Question

UFO Industries makes 1/3 of the

world's widgets. IOU Corporation
makes 2/5 of the world's widgets.
DDT Enterprises makes 1/6 What
fraction is made by other
companies?
CO

Answer 1

Answer:
`\bold{(1)/(10)}`

Explanation:

All of the fractions should equal to 1. Let x represent the unknown fraction.

`\underline{\text{UFO}}\quad +\quad \underline{\text{IOU}}\quad +\quad \underline{\text{DDT}}\quad +\quad \underline{\text{Other}}\quad =\quad All\\\\(1)/(3)\qquad +\qquad (2)/(5)\qquad +\quad (1)/(6)\qquad +\qquad x\qquad = \quad1\\\\\\\text{The LCM is 30, multiply each fraction to represent this:}\\(1)/(3)\bigg((10)/(10)\bigg) +\ (2)/(5)\bigg((6)/(6)\bigg)\ +\ (1)/(6)\bigg((5)/(5)\bigg)\ +\ x\bigg((30)/(30)\bigg) = \quad1\bigg((30)/(30)\bigg)`

`(10)/(30)\qquad +\qquad (12)/(30)\qquad +\quad (5)/(30)\qquad +\qquad (30x)/(30)\qquad = \quad(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=(3)/(30)\\\\\\.\qquad \qquad \qquad x=\large\boxed{(1)/(10)}`