To find the total distance Mary walked, we need to add the two distances together: \(2 \frac{1}{4}\) miles and \(5 \frac{7}{8}\) miles.
First, let's convert each mixed number to an improper fraction:
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\(2 \frac{1}{4}\): \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
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\(5 \frac{7}{8}\): \[ 5 \frac{7}{8} = \frac{5 \times 8 + 7}{8} = \frac{40 + 7}{8} = \frac{47}{8} \]
Now we need to add \(\frac{9}{4}\) and \(\frac{47}{8}\). To do this, we need a common denominator. The least common denominator (LCD) of 4 and 8 is 8.
Next, we convert \(\frac{9}{4}\) to an equivalent fraction with a denominator of 8: \[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \]
Now we can add the two fractions: \[ \frac{18}{8} + \frac{47}{8} = \frac{18 + 47}{8} = \frac{65}{8} \]
Next, we can convert \(\frac{65}{8}\) back to a mixed number: \[ 65 \div 8 = 8 \quad \text{(with a remainder of 1)} \]
Thus, \(\frac{65}{8} = 8 \frac{1}{8}\).
Therefore, the total distance Mary walked is \(8 \frac{1}{8}\) miles.
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