Fraction Calculator

What is a Fraction?

A fraction represents a part of a whole. It is written as a/b where a is the numerator (the part you have) and b is the denominator (total parts). Fractions are fundamental in mathematics — from simple division to advanced calculus.

Adding and Subtracting Fractions

To add or subtract fractions, you must first find a common denominator — the Least Common Multiple (LCM) of both denominators. Then adjust the numerators accordingly.

Example — Addition: 1/3 + 1/4

Example — Subtraction: 3/4 − 1/6

Multiplying and Dividing Fractions

Fraction multiplication is simpler than addition — just multiply numerators together and denominators together, then simplify.

Example — Multiplication: 2/3 × 3/5

Example — Division: 3/4 ÷ 2/5 (flip and multiply)

Tip: Before multiplying, "cross-cancel" common factors between any numerator and any denominator to keep numbers small.

Simplifying (Reducing) Fractions

A fraction is simplified (in its lowest terms) when the numerator and denominator have no common factor other than 1. Divide both by their GCD.

Use our GCD Calculator to find the greatest common divisor of any two numbers.

Real-World Uses of Fractions

Fractions appear everywhere in practical life — cooking, construction, time management, finance, and medicine.

• Cooking: Scaling recipes — if a recipe needs 3/4 cup and you're making half the batch, you need 3/4 × 1/2 = 3/8 cup.
• Construction: Measuring lumber (1¼ inches), mixing concrete (3 parts gravel to 1 part cement = 3/1 ratio).
• Finance: Interest rates, stock splits (2-for-1 split = each share becomes 2 × 1/2 value shares).
• Medicine: Drug dosages (¼ tablet, ½ teaspoon of medicine).
• Music: Time signatures — 3/4 time (3 beats per bar), 4/4 time (4 beats per bar).
• Probability: Chances expressed as fractions — P(heads) = 1/2, P(six on die) = 1/6.