Addition of Rational Numbers
We will learn the operation of addition of rational numbers. The addition of rational numbers is carried out in the same way as that of addition of fractions. If two rational numbers are to be added we should first convert each of them into a rational number with positive denominator.
In addition we divide the rational numbers into the following two categories:
1. When Given Numbers have same Denominator:
In this case, we define (a/b + c/b) = (a + c)/b
For example:
(i) Add 3/7 and 56/7
Solution:
3/7 + 56/7
= (3 + 56)/7
= 59/7, [Since, 3 + 56 = 5 9]
Therefore, 3/7 + 56/7 = 59/7
(ii) Add 8/13 and -5/13
Solution:
3/13 + -5/13
= [3 + (-5)]/13
= (3 -5)/13
= -2/13, [Since, 3 - 5 = -2]
Therefore, 3/13 + -5/13 = = -2/13.
2. When Denominators of Given Numbers are Unequal:
In this case we take the (least common multiple) LCM of their denominators and
express each of the given numbers with this LCM as the common denominator. Now,
we add these numbers as shown above.
For example:
(i) Add 5/6 and 7/9
Solution:
Clearly, denominators of the given numerators are positive.
The LCM of the denominators 6 and 18 is 18.
Now, we express 5/6 and 7/9 into forms in which both of them have the same denominator 18.
We have,
5/6 = 5 × 3/6 × 3 = 15/18
and
7/9 = 7 × 2/9 × 2 = 14/18
Therefore, 5/6 + 7/9
= 15/18 + 14/18
= (15 + 14)/18
= 29/18
(ii) Add 5/6 and -3/7
Solution:
The denominators of the given rational numbers are 6 and 7 respectively.
The LCM of 6 and 7 is 42.
Now, we rewrite the given rational numbers into forms in which both of them have the same denominator.
5/6 = 5 × 7/6 × 7 = 35/42
and
-3/7 = -3 × 6/7 × 6 = -18/42
Therefore, 5/6 + -3/7
= 35/42 + -18/42
= 35 - 18/42
=17/42
(iii) Find the sum:
-9/16 + 5/12
Solution:
LCM of 16 and 12 = (4 × 4 × 3) = 48.
Therefore, -9/16 + 5/12
= 3 × (-9) + 4 × 5/48
= (-27) + 20/48
= -7/48
● Rational Numbers
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
Equivalent form of Rational Numbers
Rational Number in Different Forms
Properties of Rational Numbers
Lowest form of a Rational Number
Standard form of a Rational Number
Equality of Rational Numbers using Standard Form
Equality of Rational Numbers with Common Denominator
Equality of Rational Numbers using Cross Multiplication
Comparison of Rational Numbers
Rational Numbers in Ascending Order
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
Rational Numbers on the Number Line
Addition of Rational Number with Same Denominator
Addition of Rational Number with Different Denominator
Properties of Addition of Rational Numbers
Subtraction of Rational Number with Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
Simplify Rational Expressions Involving the Sum or Difference
Multiplication of Rational Numbers
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
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