Addition of Rational Numbers


 
 
Concept Explanation
 

Addition of Rational Numbers

In order to perform addition of two rational numbers there can be two situations

Type 1: Rational Numbers With Same Denominators:

In order to add two rational numbers having the same denominator, we follow the following steps:

  • Step I: Obtain the numerators of the two given rational numbers and their common denominator.
  • Step II: Add the numerators obtained in step I.
  • Step III: Write a rational number whose numerator is the sum obtained in step II, and whose denominator is the common denominator of the given rational numbers.
  • It follows from the above steps that if frac{p}{q} and frac{r}{q}are two rational numbers with the q as the same denominator, then:

    frac{p}{q}+frac{r}{q}=frac{p+r}{q}

    Illustration: Add frac{3}{5} and frac{13}{5},

    Solution: As the two rational numbers have the same denominator 

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    Sample Questions
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    Question : 1

    Add:  frac{7}{2}+frac{7}{2}=

    Right Option : C
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    Question : 2

    Add the following numbers and simplify them :-

    1. frac{8}{-15} + frac{4}{-3}

    2. frac{7}{-26} + frac{16}{39}

    Right Option : D
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    Explanation
    Question : 3

    Evaluate and choose the correct option frac{2}{5}+left ( -frac{5}{6} right )+left ( -frac{7}{9} right ).

    Right Option : A
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