Fraction Calculator

Last Updated:

Add, subtract, multiply, or divide any two fractions. Results auto-simplified using GCD and shown as proper or mixed numbers.

Result

5/6

📐 Formula

Addition: (a/b) + (c/d) = (ad+bc)/(bd). Subtraction: (ad−bc)/(bd). Multiplication: ac/bd. Division: (a/b)÷(c/d) = ad/(bc)

How to Use the Fraction Calculator

1

Enter the fractions

Input numerator and denominator for each fraction. For mixed numbers (e.g. 2½), enter the whole number separately and the calculator combines them automatically.

2

Select the operation

Choose addition, subtraction, multiplication, or division. Each operation follows specific rules — the calculator shows step-by-step working so you can verify the method.

3

Read the simplified result

Results are automatically reduced to lowest terms (simplified). The calculator also shows the decimal equivalent and, where applicable, converts back to a mixed number.

4

Use the step-by-step view

For learning or checking work, expand the working section to see each step: finding common denominators, cross-multiplying, simplifying by greatest common divisor.

Fraction Arithmetic: The Four Operations

Addition and subtraction require a common denominator. ½ + ⅓: common denominator is 6, so 3/6 + 2/6 = 5/6. For unlike denominators, multiply each fraction's numerator by the other's denominator: (1×3 + 1×2) ÷ (2×3) = 5/6. Multiplication is simpler: multiply numerators together and denominators together. ½ × ⅔ = (1×2) ÷ (2×3) = 2/6 = 1/3. Division — multiply by the reciprocal: ½ ÷ ⅔ = ½ × 3/2 = 3/4. Invert the second fraction and multiply.

Simplifying Fractions: Finding the GCD

A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. To simplify: find the Greatest Common Divisor (GCD) of both numbers and divide both by it. For 18/24: GCD(18,24) = 6. 18÷6 = 3, 24÷6 = 4. Simplified: 3/4. Euclid's algorithm finds the GCD efficiently: GCD(18,24) = GCD(24 mod 18, 18) = GCD(6,18) = GCD(18 mod 6, 6) = GCD(0,6) = 6.

Converting Between Fractions, Decimals, and Percentages

Fraction to decimal: divide numerator by denominator. ¾ = 3 ÷ 4 = 0.75. Decimal to fraction: identify the place value of the last digit (0.75 = 75/100), then simplify (75/100 = 3/4). Fraction to percentage: convert to decimal, multiply by 100. ⅜ = 0.375 = 37.5%. Some fractions produce repeating decimals: ⅓ = 0.333..., ⅙ = 0.1666..., 1/7 = 0.142857142857... These cannot be expressed as exact finite decimals but remain exact as fractions — one reason fractions are preferred in algebra and exact computation.

Mixed Numbers and Improper Fractions

A mixed number (2½) combines a whole number with a fraction. An improper fraction has a numerator larger than its denominator (5/2). They are equivalent: 2½ = 5/2. To convert mixed to improper: multiply the whole number by the denominator and add the numerator — 2½ = (2×2 + 1)/2 = 5/2. To convert back: divide numerator by denominator — 5÷2 = 2 remainder 1, so 2½. For arithmetic, improper fractions are generally easier to work with than mixed numbers — convert first, calculate, then convert the result back if a mixed number is preferred.

Sources & Methodology

Calculations are based on the most current publicly available data from authoritative government and industry sources:

Frequently Asked Questions

Find the least common denominator (LCD), convert both fractions to equivalent fractions with the LCD, then add the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Multiply numerators together and denominators together, then simplify. Example: 2/3 × 3/4 = 6/12 = 1/2. You can also simplify before multiplying by cross-canceling common factors.
An improper fraction has a numerator larger than its denominator (e.g., 7/4). It equals a value greater than 1. It can be converted to a mixed number: 7/4 = 1¾.
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. Example: 3½ = (3 × 2 + 1) ÷ 2 = 7/2. To convert back: divide numerator by denominator; the quotient is the whole number and the remainder is the new numerator. Example: 7/2 = 3 remainder 1 = 3½.