Question

If a bookshelf is \[21\dfrac{1}{8}\] inches long, how many \[1\dfrac{7}{8}\]inch thick books will the bookshelf hold?

Answer 1

Hint: In this problem, we have to find how many books can be fixed in the given bookshelf. We have been given a mixed fraction, to solve it in an easier manner, we can convert the mixed fraction into improper fraction. Then we can use the dividing fraction method to divide the improper fraction to get the final answer.

Complete step by step answer:
We know that the given length of the bookshelf is \[21\dfrac{1}{8}\] inches.
We also know that the thickness of the book is \[1\dfrac{7}{8}\] inch.
Now we can convert both mixed fraction into an improper fraction.
We can take the mixed fraction length of the bookshelf \[21\dfrac{1}{8}\],
Here, we can multiply the number 21 with the denominator and then add the product to the numerator, we get
\[\begin{align}
  & \Rightarrow 21\dfrac{1}{8}=21+\dfrac{1}{8} \\
 & \Rightarrow \dfrac{\left( 21\times 8 \right)+1}{8}=\dfrac{168+1}{8} \\
 & \Rightarrow \dfrac{169}{8} \\
\end{align}\]
Similarly, we can multiply the number 1 with the denominator and then add the product to the numerator, we get
\[\begin{align}
  & \Rightarrow 1\dfrac{7}{8}=1+\dfrac{7}{8} \\
 & \Rightarrow \dfrac{\left( 1\times 8 \right)+7}{8}=\dfrac{8+7}{8} \\
 & \Rightarrow \dfrac{15}{8} \\
\end{align}\]
Now we found the improper fraction of the length of the bookshelf and the thickness of the book.
We have to find how many \[\dfrac{15}{8}\] thickness of books can fit into \[\dfrac{169}{8}\] inches of the bookshelf.
We have to divide the inches of the bookshelf to the thickness of the books, we get
\[\begin{align}
  & \Rightarrow \dfrac{169}{8}\div \dfrac{15}{8} \\
 & \Rightarrow \dfrac{\dfrac{169}{8}}{\dfrac{15}{8}}=\dfrac{169}{8}\times \dfrac{8}{15} \\
\end{align}\]
Now we can cancel the similar terms and simplify it,
\[\Rightarrow \dfrac{169}{15}=11.27\]
We know that we cannot fit a partial book onto the bookshelf, so we can round down to 11.
Therefore, 11 books can fit on the bookshelf.


Note:
Students make mistakes in solving the fraction part, which should be concentrated. We should know how to solve a problem using the dividing fraction method. We should also know how to convert the mixed fraction into an improper fraction to solve these types of problems.