Question

Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?
There are 16 cups in a gallon.
A.) 0.5 gallons over 1 day× 16 cups over 1 gallon × 1 week over 7 days
B.)0.5 gallons over 1 day× 1 gallon over 16 cups × 7 days over 1 week
C.)0.5 gallons over 1 day× 1 gallon over 16 cups × 1 week 7 days
D.)0.5 gallons over 1 day× 16 cups over 1 gallon × 7 days over 1 week

Answer 1

D.) 0.5 gallons over 1 day× 16 cups over 1 gallon × 7 days over 1 week

Thx to @Edufirst

Answer 2

Answer: option D.) 0.5 gallons / 1 day × 16 cups / 1 gallon × 7 days / 1 week

Explanation:

The answer is found by doing analyzing the dimensions (units) of the quantities, placing each factor in a way that lead to the cancellation of the  dimensions (units) until you reach the desired units.

You want to find an amount whose final (desired) units are  number of cups of water per week.

Therefore, you have to change the given volume of water, that is in gallons, to cups, and the given unit of time, that is in days, to weeks.

To do that, you use the conversion factors derived from the equivalences of the units:

• 16 cups = 1 gallon

        division property ⇒ 1 = 16 cups / gallon

• 1 week = 7 days

       division property ⇒ 1 = 7 days / week

The final step is multiply the given amount,  0.5 gallons of water per day, by the conversion factors that wre just built:

       0.5 gallon / 1 day = 0.5 gallon / (1 day) × 16 (cups / gallon) × (7 days / week)

When you follow the units in the expression of the right you verify that:

• gallon appears first time in the numerator and a second time in the denominator so they cancel one to each other.

• day appears first time in the numerator and a second time in the denominator, so they also cancel each other.

• the units left are cups / week, which means that you are getting the  number of cups of water she drinks in a week