# 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 .

# 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.