Fractions show up everywhere: recipes, measurements, homework and discounts. Once you know four simple rules, you can handle any fraction problem. Want the answer instantly? Use our fraction calculator.
The parts of a fraction
In 3/4, the top number (3) is the numerator and the bottom number (4) is the denominator. The denominator tells you how many equal parts make a whole; the numerator tells you how many parts you have.
1. Adding fractions
If the denominators are the same, add the numerators and keep the denominator: 1/5 + 2/5 = 3/5.
If they are different, find a common denominator first. The easiest is to multiply the two denominators:
- 3/4 + 2/3: common denominator 4 x 3 = 12.
- Convert: 3/4 = 9/12 and 2/3 = 8/12.
- Add: 9/12 + 8/12 = 17/12.
- Convert to a mixed number: 17/12 = 1 5/12.
2. Subtracting fractions
Same method as adding: get a common denominator, then subtract the numerators. 5/6 – 1/4 = 10/12 – 3/12 = 7/12.
3. Multiplying fractions
No common denominator needed. Multiply straight across: 2/3 x 3/5 = 6/15, which simplifies to 2/5. Tip: you can cancel common factors before multiplying to keep numbers small.
4. Dividing fractions
Keep the first fraction, change division to multiplication, and flip the second fraction (use its reciprocal): 3/4 / 1/2 = 3/4 x 2/1 = 6/4 = 1 1/2.
Working with mixed numbers
Convert mixed numbers to improper fractions first. 2 1/3 = (2 x 3 + 1)/3 = 7/3. Do the operation, then convert back if you want a mixed number.
Simplifying the answer
Divide the numerator and denominator by their greatest common divisor (GCD). For 18/24 the GCD is 6, so 18/24 = 3/4.
Common mistakes
- Adding denominators: 1/2 + 1/3 is not 2/5. It is 5/6.
- Forgetting to flip the second fraction when dividing.
- Not simplifying the final answer.
Practice
Try these, then check them with the fraction calculator: 1/2 + 3/8, 7/10 – 1/4, 4/9 x 3/8, 5/6 / 2/3. Answers: 7/8, 9/20, 1/6, 1 1/4.