Answer: [tex]\frac{11}{2}[/tex]
Step-by-step explanation:
We need to count the total distance that all the students ran. We first need to identify that the X represents one student. So, we can see that 2 students ran 1/4 of a kilometer, 1 student ran 3/4 of a kilometer, etc.
Let's start off with the students we see that have ran [tex]\frac{1}{4\\}[/tex] of a kilometer.
There are two students who have done this, so we have:
= 2([tex]\frac{1}{4\\}[/tex])
= [tex]\frac{1}{2}[/tex]
Next, we have the students that ran [tex]\frac{3}{4}[/tex] of a kilometer.
There is only one student that did this, so we have:
= 1 ([tex]\frac{3}{4}[/tex])
= [tex]\frac{3}{4}[/tex]
Now, we have the students that ran 1[tex]\frac{1}{4\\}[/tex] of a kilometer, or [tex]\frac{5}{4}[/tex] of a kilometer.
There are two students who have done this, so we have:
= 2([tex]\frac{5}{4}[/tex])
= [tex]\frac{10}{4}[/tex]
= [tex]\frac{5}{2}[/tex]
Lastly, we have the students that ran 1[tex]\frac{3}{4}[/tex] of a kilometer, or [tex]\frac{7}{4}[/tex].
There is only one student who did this, so we have:
= 1 ( [tex]\frac{7}{4}[/tex])
= [tex]\frac{7}{4}[/tex]
Since we have all the distances now, we have to add them up!
= [tex]\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] + [tex]\frac{5}{2}[/tex] + [tex]\frac{7}{4}[/tex]
We need to find a common denominator, which is 4.
= [tex]\frac{2}{4}[/tex] + [tex]\frac{3}{4}[/tex] + [tex]\frac{10}{4}[/tex]+ [tex]\frac{7}{4}[/tex]
= [tex]\frac{22}{4}[/tex]
This can be simplified to:
= [tex]\frac{11}{2}[/tex]
Hope this helps! :)
