# Comparison of Rational Number

Comparison of Rational Number

In order to compare any two Rational Numbers, use the following steps :

1) Obtain the given rational numbers.
2) Write the given rational numbers so that their denominators are positive.
3) Find the LCM of the denominators.
4) Make the denominators same using LCM.
5) Now, compare the numerators and give then proper inequality sign.

Some solved examples :

1) Which of the two rational numbers 3 / 5 and
– 2 / 3 is greater ?

Solution :

As here one rational number is positive and other is negative. And we know that positive numbers are always greater than the negative numbers. So 3 / 5 > - 2 / 3.
________________________________________________________________
2) Which of the two rational numbers 5 / 7 and 2 / 5 is greater?

Solution :

The denominators of 5 /7 and 2 / 5 are positive and different. So find the LCM of 7 and 5, which is 35.

5 / 7 = ( 5 x 5 ) / ( 7 x 5 ) = 25 / 35

2 / 5 = ( 2 x 7) / ( 5 x 7) = 14 / 35

From the above its clear that 25 / 35 is greater than 14 / 35.
________________________________________________________________
3) Arrange the rational numbers -7 / 10, 5 / -8 , 2 / -3 in ascending order.

Solution :

First write the rational numbers with positive denominator so it becomes - 7 / 10, - 5 / 8 , - 2 / 3 .

Find the LCM of denominators ( LCM of 10, 8, 3 is 120 )

- 7 / 10 = ( -7 x 12 ) / (10 x 12 ) = - 84 / 120

-5 / 8 = ( -5 x 15) / ( 8 x 15 ) = - 75 / 120

- 2 / 3 = ( 2 x 40 ) / ( 3 x 40 ) = - 80 / 120

Comparing the numerators of these numbers, we get

- 84 < - 80 < - 75

∴ - 84 / 120 < - 80 / 120 < - 75 / 120 ⇒ -7 / 10 < 2 / -3 < 5 / -8
________________________________________________________________

Rational number

Representation of rational number on number line
Comparison of rational number