Using the given number line, write the expression that represents the distance between 𝐴 and 𝐵.
To find the distance between two values on a number line, we want to know the absolute value of their difference. That means we could take the absolute value of 𝐴 minus 𝐵 or we could take the absolute value of 𝐵 minus 𝐴. 𝐴 is negative four-fifths. So we plug that in. 𝐵 is positive one-fifth, and so we plug that in and bring everything else down. One option is then the absolute value of negative four-fifths minus one-fifth and the second option is the absolute value of one-fifth minus negative four-fifths.
The first option would give the absolute value of negative five-fifths and the second option would give the absolute value of five-fifths, both of which are one. However, our question was only asking us to write the expression and not to solve it. And so, here are the two expressions that could solve for the distance between 𝐴 and 𝐵.