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

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: \(1 \frac{1}{4}\)