Question

How do you solve `\frac { w } { 3} + \frac { 2} { 5} = \frac { 1} { 15}`?

Answer 1

`w=-1`

Explanation:

You need to find the (lowest) common denominator and since `3` and `5` are primes and `15=3 cdot 5` we have `"LCD"(3,5,15)=15`. We multiply both sides of the equation by `15`:
$$15\cdot \frac { w } { 3} +15\cdot \frac { 2} { 5} =15\cdot \frac { 1} { 15}$$
$$5w+3 \cdot 2=1$$
$$5w+6=1$$
$$5w=1-6$$
$$5w=-5$$
$$w=-1$$