Question

How do you solve `\frac { 2} { 5} m - \frac { 1} { 5} = \frac { 9} { 40}`?

Answer 1

See a solution process below: `m = 17/16`

Explanation:

First, multiply each side of the equation by `color(red)(4)` to eliminate the fractions while keeping the equation balanced:

`color(red)(40)(2/5m - 1/5) = color(red)(40) xx 9/40`

`(color(red)(40) xx 2/5m) - (color(red)(40) xx 1/5) = cancel(color(red)(40)) xx 9/color(red)(cancel(color(black)(40)))`

`(cancel(color(red)(40))8 xx 2/color(red)(cancel(color(black)(5)))m) - (cancel(color(red)(40))8 xx 1/color(red)(cancel(color(black)(5)))) = cancel(color(red)(40)) xx 9/color(red)(cancel(color(black)(40)))`

`16m - 8 = 9`

Next, subtract `color(red)(8)` from each side of the equation to isolate the `m` term while keeping the equation balanced:

`16m - 8 + color(red)(8) = 9 + color(red)(8)`

`16m - 0 = 17`

`16m = 17`

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

`(16m)/color(red)(16) = 17/color(red)(16)`

`(color(red)(cancel(color(black)(16)))m)/cancel(color(red)(16)) = 17/16`

`m = 17/16`