Let's get all of the distances lined up:
[tex] \frac{15}{4} [/tex] = home to office
[tex] \frac{2}{3} [/tex] to a restaurant
[tex] \frac{2}{3} [/tex] back to the office
[tex]2[/tex] = store
[tex] \frac{11}{6} [/tex] = back home
So then we just add up all of the numbers. However we need to make sure that there is a common denominator. Let's make the common denominator 12, since that is a common factor to all of the denominators in the problem:
[tex] \frac{45}{12} [/tex] = home to office
[tex] \frac{8}{12} [/tex] to a restaurant
[tex] \frac{8}{12} [/tex] back to the office
[tex] \frac{24}{12} [/tex] = store
[tex] \frac{22}{12} [/tex] = back home
Then let's add them up:
[tex] \frac{45}{12} + \frac{8}{12}+ \frac{8}{12}+ \frac{24}{12}+ \frac{22}{12}= \frac{107}{12} miles [/tex]
This does not reduce to a nice number, however, we can simplify to:
[tex]8 \frac{11}{12}miles [/tex]
