Fraction Calculator: How to Add, Subtract, Multiply, and Divide Fractions

Fractions are everywhere — from cooking recipes to construction measurements to financial calculations. Yet many people freeze when faced with adding 3/4 and 5/8 or dividing 2/3 by 1/4. Our Fraction Calculator handles all fraction operations instantly, showing step-by-step solutions so you can learn the process while getting the answer. This guide walks through the fundamentals of fraction arithmetic.

Fraction Basics

A fraction represents a part of a whole. The top number is the numerator (how many parts you have), and the bottom number is the denominator (how many parts make a whole). A proper fraction has a numerator smaller than the denominator (3/4), while an improper fraction has a numerator larger than the denominator (7/4).

Mixed numbers combine a whole number and a fraction, like 1 3/4. Before performing operations, convert mixed numbers to improper fractions: multiply the whole number by the denominator, add the numerator, and place over the original denominator.

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator. If they already do, simply add or subtract the numerators and keep the denominator. For example, 3/8 + 2/8 = 5/8.

When denominators differ, find the least common denominator (LCD) — this is the least common multiple of the denominators. For 3/4 + 5/6, the LCD is 12. Convert each fraction: 3/4 = 9/12, 5/6 = 10/12. Then add: 9/12 + 10/12 = 19/12, or 1 7/12.

Our Fraction Calculator does this automatically, showing each conversion step so you can follow along and learn the process.

Multiplying Fractions

Multiplying fractions is simpler than adding or subtracting. Multiply the numerators together and multiply the denominators together. For example, 2/3 × 4/5 = (2×4)/(3×5) = 8/15.

To multiply mixed numbers, first convert them to improper fractions. For 1 1/2 × 2 1/3: convert to 3/2 × 7/3 = 21/6 = 3 1/2. Always simplify your final answer by dividing the numerator and denominator by their greatest common factor.

Dividing Fractions

To divide fractions, multiply the first fraction by the reciprocal of the second. The reciprocal is the fraction flipped upside down. For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.

A real-world example: If a recipe calls for 3/4 cup of flour and you want to halve it, you divide 3/4 by 2: 3/4 ÷ 2 = 3/4 × 1/2 = 3/8 cup.

Simplifying Fractions

Always reduce your answer to the lowest terms. Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For 12/18, the GCF is 6, so the simplified fraction is 2/3. Our Fraction Calculator automatically simplifies every answer.

Practical Uses for Fractions

Fractions appear in everyday situations: adjusting recipe quantities, measuring materials for home improvement projects, calculating discounts, dividing bills among friends, and working with financial ratios. Mastery of fractions makes these tasks faster and reduces errors.

Start Calculating

Use our Fraction Calculator below to solve any fraction problem with step-by-step solutions. Also explore our GCF and LCM Calculator for finding common denominators, and our Percentage Calculator for working with percentages.