RATIO AND PROPORTION

Ratio
 

Look at the figure above.
X compared with Y is 6 cm to 4 cm.
We say that the ratio of the length of X to the length of Y is 6 cm : 4 cm = 3 : 2.

As a fraction: X is 3/2 of Y
                     Y is 2/3 of X

Examples: 

1. All and Bala shared $80 in the ratio 3 : 7. How much did Bala receive?

   

   Total number of units = 3 + 7
   = 10

   Value of 10 units = $80

   Value of 1 unit = $80
                              10
   = $8 

   Amount of money that Bala received = 7 x $8
   = $56
    
   

   2. Two bags of rice A and B weigh 3 1/2 kg and 2 kg respectively. Find the ratio of the weight of A to the weight of B.

   Weight of A: Weight of B
   = 3 1/2 kg : 2kg
   = 7/2 : 2
   = 7/2 x 2 : 2 x 2
   = 7 : 4

   The ratio of A : B = 7 : 4.
   

   Direct Proportions

   1 pen costs $3.00,
   2 pens cost $6.00,
   3 pens cost $9.00, and so on. 

   We see that as the number of pens increases, the amount of money also increases. 

   Examples:

   1. If a dozen files cost $14.40, how many files can you buy with $21.60?

   Cost of 12 files = $14.40

   $21.60 is the cost of $21.60 x 12 = 18 files
                                    $14 40

   I can buy 18 files with $21.60.

   
   2. If 40 cm² of a metal sheet weighs 200 g, find the weight in kg of 160 cm² of the metal sheet.

   Weight of 40 cm² of the metal sheet = 200 g

   Weight of 160 cm² of the metal sheet = 160 x 200 g
                                                                    40
   = 800 g
   = 0.8 kg