# Mixed Numbers and Improper Fractions

Updated February 21, 2017 | Factmonster Staff A mixed number is a combination of a whole number and a fraction. For example, if you have two whole apples and one half apple, you could describe this as 2 + 1/2 apples, or 21/2 apples.

### Writing Mixed Numbers as Fractions

This mixed number can also be expressed as a fraction. Each whole apple contains two half apples. Your two whole apples are also four half apples. Four half apples plus one half apple is five half apples. So you have 5/2 apples.

To put this another way: to turn a mixed number into a fraction, multiply the whole number by the denominator (the bottom part), and add the result to the numerator (the top part).

21/2 = ?
Multiply the whole number by the denominator.
The whole number is 2.
The denominator is 2.
2 x 2 = 4.
Add the result to the numerator:
The numerator is 1.
4 + 1 = 5
The numerator is 5. The denominator remains 2.
21/2 = 5/2

### Another Example

Let's try another example:

52/3 = ?
Multiply the whole number by the denominator.
The whole number is 5.
The denominator is 3.
5 x 3 = 15.
Add the result to the numerator:
The numerator is 2.
15 + 2 = 17
The numerator is 17. The denominator remains 3.
52/3 = 17/3

### Proper and Improper Fractions

A fraction in which the numerator is smaller than the denominator, like 1/3 or 2/5 is called a proper fraction. A fraction in which the numerator is larger than or equal to the denominator, like 5/2, 17/3, or 6/6 is called an improper fraction. (To put it another way, a fraction with a value less than 1 is a proper fraction. A fraction with a value greater than or equal to 1 is an improper fraction.)

As we have shown above, mixed numbers can be written as improper fractions. Similarly, improper fractions can be written as mixed numbers.

### Writing Improper Fractions as Mixed Numbers

To write an improper fraction as a mixed number, divide the numerator (top part) by the denominator (bottom part). The quotient is the whole number, and the remainder is the numerator.

How would you express 17/4 as a mixed number?
Divide the numerator by the denominator:
17 ÷ 4 = 4, with a remainder of 1
The quotient, 4, is the whole number. The remainder, 1, is the numerator. The denominator remains 4.
17/4 = 41/4

### Two More Examples

Let's try another couple of examples:

14/9 = ?
Divide the numerator by the denominator:
14 ÷ 9 = 1, with a remainder of 5
The quotient, 1, is the whole number. The remainder, 5, is the numerator. The denominator remains 9.
14/9 = 15/9

If there is no remainder, just take the quotient as the whole number:

20/5 = ?
Divide the numerator by the denominator:
20 ÷ 5 = 4
The quotient, 4, is the whole number. There is no remainder.
20/5 = 4

For more fun and practice with mixed numbers and improper fractions, see the Fraction Cafe!