# Subtraction of Rational Numbers

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

In this section we will discuss about subtraction of rational numbers.

Subtraction of Rational-numbers :

In subtraction of rational-numbers apply the same method as that of addition of rational numbers.

Some solved examples :

1) Subtract 3 /4 from 5 / 6

Solution :

Subtract 3 /4 from 5 / 6 ⇒ 5 / 6 – 3 / 4

As the denominators are different.

LCM of 6 and 4 is 12.

5 / 6 = ( 5 x 2) / ( 6 x 2) = 10 / 12

3 / 4 = ( 3 x 3 ) / ( 4 x 3) = 9 / 12

10 / 12 – 9 / 12 = ( 10 – 9 ) / 12 = 1 / 12.
________________________________________________________________
2) Subtract -3 / 8 from – 5 / 7

Solution :

Subtract - 3 / 8 from - 5 / 7 ⇒ - 5 / 7 – ( - 3 / 8)
As the denominators are different.

LCM of 8 and 7 is 56.

- 5 / 7 = (- 5 x 8) / ( 7 x 8) = - 40 / 56

- 3 / 8 = ( - 3 x 7 ) / ( 8 x 7) = - 21 / 56

- 40 / 56 – ( -21 / 56 ) = ( -40 + 21 ) / 56 = -19 / 56 ( since – ( - 21 / 56) = + 21 / 56.
________________________________________________________________
3) The sum of two rational numbers is -3 / 5. If one of the number is – 9/ 20. Find the other.

Solution :

Sum of two numbers = - 3 / 5 , one number = - 9 / 20.

∴ The other number = sum – one number

= - 3 / 5 – ( - 9 / 20 )

= - 3 / 5 + 9 / 20 ( since [ – ( - 9 / 20 ) = + ( 9 / 20 ) ]
 (- 3) x 4 + 9 x 1 = ----------------         20    - 12 + 9 = -------------          20    - 3 = -----      20

Rational number

Representation of rational number on number line
Comparison of rational number