Comparing rational numbers

Chapter 8 Class 7 Rational Numbers
Concept wise

We can have 3 cases

1. Both numbers are positive
2. Both numbers are negative
3. One is positive, one is negative

Let’s look at each of them separately

## Both numbers are positive

2/3 & 4/3

Here, denominator is same.

So, we compare numerator.

2 < 4

∴ 2/3 < 4/3

1/2 & 2/3

First of all, we make denominator same

Common denominator = LCM of 2 & 3

= 2 × 3

= 6

## Both numbers are negative

When both numbers are negative,

we ignore the signs & compare

And then we reverse the order

(-2)/3 & (-4)/3

Ignoring signs

2/3 & 4/3

Here, denominator is same.

So, we compare numerator.

2 < 4

∴ 2/3 < 4/3

Multiplying −1 both sides

2/3 × −1 > 4/3 × −1

(-2)/3 > (-4)/3

(- 1 )/ 2 & (- 2 )/3

Ignoring signs

1/2 & 2/3

Making denominator same

Common denominator = LCM of 2 & 3

= 2 × 3

= 6

Multiplying −1 both sides

1/2 × −1 > 2/3 × −1

(-1)/2 > (-2)/3

## One number is negative, one is positive

The negative number is always smaller

(-2)/3 & 4/3

(-2)/3 < 4/3

And,

1/2 & 2/(-3)

1/2 > 2/(-3)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.