Question

How do you solve `6/z=3/5`?

Answer 1

`10`

Explanation:

`6/z=3/5`
`6/3=z/5`
`2=z/5`
`2×5=z`
`z=10`

Answer 2

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)(5)color(blue)(z)`. This will eliminate the fractions while keeping the equation balanced:

`color(red)(5)color(blue)(z) xx 6/z = color(red)(5)color(blue)(z) xx 3/5`

`color(red)(5)cancel(color(blue)(z)) xx 6/color(blue)(cancel(color(black)(z))) = cancel(color(red)(5))color(blue)(z) xx 3/color(red)(cancel(color(black)(5)))`

`30 = 3z`

Now, divide each side of the equation by `color(red)(3)` to solve for `z` while keeping the equation balanced:

`30/color(red)(3) = (3z)/color(red)(3)`

`10 = (color(red)(cancel(color(red)(3)))z)/cancel(color(red)(3))`

`10 = z`

`z = 10`

Another method to solve an equation of two fractions is to "flip" the fractions and then solve for `z`:

`z/6 = 5/3`

Now multiply each side of the equation by `color(red)(6)` to solve for `z`:

`color(red)(6) xx z/6 = color(red)(6) xx 5/3`

`cancel(color(red)(6)) xx z/color(red)(cancel(color(black)(6))) = 30/3`

`z = 10`