# Multiplying fractions and mixed numbers

## In a nutshell

Fractions and mixed numbers can be multiplied by whole numbers.

##### Example 1

*At a restaurant three people choose pizza from the menu. Each person eats *$\frac{3}{4}$* of a pizza. How much pizza do they eat altogether?*

*Three lots of three quarters totals nine quarters.*

$\frac{3}{4}\times3 = \underline{\frac{9}{4}}$

## Multiplying fractions by whole numbers

#### procedure

1. | Multiply the numerator of the fraction by the whole number. **Note:** The denominator does not change. |

2. | Simplify the fraction if possible. |

##### Example 2

*Multiply $\frac{3}{12}$ by $3$. Give your answer as a fraction in its simplest form.*

*Multiply the numerator of the fraction by the whole number:*

*$\frac{3\times3}{12} = \frac{9}{12}$*

*Simplify the fraction:*

*$\frac{9\div3}{12\div3}=\underline{\frac{3}{4}}$*

## Multiplying mixed numbers by whole numbers

#### procedure

1. | Convert the mixed number into an improper fraction. |

2. | Multiply the numerator of the fraction by the whole number. |

3. | Convert the answer to Step 2 back into a mixed number. |

4. | Simplify the fraction if possible. |

##### Example 3

*Multiply $2\frac{1}{4}$ by $4$. Give your answer as a mixed number in its simplest form.*

*Convert the mixed number into an improper fraction:*

*$2\frac{1}{4} = \frac{2\times4+1}{4} = \frac{9}{4}$*

*Multiply the numerator of the fraction by the whole number:*

*$\frac{9}{4}\times4=\frac{36}{4}$*

*Convert the fraction back into a mixed number:*

*$36\div4=\underline{9}$*

*Note:** This question has no remainder, so the answer is a whole number with no fraction part.*