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Find each difference. See Example 4. $$-\frac{1}{2}-\left(-\frac{1}{3}\right)$$

Most important goal to begin with here is going to be to get ourselves a common denominator, right? Yes. We have order of operations with Prince season all of that to worry about. But if these fractions don't have a common denominator, I can't combine them. So we're not going to get anywhere right now. We have denominators of eight, two and four. So that means we're trying to figure out what is the least what is the lowest number that 82 and four can all multiply up to. Technically, you don't have to find the lowest, but it does make it easier, right? You don't have to find at least come, denominator. Just a common one is fine. You can always reduce later, but least is certainly going to make it easiest on you. In this case, I believe the least common denominator looks like it would be eight because eight obviously is already eight, So it's good, but two and four can both multiply up to eight for us. So in this case, that means we're gonna leave five eights the way it is, but we need to take negative 1/2, and we need to change it to something over eight, and we also need to take 3/4 and change it to something over eight. So we'll start with negative 1/2. Question is two times what gives me eight. Well, two times four gets eight. So that means the foregoing multiplied by four and the denominator. We also have to multiply by four in the numerator. Negative one times four is negative. Four. So we have negative four eights. Looking at 3/4 Question is four times what gives us a Well, it's just the reverse of what we did on the earlier fraction. Four times two gives us eight. If we're gonna multiply by two in the denominator, we have to multiply by two in the numerator three times to gives us six. Meaning what we're really looking at for a problem here now is 5/8 minus a negative. 4/8, minus 6/8. That's the problem we want to think of that we're doing right now. We can forget what we started with. This is what we're dealing with now. Common denominators were actually able to combine these fractions. So let's do so now. We can worry about order of operations, which does say that we need to take care of parentheses first. So that means that for now, we're just gonna leave the 5/8 alone. That will be the last thing that we deal with. Right now. We want to focus on what's inside the parentheses. Negative 4/8 minus 6/8 is the same thing as negative four eights plus negative 6/8. Which means what's happening inside the parentheses is we're adding two numbers of, like signs, meaning we're actually gonna combine them. So rewrite the five eights here real quick. All right, we know our answer inside the prince sees is going to be eight in the denominator, right? That's the whole point of getting the common denominator in the first place is we know that the denominator is going to stay the same. The question is, what is negative four plus negative six again because they are both negative, they are like signs. We want to truly combine their absolute values, meaning we want to take four plus six. Four plus six is 10 and we just have to remember that since it was negative four plus negative six it should be negative. 10 which means we're taking 58 minus a negative, 10 eights minus and negative. That double negative means that really, though, should cancel out. And we're doing 5/8 plus 10 eights but double negatives as they cancel each other out. So in that case, then we're taking 5/8 plus 10/8. We know the answer is going to be eight in the denominator five plus 10. They're both positive, which means we truly are adding them together because they're like terms. Five plus 10 is 15. The only question left ask is this. 15 eights are final answer or do 15 and eight share any factors that would allow us to reduce this fraction? In this case, 15 and eight do not share any factors, so this would be your final answer.

First thing I noticed with this is that you are subtracting a negative meaning. We've got a double negative here, so we don't leave. That's a double negative when we can express that much simpler. We can express this as 1/3 plus 4/3. All right, cause minus and negative is the same thing is just adding once you've done that, there's really not much more to this problem because noticed that we already have a common denominator. Both of them have three on the bottom. So we're already ready that we can go ahead and combine these. We have to have three is our denominator. We have to combine our enumerators. So one plus four, it gives us five and 5/3 would be our answer.

Okay, so we can start every reading one as a function. So that's 2/2 minus 3/2, which is equal to negative 1/2.

First thing I noticed with this one is that we are subtracting a negative number. We got this double negative right here, so we don't need to leave it that way. We know minus and negative is the same thing as Plus same thing is adding, So it's go ahead and change this to 1/2 plus 1/4. Okay, that looks much nicer now. Besides that, in order to combine fractions, we do require common denominator, which we don't have. Right now we have a denominator of two and a nominator of four. So when you try and come up with some number that two and four can both multiply up to in this case, the easiest way to do that would actually be to just leave 1/4 as it is because we know two times two is four. So we can take just the 1/2 here and we can try and change it into something over four. Like we just said two times two does give us four. But if I'm gonna multiply my denominator by two after, multiply the numerator by two as well. So one times two would give us 2/4 as our fraction. So now we can look at this as 2/4 plus 1/4. Since we've got a common denominator, that means we are able to go ahead and finish this out. We know our answer will be over for because the denominator is just rewritten. We only actually combine actually add the numerator. And in this case, two plus one would give us three. So our answer is 3/4.