Question

Money enjoys running he takes one of three trails. Trail a is 5 9/10 miles long trail b is 5 1/7 miles trail c is 5 5/9 miles order the trails from shortest to longest

Answer 1

To compare the lengths of the trails, we need to convert the mixed numbers into improper fractions.

1. **Trail A: 5 9/10 miles**
\[
5 \frac{9}{10} = \frac{5 \times 10 + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10}
\]

2. **Trail B: 5 1/7 miles**
\[
5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7}
\]

3. **Trail C: 5 5/9 miles**
\[
5 \frac{5}{9} = \frac{5 \times 9 + 5}{9} = \frac{45 + 5}{9} = \frac{50}{9}
\]

Next, we need to compare these fractions: \(\frac{59}{10}\), \(\frac{36}{7}\), and \(\frac{50}{9}\). To do this, we can find a common denominator, which will be 630 (the least common multiple of 10, 7, and 9).

Now we convert each fraction:

1. **For Trail A:**
\[
\frac{59}{10} = \frac{59 \times 63}{10 \times 63} = \frac{3717}{630}
\]

2. **For Trail B:**
\[
\frac{36}{7} = \frac{36 \times 90}{7 \times 90} = \frac{3240}{630}
\]

3. **For Trail C:**
\[
\frac{50}{9} = \frac{50 \times 70}{9 \times 70} = \frac{3500}{630}
\]

Now we can compare the numerators:

- Trail A: \(\frac{3717}{630}\)
- Trail B: \(\frac{3240}{630}\)
- Trail C: \(\frac{3500}{630}\)

Ordering the trails from shortest to longest based on the numerators:

1. Trail B: 5 1/7 miles (\(\frac{3240}{630}\))
2. Trail C: 5 5/9 miles (\(\frac{3500}{630}\))
3. Trail A: 5 9/10 miles (\(\frac{3717}{630}\))

So, the order from shortest to longest is:
**Trail B, Trail C, Trail A.**