To find the total distance Mary walked, we need to add the two distances she walked in the morning and afternoon.
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Convert the mixed numbers to improper fractions:
- For 2 1/4: \[ 2 \times 4 + 1 = 8 + 1 = 9 \quad \text{(so } 2 \frac{1}{4} = \frac{9}{4}\text{)} \]
- For 5 7/8: \[ 5 \times 8 + 7 = 40 + 7 = 47 \quad \text{(so } 5 \frac{7}{8} = \frac{47}{8}\text{)} \]
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Now, we need to add \(\frac{9}{4}\) and \(\frac{47}{8}\). To do this, we need a common denominator:
- The least common multiple of 4 and 8 is 8. Convert \(\frac{9}{4}\) to have a denominator of 8: \[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \]
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Now add \(\frac{18}{8}\) and \(\frac{47}{8}\): \[ \frac{18}{8} + \frac{47}{8} = \frac{18 + 47}{8} = \frac{65}{8} \]
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Convert \(\frac{65}{8}\) back to a mixed number:
- Divide 65 by 8:
- 8 goes into 65 eight times (8 x 8 = 64) and the remainder is 1.
- So, \(\frac{65}{8} = 8 \frac{1}{8}\)
- Divide 65 by 8:
Thus, the total distance Mary walked is \(8 \frac{1}{8}\) miles, which matches option c. 8 1/8.
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