Fraction Calculator
Add, subtract, multiply, and divide fractions — with the result fully simplified.
= 0.8333
To add fractions, cross-multiply: a/b + c/d = (a·d + b·c) ÷ (b·d). So 1/2 + 1/3 = (1×3 + 2×1) ÷ (2×3) = 5/6. For multiplication, go straight across; for division, flip the second fraction and multiply.
The four fraction operations
Each operation has its own rule. Addition and subtraction need a common denominator; multiplication goes straight across the top and bottom; division flips the second fraction and multiplies. A quick shortcut for + and − is the cross-multiplication formula below, which builds the common denominator for you.
cross-multiply for + and −; for × multiply across, for ÷ flip and multiply
Worked example
Add 1/2 + 1/3:
- 1 Cross-multiply the numerators. a·d + b·c = 1×3 + 2×1 = 3 + 2 = 5.
- 2 Multiply the denominators. b·d = 2 × 3 = 6, giving 5/6.
- 3 Reduce to lowest terms. gcd(5, 6) = 1, so 5/6 is already simplified — as a decimal, 5 ÷ 6 ≈ 0.8333.
The four operations
For fractions a/b and c/d. Always reduce the result by the greatest common divisor.
| Operation | Rule | Example |
|---|---|---|
| Add | (ad + bc) ÷ bd | 1/2 + 1/3 = 5/6 |
| Subtract | (ad − bc) ÷ bd | 1/2 − 1/3 = 1/6 |
| Multiply | (a·c) ÷ (b·d) | 2/3 × 3/4 = 1/2 |
| Divide | (a·d) ÷ (b·c) | 1/2 ÷ 1/4 = 2 |
Simplifying and common pitfalls
Always reduce. Divide the numerator and denominator by their greatest common divisor — 6/8 becomes 3/4 after dividing both by 2.
Don’t add denominators. 1/2 + 1/3 is not 2/5. You must convert to a common denominator first; the cross-multiply formula does this automatically.
Dividing flips the second fraction. 1/2 ÷ 1/4 multiplies by the reciprocal 4/1, giving 4/2 = 2 — dividing by a fraction less than 1 makes the result larger.