How to Add, Subtract, Multiply, and Divide Fractions

Rule: find a common denominator, convert each fraction, then add numerators.

Example: 1/3 + 1/4. The least common denominator (LCD) is 12. Convert: 4/12 + 3/12 = 7/12.

Example with like denominators: 2/5 + 1/5 = 3/5. When denominators match, just add the tops.

Mixed numbers: convert to improper fractions first. 2 1/3 + 1 1/4 = 7/3 + 5/4 = 28/12 + 15/12 = 43/12 = 3 7/12.

Same process as addition, but subtract numerators instead.

Example: 5/6 − 1/4. LCD = 12. Convert: 10/12 − 3/12 = 7/12.

Watch for negatives: 1/4 − 5/6 = 3/12 − 10/12 = −7/12.

Rule: multiply the numerators, multiply the denominators. No common denominator needed.

Example: 2/3 × 4/5 = 8/15.

Tip: cross-cancel before multiplying to keep numbers small. 3/4 × 8/9: the 3 and 9 share a factor of 3 (giving 1/4 × 8/3), and the 4 and 8 share a factor of 4 (giving 1/1 × 2/3) = 2/3.

Multiplying by a whole number: treat the whole number as a fraction over 1. 5 × 2/3 = 5/1 × 2/3 = 10/3 = 3 1/3.

Rule: flip the divisor (take its reciprocal), then multiply.

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.

Why does this work? Dividing by 2/5 is the same as asking "how many 2/5s fit into 3/4?" Multiplying by the reciprocal answers that question.

Dividing by a whole number: 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6.

After every operation, simplify by dividing both numerator and denominator by their greatest common divisor (GCD).

Example: 8/12. GCD of 8 and 12 is 4. 8 ÷ 4 = 2, 12 ÷ 4 = 3. Simplified: 2/3.

If the numerator is larger than the denominator, convert to a mixed number: 15/4 = 3 3/4.

The Fraction Calculator automatically simplifies every result and shows both improper and mixed-number forms.