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Arithmetic

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A box in a college bookstore contains books, and each book in the box is a history book, an English book or a science book. If one-third of these books are history books and one-sixth are English books, what fraction of the books are science books?

A. 1/3
B. 1/2
C. 2/3
D. 3/4



****please explain this problem to me because I'm sure to have similar ones like this on my real exam.


Thank you in advance

  • Arithmetic -

    B-1/2
    Let no. of books be x
    No. of history books equal x into 1/3 I.e.x/3
    No. Of English books equal x into 1/3 I.e. x/6
    Rest books = no. Of science books
    =total books -(history books+English books)
    =×-(×/3 +×/6)
    =x-(3x/6)
    =x-x/2
    =x/2 books are of science of total books I.e. x
    No of science book is 1/2 of total books

  • Arithmetic -

    Thank You

  • Arithmetic -

    As per the probability rule
    Total of all probability is 1

    So,
    P(History)+P( English)+P( Science) = 1

    1/3 + 1/6 + P( Science) = 1

    P( Science) = 1- (1/3 + 1/6) = 1 - 1/2


    P( Science) = 1/2

  • Arithmetic -

    1/3+1/6+ science = Find the LCM (lowest common Multiple).
    the LCM for 1/3 is 2.
    the LCM for 1/6 is 1.
    Multiply both numerator and denominator, which gives you
    2/6 + 1/6 = science
    then add the 2 and 1
    copy the 6 at the bottom which result 3/6 then simplify to lowest form which 1/2.

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