Question

How do you solve `\frac { 36} { z } = \frac { 16} { 40}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by the common denominator of the two fractions which is `color(red)(40)color(blue)(z)`. This will eliminate the fractions while keeping the equation balanced:

`color(red)(40)color(blue)(z) xx 36/z = color(red)(40)color(blue)(z) xx 16/40`

`color(red)(40)cancel(color(blue)(z)) xx 36/color(blue)(cancel(color(black)(z))) = cancel(color(red)(40))color(blue)(z) xx 16/color(red)(cancel(color(black)(40)))`

`1440 = 16z`

Now, we can divide each side of the equation by `color(red)(16)` to solve for `z` while keeping the equation balanced:

`1440/color(red)(16) = (16z)/color(red)(16)`

`90 = (color(red)(cancel(color(black)(16)))z)/cancel(color(red)(16))`

`90 = z`

`z = 90`

Another method to solve for `z` is to "flip" the two fractions and then solve for `z`. Flipping the fractions gives:

`z/36 = 40/16`

Now, multiply each side of the equation by `color(red)(36)` to solve for `z` while keeping the equation balanced:

`color(red)(36) xx z/36 = color(red)(36) xx 40/16`

`cancel(color(red)(36)) xx z/color(red)(cancel(color(black)(36))) = 1440/16`

`z = 90`