To find the number of cups of water Katrina drinks in a week, we need to perform a unit conversion and multiplication over the number of days in a week.
Here’s a step-by-step breakdown:
1. Gallons to Cups Conversion:
Katrina drinks 0.5 gallons of water per day. Since there are 16 cups in 1 gallon, we need to convert gallons to cups.
2. Daily Consumption in Cups:
We calculate the daily consumption in cups by multiplying the number of gallons consumed per day by the number of cups in a gallon:
[tex]\[
0.5 \text{ gallons/day} \times 16 \text{ cups/gallon}
\][/tex]
This simplifies to:
[tex]\[
8 \text{ cups/day}
\][/tex]
3. Weekly Consumption:
We then multiply the daily consumption in cups by the number of days in a week. There are 7 days in a week, so:
[tex]\[
8 \text{ cups/day} \times 7 \text{ days/week}
\][/tex]
This simplifies to:
[tex]\[
56 \text{ cups/week}
\][/tex]
Given the expressions provided:
- [tex]\(\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \times \frac{1 \text { week }}{7 \text { days }}\)[/tex]
- [tex]\(\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{1 \text { gallon }}{16 \text { cups }} \times \frac{7 \text { days }}{1 \text { week }}\)[/tex]
- [tex]\(\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{1 \text { gallon }}{16 \text { cups }} \times \frac{1 \text { week }}{7 \text { days }}\)[/tex]
- [tex]\(\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \times \frac{7 \text { days }}{1 \text { week }}\)[/tex]
The correct expression that represents the steps we took is:
[tex]\[
\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \times \frac{7 \text { days }}{1 \text { week }}
\][/tex]
This expression correctly converts gallons to cups (by multiplying by [tex]\(\frac{16 \text{ cups}}{1 \text{ gallon}}\)[/tex]) and then multiplies by the number of days in a week.
Therefore, the correct expression is the last one:
[tex]\[
\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \times \frac{7 \text { days }}{1 \text { week }}
\][/tex]
