Question

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?

Answer 1

Hint: This question can be solved based on fractions. We need to assume the value of books in the college bookstore be 1. And the categories of books are History, English and Science books. History books are one third of total books that can be written as $\dfrac{1}{3}$and English books are one sixth of the total books and that can be written as$\dfrac{1}{6}$. Now if we subtract the total number of books from the fractions formed can give us the value of science books.

Complete step-by-step answer:
Given, a box in the college bookstore contains books
Let the value of those books be 1
Now, there were three categories of books, History, English and Science.
Given, history books are one third of the total books$ = \dfrac{1}{3}$
And English books are one sixth of total books$ = \dfrac{1}{6}$
Let the value of Science books be x.
Therefore, we can write
$ \Rightarrow 1 = \dfrac{1}{3} + \dfrac{1}{6} + {\text{x}}$
$ \Rightarrow \dfrac{1}{3} + \dfrac{1}{6} + {\text{x = 1}}$
$ \Rightarrow \left( {\dfrac{1}{3} + \dfrac{1}{6}} \right) + {\text{x = 1}}$
We now send the left hand side values except value x to the other side by changing signs
$ \Rightarrow {\text{x}} = 1 - \left( {\dfrac{1}{3} + \dfrac{1}{6}} \right)$
Add the proper fraction $\left( {\dfrac{1}{3} + \dfrac{1}{6}} \right) = \dfrac{{2 + 1}}{6} = \dfrac{3}{6} = \dfrac{1}{2}$
$ \Rightarrow {\text{x}} = 1 - \dfrac{1}{2}$
$ \Rightarrow {\text{x}} = \dfrac{1}{2}$
Therefore, the fraction of Science books from the total number of books = $\dfrac{1}{2}$

Note: Fraction represents equal parts of a collection. When we divide this collection into equal parts, each part is called a fraction. There are three types of fraction. Proper fraction is where the numerator is less than the denominator. Improper fraction is where numerator is greater than (or equal to) the denominator. Mixed fraction is a combination of a whole number and a proper fraction. We now have solved the above question using addition of proper fractions.