Fraction Calculator

How to Calculate Fractions

A fraction represents a part of a whole, written as a numerator over a denominator. Below are all the operational formulas and calculation steps displayed in LaTeX:

Addition Formula

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

How to calculate:

$$ \text{Numerator} = ad + bc, \quad \text{Denominator} = bd $$

Subtraction Formula

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

How to calculate:

$$ \text{Numerator} = ad - bc, \quad \text{Denominator} = bd $$

Multiplication Formula

$$ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} $$

How to calculate:

$$ \text{Result} = \frac{ac}{\gcd(ac, bd)} \div \frac{bd}{\gcd(ac, bd)} $$

Division Formula

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

How to calculate:

$$ \left(\frac{c}{d}\right)^{-1} = \frac{d}{c} \implies \text{Result} = \frac{a \times d}{b \times c} $$

Frequently Asked Questions

How do I reduce a fraction to its lowest terms?

Divide both the numerator and the denominator by their Greatest Common Divisor (GCD). Our calculator simplifies every result automatically.

What is the difference between proper and improper fractions?

In a proper fraction, the numerator is less than the denominator (e.g. 3/4). In an improper fraction, the numerator is greater than or equal to the denominator (e.g. 5/4), which can also be written as a mixed number (1 1/4).

Decimal to Fraction Converter

How to Calculate Fractions

Addition Formula

Subtraction Formula

Multiplication Formula

Division Formula

Frequently Asked Questions

How do I reduce a fraction to its lowest terms?

What is the difference between proper and improper fractions?

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