Question

How do you solve `-\frac { 2} { 5} = - \frac { 2} { 3} + s`?

Answer 1

`s=4/15`

Explanation:

Isolate s by adding `2/3` to both sides of the equation.

Adding the same value to both sides retains the 'balance' of the equation.

`-2/5color(red)(+2/3)=cancel(-2/3)color(red)cancel(+2/3)+s`

`rArrs=-2/5+2/3larrcolor(magenta)"reversing the equation"`

Before we can add these fractions we require them to have a
`color(blue)"common denominator"`

Multiplying the numerator/denominator of the first fraction by 3 and multiplying the numerator/denominator of the second fraction by 5, gives a common denominator.

`rArrs=(-2/5xx3/3)+(2/3xx5/5)`

`color(white)(xxxx)=-6/15+10/15larrcolor(red)" common denominator"`

Now the denominators are the same we can add the numerators.

`rArrs=(-6+10)/15=4/15`