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

Comparing rational numbers - Part 2

 

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)

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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 and Computer Science at Teachoo