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 positive.jpg

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

both numbers are negative.jpg

 

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)

  1. Chapter 9 Class 7 Rational Numbers
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.