Error Analysis Henry incorrectly said the rate StartFraction one fourth gallon Over one twelfth minute EndFraction

Question

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
  
enter your response here gallon​(s​) per minute.
​(Simplify your answer. Type an​ integer, proper​ fraction, or mixed​ number.)

Answer 1

To find the correct unit rate for \(\frac{1/4 \text{ gallon}}{1/12 \text{ minute}}\), we will first perform the division of these two fractions.

We can use the fact that dividing by a fraction is the same as multiplying by its reciprocal.

1. Write the division of fractions: \[ \frac{1/4}{1/12} \]

2. Multiply by the reciprocal of the denominator: \[ = \frac{1}{4} \times \frac{12}{1} = \frac{1 \cdot 12}{4 \cdot 1} = \frac{12}{4} \]

3. Simplify the fraction: \[ \frac{12}{4} = 3 \]

Thus, the correct unit rate is: \[ 3 \text{ gallons per minute.} \]

Part 2: Identifying Henry's likely error

Henry probably miscalculated the unit rate when he divided the two fractions. It's possible that he did not properly multiply by the reciprocal or made an arithmetic error during simplification. His answer of \(\frac{1}{48}\) does not accurately result from the correct calculation of \(\frac{1/4}{1/12}\).

In summary, the correct unit rate is: \[ 3 \text{ gallons per minute.} \]