# Arithmetic

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.

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1. 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

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2. Thank You

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3. 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

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4. 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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