Question

Three friends went hiking on a trail, the first one went 1 3/7 miles, the second went 1 4/14 miles and the third went 1 1/4, identify the numerical order of the distances hiked from most to least

Answer 1

To compare the distances hiked by the three friends, we need to convert all of them to improper fractions for easier comparison.

1. **First Friend**: \(1 \frac{3}{7}\)
- Convert to improper fraction:
\[
1 \frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{7 + 3}{7} = \frac{10}{7}
\]

2. **Second Friend**: \(1 \frac{4}{14}\)
- Simplify: \( \frac{4}{14} = \frac{2}{7} \)
- Convert to improper fraction:
\[
1 \frac{4}{14} = 1 \frac{2}{7} = \frac{7 \times 1 + 2}{7} = \frac{7 + 2}{7} = \frac{9}{7}
\]

3. **Third Friend**: \(1 \frac{1}{4}\)
- Convert to improper fraction:
\[
1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}
\]

Now we have the distances in improper fraction form:
- First Friend: \(\frac{10}{7}\)
- Second Friend: \(\frac{9}{7}\)
- Third Friend: \(\frac{5}{4}\)

Next, we will convert \(\frac{5}{4}\) into a fraction with a denominator of 7 to compare all of them:

\[
\frac{5}{4} = \frac{5 \times 7}{4 \times 7} = \frac{35}{28}
\]

Now we'll express all distances with a common denominator, let's use 28:
- \(\frac{10}{7} = \frac{10 \times 4}{7 \times 4} = \frac{40}{28}\)
- \(\frac{9}{7} = \frac{9 \times 4}{7 \times 4} = \frac{36}{28}\)
- \(\frac{5}{4} = \frac{35}{28}\)

Now we can sort the fractions:
- \(\frac{40}{28} \) (First Friend)
- \(\frac{36}{28} \) (Second Friend)
- \(\frac{35}{28} \) (Third Friend)

Thus, the order of distances hiked from most to least is:
1. First Friend: \(1 \frac{3}{7}\)
2. Second Friend: \(1 \frac{4}{14}\)
3. Third Friend: \(1 \frac{1}{4}\)