Question

How do you evaluate `(\frac{3}{5}-\frac{1}{6})\div (-\frac{1}{3})`?

Answer 1

`-39/30`

Explanation:

This problem looks very difficult because it has the `-:` sign.

First, we should change the `-:` to a multiplication sign in order to make this problem easier. We do this by flipping one of the parts of this problem, like this:
`(3/5 - 1/6) * (-3/1)`

Now, we use the distributive property to solve this. The `-3/1` multiplies to everything inside the problem like this:
`-9/5 + 3/6`

Now, we have to make all the bottom (denominator) numbers to be the same in order to solve it. We use the LCD, or lowest common denominator, which in this case is `30`.

In order to make the bottom `30` for `-9/5`, we need to multiply all of it by 6, so it looks like this:
`-54/30`

We do the same thing for `3/6` by multiplying it all with `5`:
`15/30`

So now our problem looks like this:
`-54/30 + 15/30`

Since they both have a common denominator, we can combine the two expressions like this:
`(-54 + 15)/30`, and solve it like any other addition/subtraction problem:

So our answer is:
`-39/30`