How to work with fractions
A fraction has a numerator (top) and a denominator (bottom). The denominator says how many equal parts a whole is split into, and the numerator says how many of those parts you have. 3/4 means three of four equal parts.
The four operations
| Operation | Rule | Example |
|---|---|---|
| Add | a/b + c/d = (ad + bc) / bd | 1/2 + 1/3 = 5/6 |
| Subtract | a/b − c/d = (ad − bc) / bd | 1/2 − 1/3 = 1/6 |
| Multiply | a/b × c/d = ac / bd | 1/2 × 1/3 = 1/6 |
| Divide | a/b ÷ c/d = ad / bc | 1/2 ÷ 1/3 = 3/2 |
After each step, simplify by dividing the top and bottom by their greatest common factor. The GCF calculator shows how.
Worked example with mixed numbers
Multiply 1 1/2 by 2/3:
- Convert the mixed number to an improper fraction: 1 1/2 = 3/2.
- Multiply tops and bottoms: 3/2 × 2/3 = 6/6.
- Simplify: 6/6 = 1.
Fractions in real life
- Cooking: halving a recipe that needs 3/4 cup of flour gives 3/4 × 1/2 = 3/8 cup.
- Woodworking: adding 5/8 inch and 3/16 inch gives 13/16 inch.
- Time: 1 1/2 hours plus 3/4 of an hour is 2 1/4 hours.
Last reviewed October 2026.