Ratio and proportion

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 Ratio and proportion

Hello students! Today lets learn about ratio and proportion

Ratio:

What do we mean by a ratio?


                In our daily life, many a times we compare two quantities of the same type. In certain situations comparison  by division makes better sense than comparison by finding out the difference. Thus,

      “A ratio is a comparison of two quantities of the same kind by division”

Let us understand with an example.

Example :1

Here are 5 kites and 7 balloons

Figure.1

Solution:

 The ratio of kites to balloons is 5 is to 7 or 5/7 or 5:7

Here 5 is the first term and 7 is the second term.

The ratio of balloons to kites is 7 is to 5 or 7/5 or 7:5

EXAMPLE:2

Write the ratio of 13 puppies to 4 dogs in three ways

Figure.2

Solution:

     The ratio of 13 puppies to 4 dogs can be written as

  • 13 is to 4
  • 13:4
  • 13/4

EXAMPLE: 3

There are 10 cows for every 18 hens in the farm. Find out the answer to the given ratios.

Figure.3

  1. Hens to cows
  2. Cows to hens
  3. Cows to the total number of animals
  4. Hens to the total number of animals
Solution:

Given:

Number of cows=10

Number of hens=18

Therfore, 

The total number of animals= number of cows+ number of hens  = 10 + 18 = 28

  1. The ratio of hens to cow, 18:10 = 9:5

     2. The ratio of cows to hens, 10:18 = 5:9

     3. The ratio of cows to the total number of animals, 10:28 = 5:14

     4. The ratio of hens to the total number of animals, 18:28 = 9:14


Proportion:

     Piyush and Amit are excellent painters. Recently Piyush bought 20 brushes for Rs. 240.

Amit bought 15 brushes for Rs.180 from the same shop.

Amit claims that the shopkeeper overcharged Piyush. Is Amit right?
Let us see,
First the ratio of the two quantities
The ratio of quantities = 20/15
                                          = 4/3
                                          = 4:3
Then,
The ratio of price         = 240/180
                                         = 4/3
                                         = 4:3
It means, that 
the ratio of quantities = the ratio of prices
 20:15 = 240:180

Therefore, the Amit’s claim is wrong.

The shopkeeper charged Amit and Piyush the same price for the brushes.

When two ratios are equal, they are said to be in PROPORTIONS.

Ratios in proportions are represented as 20:15 :: 240:180
It is read as 20 is to 15 as 240 is to 180.
Here, 
20, 15, 240, 180 are terms .
20 and 180 are middle terms.
15 and 180 are extreme terms.

EXAMPLE: 1

Are these ratios in proportion?63 litres : 35 litres and 28 kilogram : 21 kilogram
Solution:
63 litres : 35 litres can be written as 
              63/35 = 9/5 
                         = 9:5

28 kilogram : 21 kilogram can be written as
               28/21 = 4/3
                          = 4:3

Therefore , 63:35 is not equal to 28:21

EXAMPLE: 2

Are these ratios in proportion? 40:25 and 56:35

Solution:

Here, 
40:25 = 40/25
           = 8/5
           = 8:5

56:35 = 56/35
           = 8/5
           = 8:5

40:25 is equal to 56:35
Therefore, The given ratios are in proportion.

Quiz:

 Facts:

  1. Every odd number has an 'e' in it.🤔
  2. There are 13 letters in both "eleven plus two"and "twelve plus one". 
  3. 60 is the smallest numbee which exactly divisible by all the number from 1 to 5.
  4. Lettees "a", "b", "c", do not appear anywhere in the spelling of numbers from 0 to 999.
  5. Zero(0) is the only number which cannot be represented by Roman numerals.!!






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