Question

How do you solve `\frac { 5} { 4} n - \frac { 5} { 8} = \frac { 2} { 8}`?

Answer 1

See a solution process below:

Explanation:

Step 1) Add `color(red)(5/8)` to each side of the equation to isolate the `n` term while keeping the equation balanced:

`5/4n - 5/8 + color(red)(5/8) = 2/8 + color(red)(5/8)`

`5/4n - 0 = (2 + color(red)(5))/8`

`5/4n = 7/8`

Step 2) Multiply each side of the equation by `color(red)(4)/color(blue)(5)` to solve for `n` while keeping the equation balanced:

`color(red)(4)/color(blue)(5) xx 5/4n = color(red)(4)/color(blue)(5) xx 7/8`

`cancel(color(red)(4))/cancel(color(blue)(5)) xx color(blue)(cancel(color(black)(5)))/color(red)(cancel(color(black)(4)))n = cancel(color(red)(4))/color(blue)(5) xx 7/(color(red)(cancel(color(black)(8)))2)`

`n = 7/(5 xx 2)`

`n = 7/10`