Question

A high school student read 20 books in 9 1/4 weeks. Find the student's reading rate in books per week.

Answer 1

`\textsf{Improper fraction:}\quad (80)/(37)\; \sf books\;per\;week`

`\textsf{Mixed number:}\quad 2 (6)/(37)\;\sf books\;per\;week`

Explanation:

To find the student's reading rate in books per week, we need to divide the total number of books read by the total number of weeks.

The student read 20 books in 9 1/4 weeks.

First, convert 9 1/4 weeks to an improper fraction:

`9 (1)/(4)=(9\cdot 4+1)/(4)=(36+1)/(4)=(37)/(4)`

Now, divide the total number of books read by the total number of weeks:

`\begin{aligned}\textsf{Reading rate}&=\frac{\textsf{Total number of books read}}{\textsf{Total number of weeks}}\\\\&=(20)/((37)/(4))\\\\&=20 / (37)/(4)\\\\&=20 * (4)/(37)\\\\&=(80)/(37)\; \textsf{books per week}\end{aligned}`

Convert the improper fraction back into a mixed number:

`(80)/(37)=(74+6)/(37)=(74)/(37)+(6)/(37)=2(6)/(37)`

Therefore, the student's reading rate is 80/37 books per week, or 2 ⁶/₃₇ books per week.