Question

2.2.PS-15Question Help1gallon161gallon2.Error Analysis Jessie incorrectly said the ratecan be written as the unit rate1minute8per minute. What is the correct unit rate? What was Jessie's likely error?The correct unit rate is gallon(s) per minute.(Simplify your answer. Type an integer, proper fraction, or mixed number.)Enter your answer in the answer box and then click Check Answer.1 partClear AllCheck Answerremaining

Answer 1

Notice that the initial expression can be rewritten as shown below

$\frac{\frac{1}{2}\text{gallon}}{\frac{1}{8}\text{ minute}}=\frac{\frac{1}{2}}{\frac{1}{8}}\frac{\text{ gallon}}{\text{ minute}}=\frac{8}{2}\frac{\text{ gallon}}{\text{ minute}}=4\frac{\text{ gallon}}{\text{ minute}}$

The answer is 4 gallons per minute.

The mistake is that Jessie wrongly calculated (1/2)/(1/8) which should be solved using the next rule

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$

She did

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ac}{bd}$

which is incorrect.