Comparing Ratios

In comparing ratios we will learn how to arrange the ratios.  

How to Compare Ratios?

To compare two ratios, follow these steps:

Step I: Make the second term of both the ratios equal.

For this, determine the LCM of the second terms of the ratios. Divide the LCM by the second term of each ratio. Multiply the numerator and the denominator of each ratio by the quotient.

Step II: Compare the first terms (numerators) of the new ratios.


Solved examples on comparing ratios:

1. Which of the following ratios is grater?

Compare the ratios 3 : 4 and 1 : 2. 

LCM of the second terms, i.e., 4 and 2 = 4

Now, dividing the LCM by the second term of each ratio, we get 4 ÷ 4 = 1, and 4 ÷ 2 = 2

Therefore, \(\frac{3}{4}\) = \(\frac{3 * 1}{4 * 1}\) = \(\frac{3}{4}\)

\(\frac{1}{2}\) = \(\frac{1 * 2}{2 * 2}\) = \(\frac{2}{4}\)

As 3 > 2, \(\frac{3}{4}\) > \(\frac{2}{4}\), i.e., 3 : 4 > 1 : 2

Therefore the ratio 3:4 is greater than the ratio 1:2 according to the ratio comparison rules.

 

2. Which of the following ratios is grater?

Compare the ratios 3 : 5 and 2 : 11.

LCM of the second terms, i.e., 5 and 11 = 55

Now, dividing the LCM by the second term of each ratio, we get 55 ÷ 5 = 11, and 55 ÷ 11 = 5

Therefore, \(\frac{3}{5}\) = \(\frac{3 * 11}{5 * 11}\) = \(\frac{33}{55}\)

\(\frac{2}{11}\) = \(\frac{2 * 5}{11 * 5}\) = \(\frac{10}{55}\)

As 33 > 10, \(\frac{3}{5}\) > \(\frac{2}{11}\), i.e., 3 : 5 > 2 : 11.

Therefore the ratio 3 : 5 is greater than the ratio 2 : 11 according to the ratio comparison rules.








10th Grade Math

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