Question

Henry incorrectly said the rate 1/3 pound / 1/9 gallon can be written as the unit rate 1/27 pound per gallon. What is the correct unit rate? What was Henry´s likely error?

Answer 1

The unit rate is 3 pounds per gallon.

Henry's likely error could have been that he multiplied instead of dividing.

Explanation:

Given the rate 1/3 pound / 1/9 gallon, this can be written in the unit rate by dividing 1/3 pound by 1/9 gallon. First, we will evaluate 1/3 divided by 1/9 and the unit will be in pound per gallon.

1/3 divided by 1/9 can be written as

`(1)/(3) / (1)/(9)`

This then becomes

`(1)/(3) * (9)/(1)`

`(1)/(3) * (9)/(1) = (9)/(3) = 3`

Hence, the unit rate is 3 pounds per gallon.

Henry's likely error could have been that he multiplied instead of dividing. That is, he multiplied 1/3 by 1/9, Such that he gets

`(1)/(3) * (1)/(9)`

`(1)/(3) * (1)/(9) = (1)/(27)`

Hence, the 1/27 pound per gallon he got.