Question

How do you solve `\frac { \frac { 1} { 4} } { - 3\frac { 1} { 6} } = \frac { - 1\frac { 1} { 2} } { x }`?

Answer 1

See a solution process below:

Explanation:

First, I would convert the denominator on the left side of the equation and the numerator on the right side of the equation from a mixed numbers into an improper fractions:

`(1/4)/(-[3 + 1/6]) = (-[1 + 1/2])/x`

`(1/4)/(-[18/6 + 1/6]) = (-[2/2 + 1/2])/x`

`(1/4)/(-19/6) = (-3/2)/x`

We can now cross product or cross multiply the equation:

`1/4 xx x = -19/6 xx -3/2`

`1/4x = (-19 xx -3)/(6 xx 2)`

`1/4x = (-19 xx -color(red)(cancel(color(black)(3)))1)/(color(red)(cancel(color(black)(6)))2 xx 2)`

`1/4x = 19/4`

Now, multiply each side of the equation by `color(red)(4)` to solve for `x` while keeping the equation balanced:

`color(red)(4) xx 1/4x = color(red)(4) xx 19/4`

`cancel(color(red)(4)) xx 1/color(red)(cancel(color(black)(4)))x = cancel(color(red)(4)) xx 19/color(red)(cancel(color(black)(4)))`

`1x = 19`

`x = 19`