Answer:
[tex]4\frac{1}{12}[/tex] miles.
Step-by-step explanation:
The goal of the family is to hike [tex]11 \frac{2}{3}[/tex] miles in total. Converting this to an improper fraction, we need a total of [tex]\frac{35}{3}[/tex] miles.
On Monday the family completed [tex]2 \frac{1}{12}[/tex] miles, or [tex]\frac{25}{12}[/tex] miles.
On Tuesday the family completed [tex]2 \frac{1}{3}[/tex] miles, or [tex]\frac{7}{3}[/tex] miles.
On Wednesday the family completed [tex]3 \frac{1}{6}[/tex] miles, or [tex]\frac{19}{6}[/tex] miles.
Next, we can add the total amount of hiking the family has completed from Monday-Wednesday.
[tex]distance= \frac{25}{12} + \frac{7}{3} + \frac{19}{6}[/tex]
In order to add these values, we need to convert all of the fractions so that they have the same denominator. The least common multiple (LCM) of 12, 3, and 6 is 12, so the fractions can all be converted into having a denominator of 12.
Monday's distance [tex]\frac{25}{12}[/tex] already has a denominator of 12.
Tuesday's distance is [tex]\frac{7 * 4}{3 * 4} = \frac{28}{12}[/tex].
Wednesday's distance is [tex]\frac{19 * 2}{6 * 2} = \frac{38}{12}[/tex].
Convert the total distance goal to have a denominator of 12 as well. [tex]\frac{35 * 4}{3 * 4} = \frac{140}{12}[/tex].
Sum the total distance the family has walked on Monday-Wednesday. [tex]\frac{25}{12} + \frac{28}{12} + \frac{38}{12} = \frac{91}{12}[/tex].
Subtract this value from the total hiking distance. [tex]\frac{140}{12} - \frac{91}{12} = \frac{49}{12}[/tex]. The family needs to walk [tex]\frac{49}{12}[/tex] miles, or [tex]4 \frac{1}{12}[/tex] miles on Thursday to complete their goal.
