Mixed Numbers and Improper Fractions
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 = ?
Let's try another example:
52/3 = ?
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?
Two More Examples
Let's try another couple of examples:
14/9 = ?
If there is no remainder, just take the quotient as the whole number:
20/5 = ?
For more fun and practice with mixed numbers and improper fractions, see the Fraction Cafe!