Fraction Calculator

Add, subtract, multiply, divide, simplify, and convert fractions with our free fraction calculator

Available Calculators

What is a Fraction?

A fraction represents a part of a whole number. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar. For example, 3/4 means 3 parts out of 4 equal parts. Fractions are used extensively in mathematics, cooking, measurements, and everyday calculations.

Fraction Operations

Our fraction calculator supports all basic fraction operations including addition, subtraction, multiplication, division, simplification, and conversion between fractions, mixed numbers, and decimals.

Adding Fractions

To add fractions, find a common denominator, convert both fractions, then add the numerators:

(a ÷ b) + (c ÷ d) = ((a × d + c × b) ÷ (b × d))

where LCM is the Least Common Multiple of the denominators

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together:

(a ÷ b) × (c ÷ d) = ((a × c) ÷ (b × d))

where the result should be simplified to lowest terms

Examples of Fraction Calculations

Here are several everyday situations that show how easy it is to use our fraction calculator.

Example 1: UK Recipe Scaling

A traditional British scone recipe from a cookbook in London calls for 1/2 cup of flour and 1/3 cup of sugar. You want to know the total amount.

You can use our calculator by entering:

What is 1/2 + 1/3?

The calculator returns: 5/6 cup

Find common denominator: LCM of 2 and 3 = 6
Convert: 1/2 = 3/6, 1/3 = 2/6
Add: 3/6 + 2/6 = 5/6

The formula used is:

(1 ÷ 2) + (1 ÷ 3) = (5 ÷ 6)

Example 2: Pizza Sharing in Manchester

You order a pizza from a restaurant in Manchester. You have 3/4 of the pizza and eat 1/4 of it. How much is left?

You can use our calculator by entering:

What is 3/4 - 1/4?

The calculator returns: 1/2 pizza

Subtract numerators: 3 - 1 = 2
Keep denominator: 4
Simplify: 2/4 = 1/2

The formula used is:

(3 ÷ 4) - (1 ÷ 4) = (2 ÷ 4) = (1 ÷ 2)

Example 3: Doubling a UK Recipe

A recipe from Waitrose uses 2/3 cup of milk. You want to double the recipe for a larger gathering.

You can use our calculator by entering:

What is 2 × 2/3?

The calculator returns: 1 1/3 cups

Multiply: 2 × 2/3 = 4/3
Convert to mixed number: 4/3 = 1 1/3

The formula used is:

2 × (2 ÷ 3) = (4 ÷ 3) = 1(1 ÷ 3)

Example 4: Dividing Ingredients

You have 3/4 cup of flour from a recipe and need to divide it into 2 equal portions for two separate batches.

You can use our calculator by entering:

What is 3/4 ÷ 2?

The calculator returns: 3/8 cup per portion

Divide by 2 is same as multiply by 1/2
Multiply: 3/4 × 1/2 = 3/8

The formula used is:

(3 ÷ 4) ÷ 2 = (3 ÷ 4) × (1 ÷ 2) = (3 ÷ 8)

Example 5: Simplifying UK Measurements

A building project in Birmingham requires 8/12 of a metre of material. Simplify this fraction.

You can use our calculator by entering:

Simplify 8/12

The calculator returns: 2/3 metre

Find GCD of 8 and 12: GCD = 4
Divide both by 4: 8÷4 = 2, 12÷4 = 3
Result: 2/3

The formula used is:

(8 ÷ 12) = (2 ÷ 3)

Example 6: Mixed Number Conversion

A recipe from a UK cookbook calls for 2 1/2 cups. Convert this to an improper fraction.

You can use our calculator by entering:

Convert 2 1/2 to improper fraction

The calculator returns: 5/2 cups

Multiply whole by denominator: 2 × 2 = 4
Add numerator: 4 + 1 = 5
Keep denominator: 2
Result: 5/2

The formula used is:

2(1 ÷ 2) = (5 ÷ 2)

Example 7: Improper to Mixed

You have 7/3 of a pizza from a takeaway in London. Convert to a mixed number.

You can use our calculator by entering:

Convert 7/3 to mixed number

The calculator returns: 2 1/3 pizzas

Divide: 7 ÷ 3 = 2 remainder 1
Whole part: 2
Fraction part: 1/3
Result: 2 1/3

The formula used is:

(7 ÷ 3) = 2(1 ÷ 3)

Example 8: Decimal to Fraction

A measurement in a UK construction project shows 0.75 metres. Convert to a fraction.

You can use our calculator by entering:

Convert 0.75 to fraction

The calculator returns: 3/4 metre

0.75 has 2 decimal places
0.75 = 75/100
Simplify: 75/100 = 3/4

The formula used is:

0.75 = (3 ÷ 4)

Example 9: Fraction to Decimal

A recipe from Tesco uses 3/8 cup. Convert to decimal for easier measurement.

You can use our calculator by entering:

Convert 3/8 to decimal

The calculator returns: 0.375 cups

Divide: 3 ÷ 8 = 0.375
Result: 0.375

The formula used is:

(3 ÷ 8) = 0.375

Example 10: GCSE Study Time

A student in Birmingham spends 1/4 hour on GCSE maths homework and 1/3 hour on reading. Total time?

You can use our calculator by entering:

What is 1/4 + 1/3 hour?

The calculator returns: 7/12 hour (35 minutes)

Find common denominator: LCM of 4 and 3 = 12
Convert: 1/4 = 3/12, 1/3 = 4/12
Add: 3/12 + 4/12 = 7/12
7/12 hour = 35 minutes

The formula used is:

(1 ÷ 4) + (1 ÷ 3) = (7 ÷ 12)

Summary

These examples show how our fraction calculator can handle:

  • •Adding and subtracting fractions (recipes, measurements, time calculations)
  • •Multiplying and dividing fractions (scaling recipes, calculating proportions)
  • •Simplifying fractions (reducing to lowest terms)
  • •Converting between fractions, mixed numbers, and decimals

You can adapt any real-life situation involving fractions to one of these patterns and let the calculator do the work for you.

How to Use

  1. Select the type of fraction calculation you need (addition, subtraction, multiplication, division, simplify, convert, etc.).
  2. Enter the required values in the input fields. The calculator will automatically update results in real-time.
  3. View the result and step-by-step calculation breakdown with formulas displayed using mathematical notation.

Frequently asked questions

How do I add fractions?

To add fractions, find a common denominator, convert both fractions to have that denominator, then add the numerators. The result should be simplified to lowest terms.

How do I simplify fractions?

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, 8/12 simplifies to 2/3 by dividing both by 4.

Related tools

About this tool

Published by Online Tools Center

Last updated:

Check the units, assumptions and rounding before using a result. Health and financial estimates are educational and do not replace individual professional advice.

Found an error? Send the tool name, inputs, expected result and actual result so we can investigate.

Report a problem