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 the following numbers :

    1.  frac{7}{9} and 4 .

    3. frac{5}{12} and frac{3}{8}

    Right Option : B
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    Question : 2

    Add the following numbers :

    1.  frac{3}{8} and frac{-5}{12}

    2. frac{5}{12} and frac{3}{8}

    Right Option : B
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    Question : 3

    If  large large  frac{3}{7}+x+(frac{-8}{21})+frac{5}{22}=frac{-125}{462} . Then x is : ________________________________

    Right Option : C
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    Explanation
     
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