Answer:
2/3 and -1/3
Step-by-step explanation:
We have to find which two numbers on the number line are at a distance of 1/2 from 1/6.
The two numbers that are 1/2 units away from 1/6 will be:
1) ![\frac{1}{6}+\frac{1}{2}\\\\ =\frac{1}{6}+\frac{3}{6}\\\\ =\frac{4}{6}\\\\=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D%2B%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B1%7D%7B6%7D%2B%5Cfrac%7B3%7D%7B6%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B4%7D%7B6%7D%5C%5C%5C%5C%3D%5Cfrac%7B2%7D%7B3%7D)
2) ![\frac{1}{6}-\frac{1}{2}\\\\ =\frac{1}{6}-\frac{3}{6}\\\\ =\frac{-2}{6}\\\\ =\frac{-1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D-%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B1%7D%7B6%7D-%5Cfrac%7B3%7D%7B6%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B-2%7D%7B6%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B-1%7D%7B3%7D)
Thus the two numbers are: 2/3 and -1/3
I hope this helps. When the to the power is a negative move it up or down.