Question

while checking out the book your sister wanted, you remark, \busy day, huh?\ to ben, the library employee processing your checkout. ben laughs and agrees. he tells you that they need to process each book from the donation efficiently, and that theyll be able to process two-thirds of the donation in four-fifths of a workday.

how many workdays will it take the library employees to process the entire book donation?

one and seven-eighths
eight-fifteenths
one and one-fifth
five-sixths

Explanation:

Identify the given values

We are given the following values:

• Portion of the donation processed: \(\frac{2}{3}\)
• Time taken in workdays: \(\frac{4}{5}\)

Determine the target unknown

We need to find the total workdays required to process the entire donation (\(1\) whole donation).

Set up the division

Using the Fraction Word Problems concept, we find the time per whole donation by dividing the total time by the fraction of the donation completed:

$$ \text{Total Workdays} = \frac{4}{5} \div \frac{2}{3} $$

Perform the fraction division

To divide by a fraction, multiply by its reciprocal:

$$ \text{Total Workdays} = \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} $$

Simplify the resulting fraction

Simplify the fraction and convert it to a mixed number:

$$ \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5} $$

This is written in words as "One and one-fifth".

Answer:

• One and seven-eighths
• Eight-fifteenths
• One and one-fifth (Correct answer)
• Five-sixths