetting to flip the second fraction when dividing. Dividing by 1/3 means multiplying by 3/1, not dividing straight across.
• Leaving the answer unsimplified. 4/8 and 1/2 are the same value, but 1/2 is the expected simplified form in most contexts.
• Multiplying denominators when adding. The common denominator for addition/subtraction should be the least common multiple where possible, not always the raw product. Using the raw product still gives a correct (if unsimplified) answer, but LCM keeps the numbers smaller and easier to work with.

Related calculators

Frequently Asked Questions