Fraction Calculator

About this tool

The Fraction Calculator adds, subtracts, multiplies or divides two fractions, mixed numbers, whole numbers or decimals and gives the answer in lowest terms, as a mixed number and as a decimal: 3/4 + 5/6 = 19/12 = 1 7/12 ≈ 1.583333. Every step is listed. Mixed numbers become improper fractions first, so 2 3/4 = 11/4. Addition and subtraction rewrite both fractions over the least common denominator, the LCM of the two denominators. Multiplication multiplies the numerators and the denominators, and division multiplies by the reciprocal of the second fraction. The result is then divided by the greatest common divisor of its numerator and denominator. Arithmetic uses exact big integers, so long numbers keep full precision; the decimal is exact when it ends within 10 places and is otherwise rounded to 6. Each part of an input can have up to 15 digits. A zero denominator or a division by zero gets a plain explanation instead of a wrong answer. It runs in your browser.

Why use it

• Takes fractions, mixed numbers, whole numbers, decimals and negative numbers in the same box.

• Explains the method for each operation: least common denominator for + and −, multiplying across for ×, and the reciprocal for ÷.

• Always reduces the answer with the greatest common divisor and converts improper results to mixed numbers.

• Exact big-integer arithmetic keeps answers exact even with 15-digit numerators.

• Catches zero denominators and division by zero with a clear message.

How to use

1. Type the first number: a fraction (3/4), a mixed number with a space (2 3/4), a whole number (5) or a decimal (0.25). Negatives such as -1/2 work too.
2. Choose the operation: +, −, × or ÷.
3. Type the second number. The answer updates as you type.
4. Read the result in lowest terms, the mixed number and the decimal, then follow the steps below.
5. Tap an example to load a sample problem, or use the copy buttons to copy the answer.

When it helps

• Checking fraction homework, including mixed-number problems such as 2 3/4 × 1 1/2.
• Scaling a recipe: 1 1/2 batches of a recipe that needs 3/4 cup is 3/4 × 1 1/2 = 9/8 = 1 1/8 cups.
• Adding measurements in inches, such as 5/8 + 3/16 = 13/16.
• Preparing worked answers for a class, with every step written out.

Examples

Tips

• Leave a space between the whole number and the fraction: 2 3/4 is two and three quarters, while 23/4 is twenty-three quarters.
• A negative mixed number such as -1 1/2 means -(1 + 1/2) = -3/2, not -1 + 1/2.
• To divide by a whole number, use it as a fraction over 1: 3/4 ÷ 2 = 3/4 × 1/2 = 3/8.
• Decimals are converted exactly, so 0.25 + 1/3 gives 7/12 rather than a rounded decimal.
• Using the least common denominator keeps numbers small: 1/6 + 1/4 uses 12 rather than 24.

Frequently Asked Questions

Glossary

Least common denominator

The smallest number both denominators divide into, equal to their least common multiple (LCM).

Reciprocal

A fraction turned upside down: the reciprocal of 5/6 is 6/5. Multiplying by it is the same as dividing by the original.

Lowest terms

A fraction whose numerator and denominator share no factor other than 1, such as 9/10.

Equivalent fractions

Fractions that have the same value but different numbers, such as 3/4 and 9/12.

Numerator and denominator

The top and bottom numbers of a fraction: in 3/4 the numerator is 3 and the denominator is 4.