Question

A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles.

Answer 1

A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles. I assume you mean to ask "At this rate, how many miles can the vehicle travel per gallon of gasoline?"

We need to divide to find the number of miles the vehicle can travel per gallon of gasoline.

`(Number \; of \; Gallons)/(Number \; of \; Miles) =(13(1)/(2))/(1(1)/(8)) \\ \\ Convert \; mixed\; fration\; to\; improper\; fraction\\ a(b)/(c) =(c * a+b)/(c)\\ \\ (13(1)/(2))/(1(1)/(8))=((27)/(2))/((9)/(8)) \\ \\ When \; dividing \; fractions\; flip \; the \; bottom \; fraction \; and \; multiply\; with \; top\; fraction!\\ (27)/(2) / (9)/(8) =(27)/(2) *(8)/(9)\\ \\ Cancel\; common\; factors\; to\; simplify\\`

`(27)/(2) * (8)/(9)=3 * 4=12`

Conclusion:

The number of miles that the vehicle can travel per gallon of gasoline is 12 miles.