Formula
a/b + c/d = (a·d + c·b) ÷ (b·d)a/b × c/d = (a·c) ÷ (b·d)a/b ÷ c/d = (a·d) ÷ (b·c)
- The result is divided by the greatest common divisor of numerator and denominator to reach lowest terms.
To add or subtract, give both fractions the same denominator. To multiply, multiply across. To divide, multiply by the reciprocal.
Worked examples
1/2 + 1/3
- First fraction — numerator
- 1
- First fraction — denominator
- 2
- Operation
- + Add
- Second fraction — numerator
- 1
- Second fraction — denominator
- 3
Result
5/6
Mixed number: 5/6
Decimal: 0.8333333333
Percentage: 83.333333%
1 1/2 + 2 3/4
- First fraction — numerator
- 1
- First fraction — denominator
- 2
- Operation
- + Add
- Second fraction — numerator
- 3
- Second fraction — denominator
- 4
- First whole number
- 1
- Second whole number
- 2
Result
17/4
Mixed number: 4 1/4
Decimal: 4.25
Percentage: 425%
How it works
Adding 1/2 and 1/3 needs a common denominator. The smallest is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6, and the sum is 5/6. The tool uses the least common multiple (see HCF and LCM Calculator) so the numbers stay small, then simplifies.
Multiplying is simpler: 2/3 × 3/4 = 6/12 = 1/2. Dividing flips the second fraction: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
Mixed numbers are converted to improper fractions first (2 ¾ = 11/4), and the answer is shown as both. Arithmetic uses exact integers, so there is no rounding error. See Fraction to Decimal Calculator and Fraction to Percentage Calculator for other forms.
Assumptions and limits
- Denominators must be positive whole numbers. To enter a negative fraction put the minus sign on the numerator.
- In a mixed number the fraction part must be positive; put the minus sign on the whole number.