Question

Jessie incorrectly said the rate 1/5 pound / 1/120 quart can be written as the unit rate 1/100 gallons per quart. What is the correct unit rate? What was Henry's likely error?

Answer 1

Jessie incorrectly converted units without considering the correct conversion factors. The correct unit rate is 3.2 ounces per 480 gallons, not 1/100 gallons per quart. The error likely occurred due to not using the conversion of 4 quarts equaling 1 gallon.

Step-by-step explanation:

The student, Jessie, incorrectly stated that the rate 1/5 pound per 1/120 quart can be simplified to the unit rate 1/100 gallons per quart. This is incorrect because the conversion between quarts and gallons is not considered in the calculation. To find the correct unit rate, we need to use the conversion factors.

First, it is important to know that there are 4 quarts in 1 gallon. Jessie's likely error was not considering this conversion when trying to simplify the unit rate. Hence, to correct the unit rate, we can convert pounds to ounces (since there are 16 ounces in 1 pound) and then quarts to gallons.

Here is how to correct the unit rate:

1. Convert 1/5 pound to ounces: (1/5) * 16 = 16/5 = 3.2 ounces.
2. Convert 1/120 quart to gallons: (1/120) * (1/4) = 1/480 gallons (since there are 4 quarts in a gallon).
3. The corrected unit rate is then 3.2 ounces per 1/480 gallons.

To express this in terms of ounces per gallon, we can simply invert the gallons to get the final unit rate.

Final unit rate: 3.2 ounces per (480/1) gallons = 3.2 ounces per 480 gallons.