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

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

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

Addition of Rational Numbers

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

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers





8th Grade Math Practice

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