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Part 1
Error Analysis  Henry incorrectly said the rate StartFraction one fourth gallon Over one twelfth minute EndFraction
can be written as the unit rate StartFraction 1 Over 48 EndFraction gallon
per minute. What is the correct unit​ rate? What was Henry​'s likely​ error?
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Part 1
The correct unit rate is
  
3 gallon​(s​) per minute.
​(Simplify your answer. Type an​ integer, proper​ fraction, or mixed​ number.)
Part 2
What was Henry​'s likely​ error?
A.
He multiplied both terms by the denominator. He should have divided both terms by the denominator.
B.
He multiplied both terms by the numerator. He should have multiplied both terms by the denominator.
C.
He divided both terms by the denominator. He should have multiplied both terms by the denominator.
D.
He divided both terms by the numerator. He should have divided both terms by the denominator.

1 answer

To find the correct unit rate from the rate \( \frac{1 \text{ gallon}}{1/12 \text{ minute}} \) (or \( \frac{1/4 \text{ gallon}}{1/12 \text{ minute}} \)), we need to divide \( 1/4 \) gallon by \( 1/12 \) minute.

To divide fractions, we multiply by the reciprocal of the second fraction:

\[ \frac{1/4 \text{ gallon}}{1/12 \text{ minute}} = \frac{1}{4} \times \frac{12}{1} = \frac{1 \times 12}{4 \times 1} = \frac{12}{4} = 3 \text{ gallons per minute} \]

So, the correct unit rate is 3 gallons per minute.

Part 2

Regarding Henry's likely error:

Henry said the rate could be simplified to \( \frac{1}{48} \) gallon per minute. This indicates he incorrectly manipulated the fractions.

He likely:

  • Misunderstood how to properly divide the fractions involved.
  • It looks like he multiplied instead of correctly dividing or applying the reciprocal.

Thus, the most fitting description of his error is:

A. He multiplied both terms by the denominator. He should have divided both terms by the denominator.

This accurately describes the confusion in handling the division of the fractions instead of recognizing the need to multiply by the reciprocal.