Representing Ratios

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Ratio is the quantitative comparison between quantitates or numbers. Ratio is a very commonly used operation in mathematics. Ratio helps in solving questions related to comparisons, proportions and many more. The symbol of ratio is “:”.  For example, a / b can be written as a : b. Here a / b is fraction form and a:b is the ratio form. The simplification of ratio is writing the given ratio in the most simplified from possible. 

Example 1: Are the ratio’s equivalent?
6 children want cookies and 9 children want cupcake.
8 children want cookies and 4 children want cupcake.
Solution: Here for the given question the ratio is between the numbers of children preferring cookies and cupcakes. The first ratio given is
Number of children preferring cookies: cupcake = 6: 9
Simplifying the ratio (as 6 and 9 have 3 as the common factor) gives 2: 3.
The second ratio given is
Number of children preferring cookies: cupcake = 8: 4
Simplifying the ratio (as 8 and 4 have 4 as the common factor) gives 2: 1.
Therefor the two ratios are not equivalent.
Question: Multiple choice question (Pick the correct option.)
What is equivalent ration to 3: 9?
a)    1: 3                 b) 2: 3             c) 1:3              d) None of these.
Correct answer: option a.
Explanation: Here the given ratio is 3: 9.
It can be further simplified as 3 and 9 have a common factor 3.
Therefore dividing 3 and 9 by 3 gives 3: 9 = 1: 3.
Hence the ratio 3: 9 :: 1:3.

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