How to calculate with fractions
Adding and subtracting: fractions need a common denominator. Rewrite both fractions over the same denominator, add or subtract the numerators, and keep the denominator. 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.
Multiplying: multiply the numerators together and the denominators together. 2/3 × 3/5 = 6/15, which simplifies to 2/5.
Dividing: flip the second fraction (take its reciprocal) and multiply. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4, which simplifies to 3/2.
Simplifying: divide the numerator and denominator by their greatest common divisor. This calculator does it for you, so 6/15 is shown as 2/5.
Good to know
- Answers larger than 1 are shown as improper fractions, such as 3/2. To turn that into a mixed number, divide: 3 ÷ 2 is 1 remainder 1, so 3/2 = 1 1/2.
- Use whole numbers for numerators and denominators. To use a whole number as a fraction, put it over 1, so 4 becomes 4/1.
- A denominator can never be zero, and you can't divide by a fraction whose numerator is zero.
Worked examples
1/2 + 1/3
= 5/6
The common denominator is 6: 3/6 + 2/6 = 5/6.
3/4 − 1/6
= 7/12
The common denominator is 12: 9/12 − 2/12 = 7/12.
2/3 × 3/5
= 2/5
6/15 simplifies to 2/5.
3/4 ÷ 1/2
= 3/2
3/4 × 2/1 = 6/4, which simplifies to 3/2 (or 1 1/2).
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator, usually the least common multiple of the two denominators, rewrite both fractions over it, then add the numerators. For 1/2 + 1/3 the common denominator is 6, which gives 3/6 + 2/6 = 5/6.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 6/15, the greatest common divisor is 3, so the simplified fraction is 2/5.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second. Dividing by 1/2 is the same as multiplying by 2/1.
Can I enter mixed numbers?
Not directly. Convert a mixed number to an improper fraction first. For example, 1 1/2 becomes (1 × 2 + 1)/2 = 3/2.