Subtracting Rational Numbers, deals with various concepts which are as under:-

- Subtracting Rational Numbers When Denominators are Equal
- Subtracting Rational Numbers When Denominators are Unequal

## Subtracting Rational Numbers When Denominators are Equal

**Question 1**

Subtract:

–

**Explanation**

Difference of Rational Numbers when Denominators are equal =

=

=

So, the difference of

**Question 2**

Subtract:

–

**Explanation**

Difference of Rational Numbers when Denominators are equal =

=

=

So, the difference of

## Subtracting Rational Numbers When Denominators are Unequal

**Question 3**

Subtract:

–

**Explanation**

To subtract two Rational Numbers with different Denominators, first we will find the LCM of both the Denominators.

LCM of 4 and 7 is 28

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Divide LCM by the Denominator of first number

28 ÷ 4 = 7

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 7

=

Divide LCM by the Denominator of second number

28 ÷ 7 = 4

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 4

=

Now – =

Hence, – =

**Question 4**

Subtract:

–

**Explanation**

To subtract two Rational Numbers with different Denominators, first we will find the LCM of both the Denominators.

LCM of 4 and 5 is 20

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Divide LCM by the Denominator of first number

20 ÷ 4 = 5

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 5

=

Divide LCM by the Denominator of second number

20 ÷ 5 = 4

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 4

=

Now – =

Hence, – =

## More Examples on Rational Numbers

**Question 5**

Find the number that should be added to to make it ?

**Explanation**

Let x be the number, which needs to be added to to get

+ x =

x = +

LCM of 8 and 4 is 8

x =

=

Hence, is added to to make it

**Question 6**

Find the number that should be added to to make it ?

**Explanation**

Let x be the number, which needs to be added to to get

+ x =

x = +

LCM of 5 and 6 is 30

x =

=

Hence, is added to to make it

**Question 7**

The sum of two Rational Number is -2 . If one of them is then, other Rational Number is?

**Explanation**

Let, the other Rational Number be x

We are given that the sum of the two Rational Numbers is = -2

+ x = -2

x = -2 –

x = –

LCM of denominator in the two numbers , 1 and 2 is 2

x =

x =

Hence, the other Rational Number is

**Question 8**

The sum of two Rational Number is . If one of them is then, other Rational Number is?

**Explanation**

Let, the other Rational Number be x

We are given that the sum of the two Rational Numbers is =

+ x =

x = –

LCM of denominator in the two numbers , 4 and 12 is 12

x =

x =

x =

Hence, the other Rational Number is

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