Question

In the morning, Mary walked 2 1/4 miles around the pack. In the afternoon, se walked another 5 7/8 miles. How many miles did she walk total?

a. 7 1/8
b. 7 8/12
c. 8 1/8
d. 8 8/12

Answer 1

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, we convert the mixed numbers into improper fractions:

1. \(2 \frac{1}{4} = 2 \times 4 + 1 = \frac{8 + 1}{4} = \frac{9}{4}\)
2. \(5 \frac{7}{8} = 5 \times 8 + 7 = \frac{40 + 7}{8} = \frac{47}{8}\)

Now, we 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:

\[
\frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8}
\]

Now, we can add \(\frac{18}{8}\) and \(\frac{47}{8}\):

\[
\frac{18}{8} + \frac{47}{8} = \frac{18 + 47}{8} = \frac{65}{8}
\]

Now, convert \(\frac{65}{8}\) back to a mixed number:

Divide 65 by 8, which gives 8 with a remainder of 1:

\[
65 \div 8 = 8 \quad \text{(whole number)}
\]
\[
65 - (8 \times 8) = 1 \quad \text{(remainder)}
\]

Thus, \(\frac{65}{8} = 8 \frac{1}{8}\).

This means the total distance Mary walked is \(8 \frac{1}{8}\) miles.

Among the options given, the correct answer is:

**c. 8 1/8**