Ratio and Fraction

1. 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?
b)   What fraction of the birds on the farm are chickens?

a) ratio and fraction
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.
ratio and fraction
b) ratio and fraction
125  +  50  +  25  =  200
There are a total of 200 birds on the farm.

125 : 200  =  5 : 8
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.
ratio and fraction

2. A certain departmental store rewards shoppers with points for shopping.
Alyssa has    
1 2
3
as many points as Brendan.

ratio and fraction
a)   What is the ratio of Alyssa's points to Brendan's points?
Alyssa's points : Brendan's points  =  5 : 3
b)   What is the ratio of Brendan's points to Alyssa's points?
Brendan's points : Alyssa's points  =  3 : 5
c)   What is the ratio of Alyssa's points to their total points?
Total points  =  5 units  +  3 units  =  8 units
Alyssa's points : Total points  =  5 : 8
d)   Express Brendan's points as a fraction of their total points.
ratio and fraction
Brendan's points are
3
8
of their total points.
e)   Express Brendan's points as a fraction of Alyssa's points.
ratio and fraction
Brendan's points are
3
5
of Alyssa's points.
f)   If they have a total of 72 points, how many points has Alyssa?
ratio and fraction
8 units  =  72
1 unit   =  9
5 units  =  45

Alyssa has 45 points.

3. Jason has    
1 1
2
litres of lemonade and    
3
4
litre of cider.

ratio and fraction
a)   How many times as much lemonade as cider does he have?
Quantity of lemonade : Quantity of cider
=  6 : 3
=  2 : 1

He has 2 times as much lemonade as cider.
b)   Express the quantity of cider as a fraction of the quantity of lemonade.
Quantity of cider : Quantity of lemonade
=  3 : 6
=  1 : 2

He has
1
2
as much cider as lemonade.
c)   What is the ratio of the quantity of lemonade to the total quantity of beverages that Jason has?
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.