Question

1. miles, karl, laney, and tyrone each walked from their houses to the mall. miles walked \\(\frac{4}{5}\\) mile, karl walked \\(\frac{2}{3}\\) mile, laney walked \\(\frac{1}{2}\\) mile, and tyrone walked \\(\frac{7}{8}\\) mile. order the four friends walking distances from farthest to shortest.

Explanation:

Step1: Find common denominator

The least common denominator of 5, 3, 2, 8 is 120.

Step2: Convert fractions to equivalent forms

$\frac{4}{5} = \frac{4\times24}{5\times24} = \frac{96}{120}$
$\frac{2}{3} = \frac{2\times40}{3\times40} = \frac{80}{120}$
$\frac{1}{2} = \frac{1\times60}{2\times60} = \frac{60}{120}$
$\frac{7}{8} = \frac{7\times15}{8\times15} = \frac{105}{120}$

Step3: Compare numerators

$\frac{105}{120} > \frac{96}{120} > \frac{80}{120} > \frac{60}{120}$

Step4: Map back to original values

Replace equivalent fractions with original distances and match to people.

Answer:

Tyrone ($\frac{7}{8}$ mile), Miles ($\frac{4}{5}$ mile), Karl ($\frac{2}{3}$ mile), Laney ($\frac{1}{2}$ mile)