Question

if 2/5 of all the books at the library or nonfiction and 1/5 of the non-fiction books are biographies than what fraction of the library books are nonfiction biography

Answer 1

We will investigate the fraction of non-fiction biography books in a library.

There are certain proportions that are given as follows:

`p_(non-fiction)\text{ = }\frac{Number\text{ of non-fiction books}}{Total\text{ number of books}}\text{ = }(2)/(5)`
`q_{biography\text{ }}=\text{ }\frac{Number\text{ of biography books}}{Number\text{ of non-fiction books}}\text{ = }(1)/(5)`

To determine the number of non-fictional biography books we will develop a compound proportions that would leave to following fraction:

`\frac{Number\text{ of non-fiction biography}}{Total\text{ number of books}}`

We can write the above fraction as a compounding off two given fraction ( p and q ) as follows:

`\begin{gathered} \frac{\text{non-fiction biography books}}{\text{Total number of books}}=p_(non-fiction)\cdot q_(biography) \\ \\ \frac{\text{non-fiction biography books}}{\text{Total number of books}}=(2)/(5)\cdot(1)/(5) \\ \\ \frac{\text{non-fiction biography books}}{\text{Total number of books}}=(2)/(25) \end{gathered}`

Therefore, the fraction of non-fiction biography is:

`(2)/(25)`