Question

How do you solve `\frac { 3n } { 10} + \frac { 11} { 20} = \frac { 5} { 8}`?

Answer 1

See a solution process below:

Explanation:

Step 1) Subtract `11/20` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`(3n)/10 + 11/20 - 11/20 = 5/8 - 11/20`

`(3n)/10 + 0 = 5/8 - 11/20`

`(3n)/10 = 5/8 - 11/20`

Step 2) Put each fraction on the right side of the equation over a common denominator and subtract the fractions:

`(3n)/10 = (5/5 xx 5/8) - (2/2 xx 11/20)`

`(3n)/10 = 25/40 - 22/40`

`(3n)/10 = (25 - 22)/40`

`(3n)/10 = 3/40`

Step 3) Multiply each side of the equation by `color(red)(10)/color(blue)(3)` to solve the equation for `n` while keeping the equation balanced:

`color(red)(10)/color(blue)(3) xx (3n)/10 = color(red)(10)/color(blue)(3) xx 3/40`

`cancel(color(red)(10))/cancel(color(blue)(3)) xx (color(blue)(cancel(color(black)(3)))n)/color(red)(cancel(color(black)(10))) = cancel(color(red)(10))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/(color(red)(cancel(color(black)(40)))4)`

`n = 1/4`