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8th Class Mathematics Rational Numbers Question Bank Rational Numbers

  • question_answer
    If \[\left( \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90} \right)\]= \[\frac{p}{q}\] and HCF of (p, q) = 1 then find \[\mathbf{p}\times \mathbf{q}\] =?

    A)  90  

    B)  80             

    C)  100                             

    D)  None of these

    Correct Answer: A

    Solution :

      \[\left( 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10} \right)=\frac{p}{q}\]       \[\therefore \frac{p}{q}=\left( 1-\frac{1}{10} \right)=\frac{9}{10}\] \[\therefore p\times q=9\times 10=90\]


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