To determine the correct expression for finding the number of cups of water Katrina drinks in a week, we will follow a step-by-step approach.
1. Daily Water Consumption (gallons to cups):
- Katrina drinks 0.5 gallons of water per day.
- There are 16 cups in a gallon.
To convert her daily intake from gallons to cups, we multiply:
[tex]\[
0.5 \text{ gallons} \times 16 \text{ cups per gallon}
\][/tex]
2. Weekly Water Consumption (days to week):
- There are 7 days in a week.
To find the total weekly intake, we multiply her daily consumption in cups by the number of days in a week:
[tex]\[
(\text{Daily water consumption in cups}) \times 7 \text{ days}
\][/tex]
Now let's examine the given options to see which matches this method:
- Option 1:
[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]
This option is incorrect as multiplying by \(\frac{1 \text{ week}}{7 \text{ days}}\) doesn't calculate the total consumption; it effectively divides by 7 which is not what we need.
- Option 2:
[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]
This option is incorrect since \(\frac{1 \text { gallon}}{16 \text { cups}}\) inverses the required conversion factor.
- Option 3:
[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]
This option is incorrect as well for similar reasons to the previous one; it inverts the conversion factor and also incorrectly divides by 7.
- Option 4:
[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 option accurately converts from gallons to cups and then multiplies by the number of days in a week.
Therefore, the correct expression to find the number of cups of water Katrina drinks in a week is:
[tex]\[
\boxed{\frac{0.5 \text { gallons}}{1 \text { day}} \times \frac{16 \text { cups}}{1 \text { gallon}} \times \frac{7 \text { days}}{1 \text { week}}}
\][/tex]
