Question

Which inequality correctly compares One-third, Five-sixths, and Three-fifths? One-third < Three-fifths < Five-sixths One-third < Five-sixths < Three-fifths Five-sixths < One-third < Three-fifths Five-sixths < Three-fifths < One-third

Answer 1

Answer:

$\frac{1}{3} \: < \: \frac{3}{5} \: < \: \frac{5}{6}$

Step-by-step explanation:

We want to compare the fractions

$\frac{1}{3}, \frac{5}{6} , \frac{3}{5}$

First, we collect LCM

The LCM of 3,6, and 5 is 30

$\frac{1}{3} = \frac{10}{30} , \\ \frac{5}{6} = \frac{25}{30} , \\ \frac{3}{5} = \frac{18}{30}$

$\frac{10}{30} , \frac{18}{30} , \frac{25}{30}$

This means that

$\frac{1}{3} , \frac{3}{5} , \frac{5}{6}$

Hence,

$\frac{1}{3} \: < \: \frac{3}{5} \: < \: \frac{5}{6}$