Question 1208620
<pre>
On the number line x= 2/9 and y= 17/18. The point z divides the segment from x to y into two parts such that the distance from x to z is 5/9 of the distance from z to y. Find the distance from z to y.

To keep things uniform, let's change x to match y's denominator, 18. We than get x as: {{{matrix(1,3, (2/9)(2/2), "=", 4/18)}}} 
Distance between x and y: {{{matrix(1,5, xy, "=", (17/18) - (4/18), "=", 13/18)}}} 
With point z between xy, we get segments, xz, and zy, with xz + zy = xy ===> xz = xy - zy 
As distance from x to z is {{{5/9}}} the distance from z to y, {{{matrix(1,3, xz, "=", (5/9)zy)}}}
                                                    {{{matrix(1,3, xy - zy, "=", (5/9)zy)}}} -- Substituting xy - zy for xz 
                                                    {{{matrix(1,3, 13/18 - zy, "=", 5zy/9)}}} ----- Substituting {{{13/18}}} for xy
                                                  13 - 18zy = 10zy ----- Multiplying by LCD, 18
                                                         13 = 10zy + 18zy
                                                         13 = 28zy
                          <font size = 4><font color = red><b>Distance from z to y</font></font></b>, or {{{highlight_green(matrix(1,3, zy, "=", highlight(highlight(13/28))))}}}

It would seem a lot less complex - if it's considered so now - to draw a number line in 18s,
i.e. {{{matrix(1,7, 1/18, ",", 2/18, ",", 3/18, ",", "etc.")}}}, and marking off points x, y, and z, so this can be clearer to you.</pre>