Question

How do you solve `\frac{5}{n}=\frac{20}{16}`?

Answer 1

See the entire solution process below:

Explanation:

Multiply each side of the equation by `(color(red)(16)color(blue)(n))/color(green)(20)` to solve for `n` while keeping the equation balanced:

`(color(red)(16)color(blue)(n))/color(green)(20) xx 5/n = (color(red)(16)color(blue)(n))/color(green)(20) xx 20/16`

`(color(red)(16)cancel(color(blue)(n)))/(cancel(color(green)(20))4) xx color(green)(cancel(color(black)(5)))/color(blue)(cancel(color(black)(n))) = (cancel(color(red)(16))color(blue)(n))/cancel(color(green)(20)) xx color(green)(cancel(color(black)(20)))/color(red)(cancel(color(black)(16)))`

`16/4 = n`

`4 = n`

`n = 4`

Answer 2

`n=4`

Explanation:

Simplify `20/16` by dividing the numerator/denominator by a `color(blue)"common factor"` of 4

`rArr5/n=cancel(20)^5/cancel(16)^4`

`rArr5/n=5/4`

Since both fractions in the equation have a numerator of 5, then their denominators will be equal.

`rArrn=4" is the solution"`