The lengths of XY and YZ add up to the length of XZ:
XY + YZ = XZ
We know that XZ = 10 + 1/5 = 51/5, and XY = 4 + 2/3 = 14/3, so
14/3 + YZ = 51/5
Subtract 14/3 from both sides to solve for YZ:
YZ = 51/5 - 14/3
Find a common denominator; the least common multiple of 5 and 3 is 15, so multiply the first fraction by 3/3 and the second one by 5/5 to get
YZ = 153/15 - 70/15
YZ = (153 - 70)/15
YZ = 83/15
We have 80 = 75 + 8, so that
YZ = 83/15 = (75 + 8)/15 = 75/15 + 8/15 = 5 + 8/15
