On the following number line, two rational numbers are graphed.Represent the two numbers as fractions (or mixed numbers) in lowest terms, and write two different expressions to represent the difference between them. Then find the difference showing all your work

The first graphed rational number is at the middle of -2 and -1, thus the number represented is [tex]-1 \frac{1}{2} [/tex]

The second graphed number is five out of six places from from 0 to 1, thus the number graphed is [tex]0+ \frac{5}{6} = \frac{5}{6}[/tex]

The difference between the two numbers can be represented as
[tex]-1 \frac{1}{2} - \frac{5}{6} [/tex]
or
[tex] \frac{5}{6} -(-1 \frac{1}{2} )= \frac{5}{6} +1 \frac{1}{2}[/tex]

To find the difference,

[tex]-1 \frac{1}{2} - \frac{5}{6} \\ \\ =-1 \frac{3+5}{6} \\ \\ =-1 \frac{8}{6} =-2 \frac{2}{6} \\ \\ =-2 \frac{1}{3} [/tex]

Also,

[tex]\frac{5}{6} +1 \frac{1}{2} \\ \\ =1 \frac{5+3}{6} \\ \\ =1 \frac{8}{6} =2 \frac{2}{6} \\ \\ =2 \frac{1}{6} [/tex]