Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
Fraction Calculator

Fraction Calculator

Perform operations on fractions, convert between fraction and decimal, and simplify results.

If using an improper/proper fraction only, leave Whole = 0. Denominator must be ≠ 0.
Result: —
Max denominator (optional)
- For a mixed number type the whole part in the first box and numerator/denominator next.
- If denominator is zero the calculator will show an error.
- For decimal → fraction, the algorithm finds the closest fraction within the max denominator.

Fraction Calculator

This fraction calculator can perform operations such as addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. The numbers above the line represent numerators, while the numbers below represent denominators.

Understanding Fractions

A fraction represents part of a whole and is made up of two numbers: the numerator (top) and denominator (bottom). For example, in the fraction:

\[ \frac{3}{8} \]

The numerator is 3 and the denominator is 8. If you imagine a pie cut into 8 slices, eating 3 slices means 3/8 of the pie is consumed, while 5/8 remains. Note: the denominator cannot be zero, as division by zero is undefined.

Operations with Fractions

Addition of Fractions

When adding fractions, a common denominator is needed. The general formula is:

\[ \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \]

Example:

\[ \frac{3}{4} + \frac{1}{6} = \frac{22}{24} = \frac{11}{12} \]

This works for more than two fractions as well:

\[ \frac{1}{4} + \frac{1}{6} + \frac{1}{2} = \frac{12}{48} + \frac{8}{48} + \frac{24}{48} = \frac{44}{48} = \frac{11}{12} \]

Finding the Least Common Denominator

A more efficient method is to use the Least Common Multiple (LCM) of the denominators:

Example:

\[ \frac{1}{4} + \frac{1}{6} + \frac{1}{2} = \frac{3}{12} + \frac{2}{12} + \frac{6}{12} = \frac{11}{12} \]

Subtraction of Fractions

Fraction subtraction also requires a common denominator:

\[ \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \]

Example:

\[ \frac{3}{4} - \frac{1}{6} = \frac{14}{24} = \frac{7}{12} \]

Multiplication of Fractions

To multiply fractions, simply multiply numerators and denominators:

\[ \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \]

Example:

\[ \frac{3}{4} \times \frac{1}{6} = \frac{3}{24} = \frac{1}{8} \]

Division of Fractions

Dividing fractions means multiplying the first by the reciprocal of the second:

\[ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc} \]

Example:

\[ \frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times \frac{6}{1} = \frac{18}{4} = \frac{9}{2} \]

Simplifying Fractions

Fractions can be simplified by dividing numerator and denominator by their greatest common divisor (GCD).

Example:

\[ \frac{220}{440} = \frac{1}{2} \]

Converting Decimals to Fractions

Each decimal place corresponds to a power of 10. For example:

\[ 0.1234 = \frac{1234}{10000} = \frac{617}{5000} \]

Converting Fractions to Decimals

Fractions can be turned into decimals through division. For instance:

\[ \frac{1}{2} = 0.5 \]
\[ \frac{5}{100} = 0.05 \]
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