Mathematics, Numbers and Numerations, Fractions

Grade 5- 8

An improper fraction always has a numerator equal to or greater than the denominator. The examples below are all improper fractions.

3/2 |
9/9 |
11/10 |
15/3 |
22/12 |
12/9 |

Improper fractions are always equal to or greater than one. An improper fraction always means one or more than one whole object. It is one pizza or more than one pizza. It is one complete bag of candy or more than one complete bag.

A mixed number contains a whole number and a fraction. It is always greater than one. For example, it might be one whole pizza and part of another. A mixed number might indicate three whole pies and part of another pie. Look at the examples below.

Here are more mixed numbers.

1 1/3 |
2 2/5 |
7 1/2 |
3 1/4 |
4 2/7 |
8 1/6 |

Changing Improper Fractions to Mixed Numbers or Whole Numbers

An improper fraction can be reduced to a whole number or a mixed number by dividing the denominator into the numerator. The quotient can be written as a whole number and the remainder, if there is one, as a fraction. Look at the example below.

Here are more examples.

3/2 = 1 1/2 |
7/5 = 1 2/5 |
12/4 = 3 |

The mixed number 1 1/2 and the improper fraction 3/2 both indicate the same amount. The mixed number 1 2/5 and the improper fraction 7/5 both equal the same amount. The whole number 3 and the improper fraction 12/4 indicate the same amount.

- Improper Fractions activity pages
- pencils