# Using Tables to Compare Ratios

We use tables to write down different ratios. We also use tables to compare ratios. When comparing two ratios, it is necessary that one of the quantities must be the same. We look for equal amounts in a row or column of the tables, to compare the second amount associated with it. Sometimes we extend the tables in order to get comparable amounts.

Another method is to compare the values of the ratios. We write the values of the ratios as fractions and then use our knowledge of fractions to compare the ratios. When ratios are given in words, we create a table of equivalent ratios in order to compare the ratios.

Compare the ratios 3:7 and 5:8 using tables

### Solution

Step 1:

Writing the given ratios and their equivalent ratios in tables

 3 9 15 30 7 21 35 70
 5 10 20 30 8 16 32 48

Step 2:

We see that the ratios have identical values in last column. So we compare the second numbers associated with the identical values.

70 > 48

Step 3:

So, $\frac{30}{70} < \frac{30}{48} \space or \space \frac{3}{7} < \frac{5}{8} \space or \space 3:7 < 5:8$

Compare the ratios 12:35 and 2:5 using tables

### Solution

Step 1:

Writing the given ratios and their equivalent ratios in tables

 12 24 36 48 35 70 35 70
 2 8 14 20 5 20 35 50

Step 2:

We see that the ratios have identical values in middle column. So we compare the second numbers associated with the identical values.

36 > 14

Step 3:

The group of digits 06 keep on repeating, so we write a bar over them.

Step 4:

So, $\frac{36}{35} > \frac{14}{35} \space or \space \frac{12}{35} > \frac{2}{5} \space or \space 12:35 > 2:5$