# . comparing ratios

The term ratio means the quantitative relationship of amounts or numbers. The idea of ratio, proportion, and variation is very essential in math and in every-day life. The ratio is written in ways - as a fraction and using a colon. For example - 2:3 or 2/3. Comparison of ratios is used while 3 or more quantities are required for comparison. Suppose a ratio is mentioned between friends P and Q at the marks scored and some other relationship between Q and R, by comparing both the ratios we are able to determine the ratios of all 3 friends P, Q and R.

The two steps to compare ratio are as follows:

Step 1: Make the consequent of each the ratios equal - First, we have to find out the least common multiple (LCM) of each resultant in ratios. Once the LCM is determined, divide the LCM with each resultant of the ratio. Finally, multiply both the consequent and antecedent of each the ratios with the quotient this is obtained previously.

Step 2: Compare the first numbers i.e. the antecedent of each the ratios with each other. Once step 1 is done, then we move ahead to step 2 to find out the comparison between the 2 ratios.

For example:

compare the ratios of the given quantities 8:12 and 3:4. Which of the ratios is greater?

Solution: First find out the LCM of both the consequent in the ratios i.e. 12 and 4. LCM of 6 and 4 is 12

Once the LCM is determined, divide it with both the numbers i.e. 12 ÷ 12 =1 and 12 ÷ 4 = 3

Therefore, (8 x 1):(12 x 1) = 8 and 12  (3 x 3):(4 x 3) = 9 and 12

Since 9 > 8, the ratio 3:4 is greater than 8:12.