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

From Addition of Rational Numbers to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 04, 24 01:30 AM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  2. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Dec 04, 24 01:07 AM

    Time Duration Example
    Time duration tells us how long it takes for an activity to complete. We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton…

    Read More

  3. Worksheet on Subtraction of Money | Real-life Word Problems | Answers

    Dec 04, 24 12:45 AM

    Worksheet on Subtraction of Money
    Practice the questions given in the worksheet on subtraction of money by using without conversion and by conversion method (without regrouping and with regrouping). Note: Arrange the amount of rupees…

    Read More

  4. Worksheet on Addition of Money | Questions on Adding Amount of Money

    Dec 04, 24 12:06 AM

    Worksheet on Addition of Money
    Practice the questions given in the worksheet on addition of money by using without conversion and by conversion method (without regrouping and with regrouping). Note: Arrange the amount of money in t…

    Read More

  5. Worksheet on Money | Conversion of Money from Rupees to Paisa

    Dec 03, 24 11:37 PM

    Worksheet on Money
    Practice the questions given in the worksheet on money. This sheet provides different types of questions where students need to express the amount of money in short form and long form

    Read More

Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Equivalent Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Adding Rational Numbers

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers