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MathFractions & Ratios

Fraction Calculator

Add, subtract, multiply or divide fractions and mixed numbers. Answers are simplified automatically and shown as a mixed number and a decimal.

By Ahmed BilalUpdated Formula and official sources shown below

Simplified fraction
5/6
1/2 + 1/3
Mixed number
5/6
Decimal
0.83333333
Overview

About the Fraction Calculator

Fractions describe parts of a whole, such as 3/4 of a pizza or 1/3 of a cup. This calculator works with ordinary fractions (5/8), mixed numbers (2 1/2), whole numbers and decimals (0.75). It performs the operation exactly — without rounding — and then reduces the answer to its simplest form by dividing the numerator and denominator by their greatest common divisor. You also get the result as a mixed number and as a decimal, which is handy for measurements and recipes.

Step by step

How to use the Fraction Calculator

  1. Type the first fraction. Use a slash for fractions (3/4) and a space for mixed numbers (1 1/2).
  2. Choose the operation: add, subtract, multiply or divide.
  3. Type the second fraction.
  4. Read the simplified answer, the mixed-number form and the decimal value below.
Formula

The formula behind it

a/b + c/d = (a×d + c×b) / (b×d) a/b − c/d = (a×d − c×b) / (b×d) a/b × c/d = (a×c) / (b×d) a/b ÷ c/d = (a×d) / (b×c) Then divide top and bottom by their greatest common divisor.

Why you need a common denominator to add fractions

You can only add or subtract fractions that describe the same-sized pieces. Halves and thirds are different sizes, so 1/2 + 1/3 is first rewritten as 3/6 + 2/6 = 5/6. Multiplying and dividing do not need a common denominator: multiply straight across, or for division, flip the second fraction and multiply.

Simplifying fractions

A fraction is in its simplest form when the top and bottom share no common factor other than 1. For example, 18/24 simplifies to 3/4 because both numbers divide by 6. The calculator always shows the simplest form so answers are easy to compare.

Worked examples

Examples

Adding

1/2 + 1/3 = 3/6 + 2/6 = 5/6 ≈ 0.8333.

Mixed numbers

1 1/2 + 2 3/4 = 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4.

Dividing

3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6.

Recipe scaling

Half of 2/3 cup: 2/3 × 1/2 = 2/6 = 1/3 cup.

FAQ

Frequently asked questions

How do I enter a mixed number?

Put a space between the whole number and the fraction, for example 2 3/8. For a negative mixed number, type −2 3/8.

Can I use decimals?

Yes. Decimals such as 0.75 are converted to an exact fraction (3/4) before the calculation.

How do you divide fractions?

Keep the first fraction, flip the second one upside down, and multiply. So a/b ÷ c/d = a/b × d/c.

What is an improper fraction?

A fraction whose top number is larger than its bottom number, such as 7/3. It can also be written as the mixed number 2 1/3.

About the author: Ahmed Bilal

Ahmed Bilal is the founder of VolexTool and builds and maintains every calculator on the site. Tax rates and thresholds are taken directly from official sources such as GOV.UK, HMRC, the Canada Revenue Agency and the Australian Taxation Office, the formula is shown on every page, and each update must pass more than 600 automated checks before it goes live. Ahmed is not a tax adviser: for decisions about your own situation, speak to a qualified accountant or financial adviser.