Representing ratios

Representing ratios 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 ratios 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.