# Ratio and Fraction

Donald has 125 chickens, 50 turkeys and 25 ducks on his farm.

| *a)* | *What is the relation between the number of ducks and the number of turkeys?* |

| In terms of ratio, we say, |

| The ratio of the number of ducks to the number of turkeys is **1 : 2**. |

| In terms of fraction, we say, |

| The number of ducks is | __1__ 2 | of the number of turkeys. |

| Both the things above tell us that, |

| For every duck on the farm, there are 2 turkeys. |

| *b)* | *What fraction of the birds on the farm are chickens?* |

| There are a total of 200 birds on the farm. |

| The ratio of the number of chickens to the number of birds on the farm is **5 : 8**. |

| This means, there are **5** chickens out of every **8** birds on the farm. |

| In terms of fraction, we say, | __5__ 8 | of the birds on the farm are chickens. |

A certain departmental store rewards shoppers with points for shopping. |

Alyssa has 1 | __2__ 3 | as many points as Brendan. |

| a) | What is the ratio of Alyssa's points to Brendan's points? |

| b) | What is the ratio of Brendan's points to Alyssa's points? |

| c) | What is the ratio of Alyssa's points to their total points? |

| d) | Express Brendan's points as a fraction of their total points. |

| e) | Express Brendan's points as a fraction of Alyssa's points. |

| f) | If they have a total of 72 points, how many points has Alyssa? |

**a)** Alyssa's points : Brendan's points = 5 : 3

**b)** Brendan's points : Alyssa's points = 3 : 5

**c)** Total points = 5 units + 3 units = 8 units

Alyssa's points : Total points = 5 : 8

**d)**

| Brendan's points are | __3__ 8 | of their total points. |

**e)**

| Brendan's points are | __3__ 5 | of Alyssa's points. |

**f)**

8 units = 72

1 unit = 9

5 units = 45

Alyssa has 45 points.

Jason has 1 | __1__ 2 | litres of lemonade and | __3__ 4 | litre of cider. |

| a) | How many times as much lemonade as cider does he have? |

| b) | Express the quantity of cider as a fraction of the quantity of lemonade. |

| c) | What is the ratio of the quantity of lemonade to the total quantity of beverages that Jason has? |

**a)** Quantity of lemonade : Quantity of cider

= 6 : 3

= 2 : 1

He has 2 times as much lemonade as cider.

**b)** Quantity of cider : Quantity of lemonade

= 3 : 6

= 1 : 2

| He has | __1__ 2 | as much cider as lemonade. |

**c)** Total = 6 units + 3 units = 9 units

Quantity of lemonade : Total quantity of beverages

= 6 : 9

= 2 : 3

| The ratio of the quantity of lemonade to the total quantity of beverages that Jason has is 2 : 3. |