To calculate how many miles Anthony drives in one day, we'll first find the total distance he drives in a single trip, which includes driving to work, his friend's house, and then back home.

Step 1: Add the distances

Anthony drives the following distances:

• $\frac{2}{3}$ miles to work
• $\frac{1}{4}$ miles to his friend's house
• $\frac{5}{6}$ miles back home

To sum these, we need to find a common denominator. The least common denominator (LCD) for $3$, $4$, and $6$ is $12$.

Step 2: Convert each fraction to have the same denominator

• $\frac{2}{3}$ becomes $\frac{8}{12}$ (since $2 \times 4 = 8$)
• $\frac{1}{4}$ becomes $\frac{3}{12}$ (since $1 \times 3 = 3$)
• $\frac{5}{6}$ becomes $\frac{10}{12}$ (since $5 \times 2 = 10$)

Step 3: Add the fractions

$\frac{8}{12} + \frac{3}{12} + \frac{10}{12} = \frac{21}{12}$ Thus, in one day, Anthony drives $\frac{21}{12}$ miles, or $1 \frac{9}{12} = 1 \frac{3}{4}$ miles.

Step 4: Calculate the total distance for one week

Anthony drives the same path every day for 7 days (Sunday through Saturday). The total distance for one week is: $7 \times 1 \frac{3}{4} = 7 \times \frac{7}{4} = \frac{49}{4} = 12 \frac{1}{4}$ So, in one week, Anthony drives $12 \frac{1}{4}$ miles, or 12.25 miles.

Final Answer:

Anthony will drive $12.25$ miles in one week.

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Would you like more details on any step? Here are some related questions to explore:

1. How can I convert mixed fractions to improper fractions?
2. What is the least common denominator and how is it determined?
3. How do you add fractions with different denominators?
4. How can you simplify fractions after adding them?
5. What are some real-life applications of adding fractions?

Tip: Always check your work by simplifying fractions after performing any calculations!