### How to compare two Rational Numbers?

To compare any two Rational Number we have to follow the following steps:-

**Step I:** Express both the Rational numbers with positive Denominator.

**Step II:** Take the LCM of the positive Denominators.

**Step III:** Express both the Rational number obtained in step I with this LCM.

**Step IV:** The number with higher Numerator is greater.

### Comparing Rational Numbers Examples

**Question 1**

Fill the missing place:

___

**Explanation**

1st number =

2nd number =

If two rational numbers have common denominators, the number with higher Numerator is greater

If we compare their Numerators, we notice that

12 > 10

Accordingly >

Hence, >

**Question 2**

Fill the missing place:

___

**Explanation**

If we express both the Rational numbers with positive Denominator, we would get

1st number =

2nd number =

To express with a positive Denominator we would multiply both its Numerator and Denominator by (-1).

i.e, =

If two rational numbers have common denominators, the number with higher Numerator is greater

If we compare their Numerators, we notice that

-3 > -8

then, >

Hence, >

**Question 3**

Fill the missing place:

___

**Explanation**

If we express both the Rational numbers with positive Denominator, we would get

1st number =

2nd number =

To express with a positive Denominator we would multiply both its Numerator and Denominator by (-1).

i.e, =

Since Denominators are different, we would need to solve the given equations in the following manner

Take LCM of 5 and 4 which is 20

Multiply both the Numerator and Denominator of by 4 we would get .

=

Similarly, Multiplying Numerator and Denominator of by 5 .

=

If two rational numbers have common denominators, the number with higher Numerator is greater

On comparing Numerators of and

we find -8 > -25

then, >

Hence, >

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