How to use it
- Enter the first fraction: the whole part (optional), the numerator and the denominator.
- Choose +, −, × or ÷.
- Enter the second fraction. The result, the mixed number, the decimal and the steps update as you type.
How fractions are calculated
- Adding and subtracting. Both fractions are rewritten over the least common denominator (the LCM of the denominators), then the numerators are added or subtracted.
- Multiplying. Numerator times numerator, denominator times denominator: a/b × c/d = ac/bd.
- Dividing. Multiply by the reciprocal of the second fraction: a/b ÷ c/d = a/b × d/c. Dividing by 0 is not defined.
- Simplifying. The numerator and denominator are divided by their greatest common divisor (GCD). The result is in lowest terms.
- Mixed number. The whole part is the numerator divided by the denominator; the remainder becomes the new numerator.
Worked example
1 1/2 + 2/3:
- 1 1/2 = (1 × 2 + 1)/2 = 3/2.
- The least common denominator of 2 and 3 is 6: 3/2 = 9/6 and 2/3 = 4/6.
- 9/6 + 4/6 = 13/6. The GCD of 13 and 6 is 1, so 13/6 is already in lowest terms.
- As a mixed number 13/6 = 2 1/6, and as a decimal 2.1(6) = 2.1666…
Common mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. Bring both to sixths first: 3/6 + 2/6 = 5/6.
- Multiplying only the whole part. 1 1/2 × 2 is 3/2 × 2 = 3, not 2 1/2. Turn a mixed number into an improper fraction before you multiply or divide.
- Flipping the wrong fraction. When dividing, take the reciprocal of the second fraction (the divisor), not the first.