Question

Which expression shows the correct way to convert 150 cups into gallons?

a) (150 cups) * (1 gallon / 16 cups)
b) (150 cups) * (1 pint / 2 cups) * (1 quart / 2 pints) * (1 gallon / 4 quarts)
c) (150 cups) * (2 cups / 1 pint) * (2 pints / 1 quart) * (4 quarts / 1 gallon)
d) (4 quarts / 1 gallon) * (2 pints / 1 quart) * (2 cups / 1 pint) * (150 cups / ?)

Answer 1

The correct expression to convert 150 cups into gallons is (150 cups) * (1 gallon / 16 cups), which directly converts cups to gallons, as there are 16 cups in a gallon.

Step-by-step explanation:

The correct way to convert 150 cups into gallons is by using the relationship between cups, pints, quarts, and gallons. Expression (a) directly converts cups to gallons. However, expression (b) provides the step-by-step conversion through intermediate units. Using expression (b), you multiply by the conversion factors in a series: (150 cups) * (1 pint / 2 cups) * (1 quart / 2 pints) * (1 gallon / 4 quarts). Since the numerator and denominator represent equal quantities in each case, all are valid conversion factors.

Option a, (150 cups) * (1 gallon / 16 cups), would be the most straightforward method, as it uses the direct conversion from cups to gallons. This is because there are 16 cups in one gallon, according to the English system measurement that includes units of capacity such as cups, pints, quarts, and gallons.