Fraction Calculator

Comparing two fractions

To see which of two fractions is larger, cross-multiply. For 3/5 and 5/8, multiply 3 × 8 = 24 and 5 × 5 = 25. Since 24 < 25, 3/5 is smaller than 5/8. This works because it is the same as rewriting both over the common denominator 40: 24/40 and 25/40. Converting to decimals (0.6 and 0.625) gives the same answer and is often quickest with a calculator.

Converting between fractions, decimals and mixed numbers

To turn a fraction into a decimal, divide the numerator by the denominator: 3/8 = 0.375. Some fractions give repeating decimals, such as 1/3 = 0.333..., which is why fractions are often more exact than rounded decimals.

A mixed number like 2 3/4 becomes an improper fraction by multiplying the whole part by the denominator and adding the numerator: (2 × 4 + 3)/4 = 11/4. Converting mixed numbers to improper fractions first makes multiplication and division much easier, and you can convert back at the end by dividing: 11 ÷ 4 = 2 remainder 3, so 2 3/4.

How fraction arithmetic works

To add or subtract fractions, rewrite them with a common denominator, then combine the numerators: a/b + c/d = (ad + bc)/bd. To multiply, multiply the numerators and the denominators: a/b × c/d = ac/bd. To divide, multiply by the reciprocal: a/b ÷ c/d = ad/bc. Finally, simplify by dividing top and bottom by their greatest common divisor.

Using the least common multiple of the denominators instead of their product keeps numbers smaller and makes simplification easier.

Worked example

For 3/4 + 5/6, the least common denominator is 12: 3/4 = 9/12 and 5/6 = 10/12, so the sum is 19/12, or 1 7/12 as a mixed number. For 2/3 ÷ 4/9, multiply by 9/4 to get 18/12, which simplifies to 3/2.

Mixed numbers

Convert mixed numbers to improper fractions before calculating: 2 1/3 = (2 × 3 + 1)/3 = 7/3. Convert back at the end by dividing the numerator by the denominator; the quotient is the whole number and the remainder becomes the new numerator.