To determine the number of cups of water Katrina drinks in a week, we need to start by finding out the amount of water she drinks per day in cups, and then calculate the total for the week. Here's the step-by-step approach:
1. Convert gallons per day to cups per day:
Katrina drinks 0.5 gallons of water per day. Since there are 16 cups in a gallon, we multiply the number of gallons she drinks per day by the number of cups in a gallon:
[tex]\[ \frac{0.5 \text{ gallons}}{1 \text{ day}} \times \frac{16 \text{ cups}}{1 \text{ gallon}} = 8 \text{ cups/day} \][/tex]
2. Calculate the total number of cups consumed in a week:
Now that we know Katrina drinks 8 cups of water per day, we want to find out how many cups she drinks in a week. There are 7 days in a week, so we multiply the number of cups per day by the number of days in a week:
[tex]\[ 8 \text{ cups/day} \times 7 \text{ days/week} = 56 \text{ cups/week} \][/tex]
3. Choose the correct expression:
The correct expression should reflect the steps we took:
- Convert gallons to cups per day:
[tex]\[ \frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \][/tex]
- Multiply by the number of days in a week:
[tex]\[ \times \frac{7 \text { days }}{1 \text { week }} \][/tex]
Therefore, the complete expression 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]
So, the correct choice 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]
