Question

Helppppppppppppppppppp

Answer 1

`-6(1)/(6)`

Explanation:

Hey! Let's help you with your question there!

Mixed numbers! Not a particularly fun topic, but nonetheless we still need to solve. Let's take a look at what we know. Given the equation right away, we can already tell that between the two mixed number fractions, we're going to be adding them. Why do I say this? Although it is subtracting, it is subtracting from a negative number. When you subtract a negative number, you're essentially just adding. So, it just looks like this:

`=-8(1)/(3) +2(1)/(6)`

Now that we have that in check, let's start by solving it! To make it easier on us, we'll convert each mixed number fraction into their improper fraction forms. It would look like this:

`=-(25)/(3) +(13)/(6)`

From here, we evaluate! However, we can't evaluate it just like this. Why? It is because the denominators are different. It's possible to figure it out exactly like this but it is much harder to do. We want to make it easier for ourselves, so we use the least common multiple. The least common multiple essentially asks, what is the lowest number that both denominators can equal? In our case, it would be 6 as 6 is good on its own and 3 can get to 6 by just multiplying by 2. So it would look like:

`=-(50)/(6) +(13)/(6)`

For the first fraction, the denominator is equal to the second fraction. However, the numerator is 50! Why is that? What we did was we multiplied the entire fraction by 2 meaning that if we multiply 2 to get 6 in the denominator, we have to multiply 2 to the numerator. We can now combine these together and evaluate to get:

`=(-50+13)/(6)` - Combined together.

`=(-37)/(6)` - Numerator gets evaluated.

`=-(37)/(6)`

We have finished the evaluation! Why do we put the negative out of the numerator? It is because of the fraction rule! Basically means that if there's a negative in the numerator, then the entire fraction is negative. Now all we have to do is convert it back into a mixed number fraction and we get:

`-(37)/(6) =-6(1)/(6)`

So, therefore, the answer is the last option, 6 1/6.