Question

Rewrite 1/6 book over 2/3 hour as a unit rate​

Answer 1

Answer:

$\dfrac{1}{4}$ books per hour.

Step-by-step explanation:

Given:

For $\frac{2}{3}$ hours, part of book is $\frac{1}{6}$

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:

$\textrm{Unit rate}=\frac{\textrm{Total part of book}}{\textrm{Total part of hours}}\\\textrm{Unit rate}=\frac{1}{6}\div \frac{2}{3}$

On dividing 2 fractions, the division changes to multiplication and the second fraction is reversed. This gives,

$\textrm{Unit rate}=\frac{1}{6}\div \frac{2}{3}\\\\\textrm{Unit rate}=\frac{1}{6}\times \frac{3}{2}\\\textrm{Unit rate}=\frac{1\times 3}{6\times 2}\\\textrm{Unit rate}=\frac{3}{12}\\\textrm{Unit rate}=\frac{3\div 3}{12\div 3}=\frac{1}{4}$

Therefore, the unit rate is $\dfrac{1}{4}$ books per hour.