What Is a Mixed Number?
A mixed number combines a whole number with a fraction: 2 3/4 (two and three-fourths).
It represents a value greater than one whole. 2 3/4 means 2 whole units plus 3/4 of another unit.
Mixed numbers vs. improper fractions
The same value can be written two ways:
| Mixed Number | Improper Fraction |
|---|---|
| 1 1/2 | 3/2 |
| 2 3/4 | 11/4 |
| 3 1/3 | 10/3 |
An improper fraction has a numerator larger than its denominator (like 11/4). It represents a value greater than 1.
Converting between them
Mixed → Improper: Multiply whole number by denominator, add numerator. 2 3/4 → (2 × 4 + 3) / 4 = 11/4
Improper → Mixed: Divide numerator by denominator. 11 ÷ 4 = 2 remainder 3 → 2 3/4
When to use each
- Mixed numbers for understanding and communication: "I ran 2 1/2 miles"
- Improper fractions for computation: multiplying and dividing is easier with 5/2 than 2 1/2
Related concepts
- How to Teach Mixed Numbers: full teaching guide
- Fractions: mixed numbers are fractions greater than 1
- Fractions on a number line: placing mixed numbers past the 1 mark