Introduction to Ratio

What is ratio?

Ratio is a comparison or relation between two or more quantities.

Examples:

  1. I have 5 red cards and 3 green cards.




    • The ratio of the number of red cards to the number of green cards is 5 : 3.
      This means that for every 5 red cards there are 3 green cards.

    • The ratio of the number of green cards to the number of red cards is 3 : 5.
      This means that for every 3 green cards there are 5 red cards.

    Notes:
    1. The ratio 5 : 3 is read as 5 to 3.
    2. The numbers 5 and 3 are called the terms of the ratio.
    3. The ratio 5 : 3 is not the same as the ratio 3 : 5.

  2. I have 5 red cards, 3 green cards and 2 blue cards.




    • The ratio of the number of red cards to the number of green cards to the number of blue cards is 5 : 3 : 2.
      This means that for every 5 red cards there are 3 green cards and 2 blue cards.

    • The ratio of the number of blue cards to the number of green cards to the number of red cards is 2 : 3 : 5.
      This means that for every 2 blue cards there are 3 green cards and 5 red cards.

What is the purpose of ratio?

A ratio tells you the relation between the quantities of two or more items. So, if you are given the quantity of one of the items and their ratio, then you can calculate the quantities of the other items in the ratio.

Example:

To bake a small cake, you need:
      - 2 cups flour
      - 1 cup sugar

To bake a big cake, you need:
     - 4 cups flour
      -  A  cups sugar

Find the value of A.



Whether you bake a small cake or a big one, the ratio of flour : sugar will be 2 : 1.


The ratio of flour : sugar is 2 : 1.

    Flour : Sugar

=       2 : 1
To bake a big cake, the quantity of flour is doubled. Therefore, the quantity of sugar must also be doubled.
=       (2 : 1) × 2

=        4 : 2 --> big cake


Therefore, you will need 2 cups of sugar to bake a big cake.

Notes:
  1. Ratios do not have any unit.
  2. If you multiply/divide one of the terms of the ratio by a given number then you must also multiply/divide the rest of the terms of the ratio by the same number.