# Mixed numbers and improper fractions

## In a nutshell

A mixed number is a number which consists of a whole number and a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

##### Example 1

*Below are some examples of mixed numbers:*

*$2\frac{1}{2}, 5\frac{1}{4}, 8\frac{3}{10}$*

*Below are some examples of improper fractions:*

*$\frac{13}{2}, \frac{7}{7}, \frac{27}{5}$*

## Writing a mixed number as an improper fraction

#### procedure

1. | Multiply the whole number by the denominator of the fraction part. |

2. | Add the answer to Step 1 to the numerator of the fraction part. |

3. | Write the answer to Step 2 over the denominator of the fraction part. |

##### Example 2

*Convert the following mixed number into an improper fraction:*

*$2\frac{7}{9}$*

*Multiply the denominator and the whole number:*

*$2 \times 9 = 18$*

*Add the answer to the previous step to the numerator:*

*$18+7 = 25$*

*Write the answer to the previous step above the denominator.*

*$\underline{\frac{25}{9}} (= 2\frac{7}{9})$*

## Writing an improper fraction as a mixed number

#### procedure

1. | Divide the numerator by the denominator using long division with remainders. |

2. | Write down the whole number result. |

3. | Write the remainder over the denominator of the original improper fraction. This will be the fraction part of the mixed number. **Note:**** ***If there is no remainder, the answer is a whole number with no fraction part.* |

4. | Simplify the fraction part if required. |

##### Example 3

*Convert the following improper fraction into a mixed number:*

*$\frac{23}{7}$*

*Divide the numerator by the denominator:*

*$23 \div 7 = 3\thinspace R\thinspace2$*

*The whole number part is 3. The remainder is written over the original denominator.*

*$\underline{3\frac{2}{7}}(=\frac{23}{7})$*

**Note:** *The fraction part in this example cannot be simplified.*