Fractions trip people up because the four operations follow different rules. Once you see which one needs a common denominator and which does not, the rest is bookkeeping.
Add and subtract: find a common denominator
You can only add or subtract pieces of the same size. For 3/4 + 2/3, the common denominator is 12: 3/4 becomes 9/12 and 2/3 becomes 8/12, so the sum is 17/12, or 1 5/12 as a mixed number. For 5/6 − 1/4, use 12 again: 10/12 − 3/12 = 7/12.
Multiply: top times top, bottom times bottom
No common denominator needed. 2/3 × 3/5 = 6/15, which simplifies to 2/5 by dividing both parts by 3.
Divide: flip the second fraction and multiply
3/4 ÷ 2/3 becomes 3/4 × 3/2 = 9/8, or 1 1/8. Dividing by a fraction means asking how many of those pieces fit, and flipping does exactly that.
Using the calculator
- Enter the numerator and denominator of the first fraction, then of the second.
- Choose add, subtract, multiply or divide.
- Read the reduced fraction and its decimal value, for example “3/4 + 2/3 = 17/12 (1.416667)”.
A denominator cannot be zero. The result is always shown in lowest terms, so you can compare it with your own working. The tool takes whole numbers on each part, so convert a mixed number such as 1 1/2 to an improper fraction (3/2) first.
Common slips
- Adding the denominators as well as the numerators (1/2 + 1/3 is not 2/5).
- Flipping the wrong fraction when dividing. Only the second one is inverted.
- Forgetting to simplify. 6/15 and 2/5 are the same number, but only one is finished.
Frequently asked questions
How do I simplify a fraction by hand?
Find the greatest common factor of the top and bottom and divide both by it. For 6/15 the factor is 3, giving 2/5. The GCF guide shows how to find it.
Can I use negative fractions?
Yes, put the minus sign on the numerator, for example −3/4. The usual rules for signs apply to the result.