Answer: [tex]\bold{\dfrac{1}{10}}[/tex]
Step-by-step explanation:
All of the fractions should equal to 1. Let x represent the unknown fraction.
[tex]\underline{\text{UFO}}\quad +\quad \underline{\text{IOU}}\quad +\quad \underline{\text{DDT}}\quad +\quad \underline{\text{Other}}\quad =\quad All\\\\\dfrac{1}{3}\qquad +\qquad \dfrac{2}{5}\qquad +\quad \dfrac{1}{6}\qquad +\qquad x\qquad = \quad1\\\\\\\text{The LCM is 30, multiply each fraction to represent this:}\\\dfrac{1}{3}\bigg(\dfrac{10}{10}\bigg) +\ \dfrac{2}{5}\bigg(\dfrac{6}{6}\bigg)\ +\ \dfrac{1}{6}\bigg(\dfrac{5}{5}\bigg)\ +\ x\bigg(\dfrac{30}{30}\bigg) = \quad1\bigg(\dfrac{30}{30}\bigg)[/tex]
[tex]\dfrac{10}{30}\qquad +\qquad \dfrac{12}{30}\qquad +\quad \dfrac{5}{30}\qquad +\qquad \dfrac{30x}{30}\qquad = \quad\dfrac{30}{30}\\\\\\\text{Eliminate the denominator and simplify the numerator, then solve for x:}\\10 + 12 + 5 + 30x = 30\\.\qquad \qquad 27 + 30x = 30\\.\qquad \qquad \qquad 30x = 3\\\\.\qquad \qquad \qquad x=\dfrac{3}{30}\\\\\\.\qquad \qquad \qquad x=\large\boxed{\dfrac{1}{10}}[/tex]
