**Table of Contents**

- Comparing Two Quantities
- Comparing Two Ratios
- Summary
- Did You Know?
- What’s Next?

In the previous segment, we had a look at **proportion**. In this segment of the chapter ‘Comparing Quantities’, we will learn how to compare ratios.

## When to compare two quantities?

A ratio is a comparison of quantities. It can only be used to compare things of the same type. That is, two quantities can be compared only if both the quantities have the same units.

For example,

The distance travelled by Manu is 5 km and the distance travelled by Nikhil is 1500 m.

The ratio of the distance travelled by Manu to the distance travelled by Nikhil cannot be calculated directly as both the distances are expressed in different units. To find the ratio, it is necessary to express both the distances in the same unit (either both in metres or both in kilometres).

Now, 1 km = 1000 m

So, 5 km = 5 x 1000 m = 5000 m.

Hence, the ratio of the distance travelled by Manu to the distance travelled by Nikhil is

5000 : 1500 = ^{5000} =

1500

5000

500

1500

500

= 10 = 10: 3

3

## Comparing two ratios

While comparing two ratios, the numerator and the denominator need not have the same units. However, the numerators of both the ratios should have the same unit and the denominators of both the ratios should also have the same unit.

For example,

Ravi weighs 90 kg and is 180 cm tall whereas Teja weighs 60 kg and is 120 cm tall.

For Ravi, the ratio of weight to height is 90 : 180 = ^{90} = 1

180 2