Comparing two quantities in terms of the number of times is called a ratio. As an example, consider the weight of a cow and a man.

Let the weight of the cow = 600 kg

and the weight of the man = 60 kg

We can say that the weight of the cow is 10 times that of the man. This is known as the ‘ratio of the weight of the cow and the weight of the man'. This is represented as 10: 1

Ratios can be expressed as fractions. Let us see how.

Ratio of the weight of the cow to that of the man = $\frac{600}{60}$ = $\frac{10}{1}$ , which is equal to 10:1

We can also see that the weight of the man is $\frac{1}{10}$ to that of the cow. Hence, the ratio of the weight of the man to that of the cow = 1:10

Quantities with the same units only can be compared.For example, the weight of a man is 60kg and that of a grasshopper is 10g.

The ratio of the weight of the man to that of the grass hopper = $\frac{(60\times1000)}{10}$

$\frac{6000}{1}$ = 6000 : 1

We have converted the weight of the man into grams, so that both the quantities are in the same units.

### Equivalent Ratios

Equivalent ratios are same as equivalent fractions.

We know that $\frac{2}{3}$ = $\frac{4}{6}$

Hence, 2:3 is equivalent to 4:6. They are said to be equivalent ratios.

### Ratio Examples:

Given below are some examples on ratios

**Example 1:**

Find the ratio of 40cm and 8m.

**Solution:**

The two quantities should be of the same units for comparison. So, let us convert 8m to cm.

8m = 8 x 100cm = 800 cm

Hence, the ratio is $\frac{40}{800}$ = $\frac{1}{20}$

Therefore, the ratio is 1:20

**Example 2:**

Find an equivalent ratio of 3:5

**Solution:**

Ratio 3:5 = $\frac{3}{5}$

= $\frac{(3\times2)}{(5\times2)}$ = $\frac{6}{10}$

6:10 is an equivalent ratio of 3:5.