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Fraction Calculator Online

Add, subtract, multiply, or divide any two fractions. Shows the simplified result, decimal equivalent, and mixed number form.

Result (simplified)
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Decimal
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Mixed Number
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Working with Fractions: A Complete Guide

A fraction represents a part of a whole. The number on top is called the numerator (how many parts you have), and the number on the bottom is the denominator (how many equal parts the whole is divided into). Fractions appear everywhere — in cooking recipes, construction measurements, music time signatures, probability calculations, and algebra. Understanding how to perform the four basic operations on fractions is an essential mathematical skill.

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator (a common denominator). If the denominators are already the same, simply add or subtract the numerators and keep the denominator. If they are different, find the least common denominator (LCD) — the smallest number that both denominators divide into evenly — then convert each fraction to an equivalent fraction with that denominator before adding or subtracting.

1/2 + 1/3→5/6LCD of 2 and 3 is 6. 1/2 = 3/6, 1/3 = 2/6. 3/6 + 2/6 = 5/6.
3/4 − 1/3→5/12LCD is 12. 9/12 − 4/12 = 5/12.

Multiplying Fractions

Multiplying fractions is the simplest operation: multiply the numerators together, then multiply the denominators together. Simplify the result by dividing both by their GCD. You can also simplify before multiplying by canceling common factors between any numerator and any denominator — this keeps numbers smaller and makes the arithmetic easier.

2/3 × 3/4→1/22×3 = 6, 3×4 = 12. 6/12 simplified to 1/2.

Dividing Fractions

To divide by a fraction, multiply by its reciprocal (flip the second fraction upside down and multiply). The reciprocal of 3/4 is 4/3. So dividing by 3/4 is the same as multiplying by 4/3. This rule works because dividing by a fraction asks "how many times does this fraction fit into the dividend?" and multiplying by the reciprocal answers that question directly.

1/2 ÷ 1/4→21/2 × 4/1 = 4/2 = 2. A half contains exactly two quarters.

Simplifying Fractions Using GCD

A fraction is in its simplest form when the numerator and denominator share no common factor other than 1. The GCD (Greatest Common Divisor) is the largest number that divides both evenly. Divide both the numerator and denominator by the GCD to simplify. For example, 12/16: GCD(12,16) = 4, so 12÷4 = 3 and 16÷4 = 4, giving the simplified form 3/4.

Mixed Numbers and Improper Fractions

A mixed number combines a whole number and a fraction, such as 1½. An improper fraction has a numerator larger than its denominator, such as 3/2. They represent the same value. To convert an improper fraction to a mixed number: divide the numerator by the denominator. The quotient is the whole number and the remainder over the denominator is the fractional part. 7/4 = 1 remainder 3 = 1 3/4. The calculator shows the mixed number form for any improper result.