Answer :
Given:
Number of recycling boxes = 4
Each box is [tex]\dfrac{1}{6}[/tex] full of cans.
Kyle puts all of the cans into one box.
To find:
The equation which shows the fraction of the box that is filled with cans.
Solution:
Since, Kyle puts all of the cans into one box, so the fraction of the box that is filled with cans is
[tex]\text{Required fraction}=\text{Number of boxes}\times \text{Part of each box which is filled with cans}[/tex]
Let n be the number of recycling boxes, so, the required equation is
[tex]\text{Required fraction}=n\times \dfrac{1}{6}[/tex]
[tex]\text{Required fraction}=\dfrac{n}{6}[/tex]
Therefore, the required equation is [tex]\text{Required fraction}=\dfrac{n}{6}[/tex], where, n is number of recycling boxes.
Now, put n=4.
[tex]\text{Required fraction}=\dfrac{4}{6}[/tex]
[tex]\text{Required fraction}=\dfrac{2}{3}[/tex]
Therefore, the [tex]\dfrac{2}{3}[/tex] part of box is filled with cans.