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Addition and Subtraction of Rational Numbers

We can perform all four fundamental operations on rational numbers as we do for integers and
fractions. The addition and subtraction of rational numbers is carried out in the same way as
that of addition and subtraction of fractions.

Addition and Subtraction of Rational Numbers With the Same Denominator

When the denominator of the given rational numbers are same, then add or subtract the
numerators of the rational numbers, keeping the denominator same.

±
a c a c ac
In general, if and are two rational numbers then, ± =
b b b b b
Example 8: Evaluate the following.
−5 3 5  − 1
(a) + (b) −   While subtracting two rational
8 8 6  6  numbers, we add the additive

−  5
3
Solution: (a)    8  + 8 = − ( ) +5 8 3 = −2 = −1 Note: inverse of the rational number
that is being subtracted, to the

4
8
other rational number.
5  − 1 5  − 1
(b) −   = + additiveinverseof  
6  6  6  6 
+
5 1 51 6
= + = = = 1 FACTS
6 6 6 6 p − p
  −  1 1  Additive inverse of a rational number is q ,
q
 Additive inverseof   is .  −p p
  6  6  and additive inverse of is .
q q
+
5 − 1 5 −− ( 1) 51 6
Alternate method: − = = = = 1
6 6 6 6 6
Addition and Subtraction of Rational Number With Different Denominators

In order to add and subtract the rational numbers having different denominators, follow the
following steps:
1. Convert the given rational numbers into their standard form, if required and then find the
LCM of the denominators of the given rational numbers.
2. Write the rational numbers equivalent to the given rational numbers with this LCM as the
denominator.

3. Now, add or subtract them.
Example 9: Evaluate the following.

5  − 7 9  8  3  − 2  − 7
(a) +   (b) −−  (c) +   −  

9  12  20  15 10  5   20 
Solution: (a) LCM of 9 and 12 is 36.

1
5  − 7 54  −× 20  − 21 20 +− ( 21) − 1
×
73
Therefore, +   = +   = +   = =
9  12  94  12 3  36  36  36 36
×
×
Mathematics-7 64