Last updated: February 2026

Fractions Calculator

Add, subtract, multiply or divide two fractions

Fraction 1

Fraction 2

About This Calculator

This calculator is part of UK Calculator’s maths tools, ideal for homework help, cooking conversions, and DIY measurements. It handles all four fraction operations and always simplifies the result.

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  • Accurate: Exact mathematical results with simplification
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Complete Guide to Fractions: Rules, Methods & Examples

Fractions are one of the most fundamental concepts in mathematics, representing parts of a whole. Whether you are helping your child with homework, following a recipe, measuring materials for a DIY project, or working through a GCSE revision sheet, understanding how to work with fractions is an essential life skill. This guide covers all four operations with clear examples.

Adding Fractions

To add fractions with the same denominator, simply add the numerators and keep the denominator. For example: 2/7 + 3/7 = 5/7.

To add fractions with different denominators, find the lowest common denominator (LCD), convert each fraction, then add. For example: 1/3 + 1/4. The LCD of 3 and 4 is 12. Convert: 4/12 + 3/12 = 7/12.

Addition Rule: a/b + c/d = (ad + bc) / bd

Subtracting Fractions

Subtraction follows the same process as addition, but you subtract the numerators instead. Example: 3/4 − 1/3. The LCD of 4 and 3 is 12. Convert: 9/12 − 4/12 = 5/12.

Subtraction Rule: a/b − c/d = (ad − bc) / bd

Multiplying Fractions

Multiplication is the simplest operation with fractions. Multiply numerator by numerator and denominator by denominator. Example: 2/3 × 3/5 = 6/15 = 2/5 (simplified).

Multiplication Rule: a/b × c/d = ac / bd

Dividing Fractions

To divide fractions, flip the second fraction and multiply. UK schools teach this as “Keep, Change, Flip” (KCF). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Division Rule: a/b ÷ c/d = a/b × d/c = ad / bc

Common Fraction-Decimal-Percentage Conversions

FractionDecimalPercentage
1/20.550%
1/30.333...33.33%
1/40.2525%
1/50.220%
1/80.12512.5%
2/30.666...66.67%
3/40.7575%
7/80.87587.5%

Fractions in the UK National Curriculum

Fractions are introduced in the English and Welsh National Curriculum from Year 1 (age 5-6) and progressively developed through to GCSE level. At Key Stage 1, children learn to recognise and name simple fractions like halves and quarters. By Key Stage 2 (Years 3-6), pupils learn to add, subtract, multiply, and divide fractions, convert between fractions, decimals and percentages, and work with mixed numbers. At Key Stage 3 and GCSE, students encounter algebraic fractions and more complex operations.

Simplifying Fractions: The Greatest Common Divisor

A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until you reach zero. The last non-zero remainder is the GCD. For example, GCD(48, 18): 48 ÷ 18 = 2 remainder 12; 18 ÷ 12 = 1 remainder 6; 12 ÷ 6 = 2 remainder 0. GCD = 6. So 48/18 = 8/3.

Practical Applications of Fractions

Cooking: Recipes frequently use fractions. Scaling a recipe for 4 people up to 6 requires multiplying by 6/4 = 3/2. So half a cup becomes 3/4 of a cup, and 1/3 of a teaspoon becomes 1/2 a teaspoon.

DIY and Construction: Imperial measurements in the UK often use fractions. Drill bits, screws, and nails are sized in fractions of an inch (1/4″, 5/16″, 3/8″). Pipe fittings are measured in fractions. Knowing how to add and compare these fractions is essential for accurate work.

Finance: Interest rates, tax bands, and investment returns are often expressed as fractions or percentages. Understanding that 1/5 equals 20% helps in quick mental arithmetic when calculating discounts or tips.

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Sources & Methodology

Written by: Mustafa Bilgic

Data sources: UK National Curriculum for Mathematics, GCSE Mathematics Specification (AQA, Edexcel, OCR)

Last updated:

Calculation Method: Uses exact integer arithmetic with the Euclidean algorithm for GCD computation and automatic simplification. No floating-point rounding errors in fraction results.

Disclaimer: This calculator provides exact mathematical results for fraction operations. For educational use, always verify your understanding of the methods with your teacher or textbook.

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Expert Reviewed — This calculator uses exact mathematical algorithms. Last verified: February 2026.

Pro Tips
  • Use negative numerators for negative fractions
  • The result is always automatically simplified
  • Check the mixed number output for improper fractions
  • Use this for checking homework or verifying cooking conversions
Common Questions

Can I enter negative fractions?

Yes, use a negative numerator. For example, enter -1 as the numerator and 3 as the denominator for -1/3.

What if my result is an improper fraction?

The calculator shows both the improper fraction and the mixed number equivalent.

People Also Ask

A proper fraction has a numerator smaller than the denominator (e.g. 3/4). An improper fraction has a numerator equal to or larger than the denominator (e.g. 7/4). Improper fractions can be written as mixed numbers (1 3/4).

A negative fraction has exactly one negative sign, which can be on the numerator, denominator, or in front of the fraction. -1/3, 1/-3, and -(1/3) are all equal. By convention, the negative sign is placed on the numerator.

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