Daniel M. answered • 04/16/19
Higher Education Chemistry & Math Tutor with 6+ Years Experience
One relatively simple method we can use to solve this problem is converting our given values of information to useful conversion factors (ratios or equivalence statements) to be used for dimensional analysis. The first step would be to analyze our given information and organize it in a way to be expressed mathematically. We want to make a conversion factor out of our values or figures. We will implore this method until we cannot make a conversion factor from the given value. That value will then, preferably, be the best place to start.
To begin, we can recognize a conversion factor can easily be made with the following piece of information: "They use 1/12 of a gallon of ice cream to make one milkshake."
Mathematically, it's perfectly valid to say that 1/12 gallon of ice cream = 1 milkshake and because of this simple equivalence, we can make a conversion factor from it. However, it may be easier to interpret the above statement as a whole number integer instead of a fraction: 1 gallon of ice cream = 12 milkshakes.
The shop has 7/8 of a gallon of ice cream left, however, there is no easy or useful conversion factor to make from this information. This is a specific indicator that it would be best to start with this information. Additionally, an exact decimal can be obtained from the fraction 7/8 so it would be easier to attach a single value to a unit rather than a fraction. 7/8 is equal to 0.875 (exactly). With our information organized, we can set it up correctly to solve.
(0.875 gallons ice cream)×(12 milkshakes/gallon ice cream) = 10.5 milkshakes that can be made.
