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?


  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.

Word Problem 1

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.

Word Problem 2

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.