For 3 days Avery ran 4 1/5 miles per day and Lucy ran 2 7/8 miles per day.

How many more miles did Avery run than Lucy overall?

To find out how many more miles Avery ran than Lucy overall, we first calculate the total distance each person ran over 3 days.

### Step 1: Convert mixed numbers to improper fractions
- Avery ran 4 1/5 miles per day.
  \[
  4 \frac{1}{5} = \frac{21}{5}
  \]

- Lucy ran 2 7/8 miles per day.
  \[
  2 \frac{7}{8} = \frac{23}{8}
  \]

### Step 2: Multiply by 3 to get the total distance
- Avery's total distance:
  \[
  3 \times \frac{21}{5} = \frac{63}{5}
  \]

- Lucy's total distance:
  \[
  3 \times \frac{23}{8} = \frac{69}{8}
  \]

### Step 3: Find the difference between the distances
Now, we subtract Lucy's total distance from Avery's total distance. To do this, we first find a common denominator between \(\frac{63}{5}\) and \(\frac{69}{8}\). The least common denominator (LCD) of 5 and 8 is 40.

- Avery's total distance in terms of 40:
  \[
  \frac{63}{5} = \frac{504}{40}
  \]

- Lucy's total distance in terms of 40:
  \[
  \frac{69}{8} = \frac{345}{40}
  \]

### Step 4: Subtract the two fractions
\[
\frac{504}{40} - \frac{345}{40} = \frac{159}{40}
\]

### Step 5: Convert the improper fraction back to a mixed number
\[
\frac{159}{40} = 3 \frac{39}{40}
\]

So, Avery ran \(3 \frac{39}{40}\) miles more than Lucy.

Would you like further details or have any questions? Here are some related questions to explore further:

1. What if Avery had run 5 miles per day instead of 4 1/5?
2. How many miles did Avery and Lucy run combined?
3. How would the result change if Lucy ran 3 1/2 miles per day instead?
4. How can you use estimation to quickly check if the final result is reasonable?
5. What is the total number of miles Lucy ran in 4 days?

**Tip:** When working with fractions, always convert them to improper fractions before performing operations like multiplication or addition.

For 3 days Avery ran 4 1/5 miles per day and Lucy ran 2 7/8 miles per day. How many more miles did Avery run than Lucy overall?

Discover how to calculate the difference in total miles run by Avery and Lucy over three days using mixed numbers, improper fractions, and subtraction. Perfect for students in Grades 5-6, this problem covers key arithmetic concepts.

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