Answer:
[tex]\dfrac{1}{4}[/tex] books per hour.
Step-by-step explanation:
Given:
For [tex]\frac{2}{3}[/tex] hours, part of book is [tex]\frac{1}{6}[/tex]
To find: Unit rate
Unit rate is the part of book completed in one hour.
So, we use unitary method to determine the unit rate.
Unit rate is given as:
[tex]\textrm{Unit rate}=\frac{\textrm{Total part of book}}{\textrm{Total part of hours}}\\\textrm{Unit rate}=\frac{1}{6}\div \frac{2}{3}[/tex]
On dividing 2 fractions, the division changes to multiplication and the second fraction is reversed. This gives,
[tex]\textrm{Unit rate}=\frac{1}{6}\div \frac{2}{3}\\\\\textrm{Unit rate}=\frac{1}{6}\times \frac{3}{2}\\\textrm{Unit rate}=\frac{1\times 3}{6\times 2}\\\textrm{Unit rate}=\frac{3}{12}\\\textrm{Unit rate}=\frac{3\div 3}{12\div 3}=\frac{1}{4}[/tex]
Therefore, the unit rate is [tex]\dfrac{1}{4}[/tex] books per hour.
