Understanding Mixed Numbers and Improper Fractions
What is a mixed number? How do you convert it to an improper fraction? Learn the basics of mixed numbers with clear examples.
What is a Mixed Number?
A mixed number is a combination of a whole number and a proper fraction. It represents a value greater than 1.
Example: 2 1/2 (Two and a half). This means you have 2 whole items plus half of another one.
What is an Improper Fraction?
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). It's called "improper" not because it's wrong, but because it's "top-heavy."
Example: 5/2 (Five halves).
They Are the Same Value!
2 1/2 is exactly the same amount as 5/2.
Think about pizza: If you have 2 whole pizzas and half of another, that's 2 1/2.
If you slice them all into halves, you have 2 halves from the first, 2 from the second, and 1 from the third. Total: 5 halves (5/2).
Converting Mixed to Improper
The Formula:
(Whole Number × Denominator) + Numerator = New Numerator
For 2 1/2: (2 × 2) + 1 = 5. Keep the denominator the same. Result: 5/2.
Converting Improper to Mixed
Divide the numerator by the denominator.
- The result is the Whole Number.
- The remainder is the new Numerator.
- The denominator stays the same.
For 5/2: 5 ÷ 2 = 2 with a remainder of 1. Result: 2 1/2.
Try It Yourself
Our Fraction Calculator automatically handles mixed numbers and improper fractions, converting between them as needed for the final answer.