To find the total distance that Mary walked, we need to add the two distances together.
First, we will convert the mixed numbers to improper fractions for easier addition.
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The morning distance is \(2 \frac{1}{4}\) miles:
- Convert to an improper fraction: \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
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The afternoon distance is \(5 \frac{7}{8}\) miles:
- Convert to an improper fraction: \[ 5 \frac{7}{8} = \frac{5 \times 8 + 7}{8} = \frac{40 + 7}{8} = \frac{47}{8} \]
Now we can add these two improper fractions. Before adding, we need a common denominator. The denominators are 4 and 8. The least common multiple of 4 and 8 is 8.
Next, we convert \(\frac{9}{4}\) to a fraction with a denominator of 8: \[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \]
Now we can add: \[ \frac{18}{8} + \frac{47}{8} = \frac{18 + 47}{8} = \frac{65}{8} \]
Finally, we can convert \(\frac{65}{8}\) back to a mixed number:
- Divide 65 by 8. The quotient is 8 and the remainder is 1, so: \[ \frac{65}{8} = 8 \frac{1}{8} \]
Thus, the total distance that Mary walked is: \[ \boxed{8 \frac{1}{8}} \text{ miles.} \]
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