# Comparison of Ratio

This is one of the most important calculations and is extensively used in DI. On an average, if somebody does 100 calculations in DI at least 8 to 10 calculations will be from comparing the ratios.

Normally, there are two methods to compare two or more than two ratios:

# Cross multiplication method

Example

Let us compare 11/15 and 13/18.

Cross multiplying numerator of 1st fraction with the denominator of 2nd fraction and denominator of 1st fraction with the numerator of 2nd fraction,

 11 Ã— 18 13 Ã— 15 198 195

Since, 198 is greater than 195 the 1st fraction (11/15) is greater than the 2nd fraction (13/18).

# Decimal calculation

Obviously, here the 1st fraction
is greater than the 2nd fraction .

However, if we have to compare 3156/5438 and 3423/5822, then using any of the above two methods becomes cumbersome and time-consuming.

Here, we will compare ratios with the help of percentage.

# Percentage comparison

Let us first understand this with the help of the following ratios

1st Case

2nd Case

3rd Case

In the 1st case, percentage change in numerator (100%
â†‘) = percentage change in denominator (100%â†‘), so ratios are equal.

In the 2nd case, percentage change in the numerator (200%â†‘) > percentage change in the denominator (100%â†‘), so the 2nd ratio is greater than the 1st ratio.

In the 3rd case, percentage change in the numerator (200%â†‘) < percentage change in the denominator (300%â†‘), so the 1st ratio is greater than the 2nd ratio.

This particular example can also be seen as a general rule for determining the order of ratios.