Question

How do you solve `6/a=3/8`?

Answer 1

`frac{6}{a}=3/8`

Multiply each side by `a`:
`6=3/8a`

Isolate `a` by multiplying each side by the reciprocal of `3/8`:
`6*(8/3)=a`

`a=16`

Answer 2

Multiply each side of the equation by the lowest common denominator to eliminate the fractions and then solve for `a`. See full solution process below.

Explanation:

First, multiply each side of the equation by the lowest common denominator (in this case `color(red)(8)color(blue)(a)`)to eliminate the fractions and keep the equation balanced:

`6/color(blue)(a) xx color(red)(8)color(blue)(a) = 3/color(red)(8) xx color(red)(8)color(blue)(a)`

`6/cancel(color(blue)(a)) xx color(red)(8)cancel(color(blue)(a)) = 3/cancel(color(red)(8)) xx cancel(color(red)(8))color(blue)(a)`

`6 xx color(red)(8) = 3color(blue)(a)`

`48 = 3color(blue)(a)`

We can now divide each side of the equation by `color(red)(3)` to solve for `a` and keep the equation balanced:

`48/color(red)(3) = (3color(blue)(a))/color(red)(3)`

`16 = (color(red)(cancel(color(black)(3)))color(blue)(a))/cancel(color(red)(3))`

`16 = a`

or

`a = 16`