Addition of Rational Number with Same Denominator

We will learn the addition of rational number with same denominator. In order to add two rational numbers having the same denominator, we follow the following steps:

Step I: Let us obtain the numerators of two given rational numbers and their common denominator.

Step II: Add the numerator of two given rational numbers obtained in step I.

Step III: Write a rational number whose numerator is the sum of two given rational numbers obtained in step II and retain the common denominator (simplify if required).

From the above follows steps we conclude that if \(\frac{a}{b}\) and \(\frac{c}{b}\) are two rational numbers with the same denominator, then \(\frac{a}{b}\) + \(\frac{c}{b}\) = \(\frac{a  +  c}{b}\).

1. Find the sum \(\frac{7}{9}\) + \(\frac{-11}{9}\).

Solution:

\(\frac{7}{9}\) + \(\frac{-11}{9}\)

= \(\frac{7  +  (-11)}{9}\)

= \(\frac{7  -  11}{9}\)

= \(\frac{-4}{9}\)

2. Find the sum \(\frac{8}{-11}\) + \(\frac{3}{11}\)

Solution:

We first express \(\frac{8}{-11}\) as a rational number with positive denominator.

We have, \(\frac{8}{-11}\) = \(\frac{8  ×  (-1)}{(-11)  ×  (-1)}\) = \(\frac{-8}{11}\)

Therefore, (\(\frac{8}{-11}\) + \(\frac{3}{11}\))

= (\(\frac{-8}{11}\) + \(\frac{3}{11}\))

= \(\frac{(-8)  +  3}{11}\)

= \(\frac{-5}{11}\)

2. Add \(\frac{-7}{15}\) and \(\frac{-9}{15}\).

Solution:

\(\frac{-7}{15}\) + \(\frac{-9}{15}\)

= \(\frac{(-7)  +  (-9)}{15}\)

= \(\frac{-7  -  9}{15}\)

= \(\frac{-16}{15}\), [Since, -7 - 9 = -16]

Therefore, \(\frac{-7}{15}\) + \(\frac{-9}{15}\) = \(\frac{-16}{15}\).

3. Add \(\frac{6}{-19}\) and \(\frac{8}{19}\).

Solution:

We first express \(\frac{6}{-19}\) as a rational number with positive denominator.

We have, \(\frac{6}{-19}\) = \(\frac{6  ×  (-1)}{(-19)  ×  (-1)}\) = \(\frac{-6}{19}\)

Now, \(\frac{6}{-19}\) + \(\frac{8}{19}\)

 = \(\frac{-6}{19}\) + \(\frac{8}{19}\)

= \(\frac{-6  +  8}{19}\)

= \(\frac{2}{19}\), [Since, -6 + 8 = 2]

Therefore, \(\frac{6}{-19}\) + \(\frac{8}{19}\) = \(\frac{2}{19}\).

● 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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