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The table shows the number of different books sold by a shop. What fraction of the books sold were non-fiction, hardback books? Give your answer in its simplest form.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
& EBook & Hardback & Paperback \\
\hline
Fiction & 7 & 6 & 8 \\
\hline
Non-fiction & 5 & 13 & 1 \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
First, let's determine the total number of books sold in each category from the given table:

For fiction books:
- EBooks: 7
- Hardbacks: 6
- Paperbacks: 8

For non-fiction books:
- EBooks: 5
- Hardbacks: 13
- Paperbacks: 1

Next, we sum all these values to find the total number of books sold:
[tex]\[ 7 \, (\text{fiction eBooks}) + 6 \, (\text{fiction hardbacks}) + 8 \, (\text{fiction paperbacks}) + 5 \, (\text{non-fiction eBooks}) + 13 \, (\text{non-fiction hardbacks}) + 1 \, (\text{non-fiction paperbacks}) = 40 \][/tex]
Thus, the total number of books sold is [tex]\(40\)[/tex].

Now, we need to identify the number of non-fiction hardback books sold:
[tex]\[ \text{Non-fiction hardback books} = 13 \][/tex]

To find the fraction of the books sold that were non-fiction hardback books, we divide the number of non-fiction hardback books by the total number of books sold:
[tex]\[ \text{Fraction of non-fiction hardback books} = \frac{13}{40} \][/tex]

Since 13 is a prime number and has no common factors with 40 other than 1, the fraction [tex]\(\frac{13}{40}\)[/tex] is already in its simplest form.

Therefore, the fraction of the books sold that were non-fiction hardback books is [tex]\(\frac{13}{40}\)[/tex].

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