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## 7th grade (Illustrative Mathematics)

### Course: 7th grade (Illustrative Mathematics) > Unit 5

Lesson 13: Lesson 13: Expressions with rational numbers# Negative signs in fractions

Sal finds equivalent expressions to -g/h.

## Want to join the conversation?

- Here's my understanding of this. There are 8 possible combinations: x/y, -x/y, x/-y, -x/-y, -(x/y), -(-x/y), -(x/-y), and -(-x/-y). They can all be simplified to either x/y or -(x/y), which is x/y positive or negative. When there's no negative sign before the whole expression (the first 4 combinations), normal rules apply (pos/pos = pos, pos/neg = neg, neg/pos = neg, neg/neg = pos). When there is a negative sign before the expression (the last 4 combinations), the opposite rules apply (i.e. evaluate the expression as if it wasn't there and then take the negative of the result you get).(7 votes)
- At4:35, I still don't get why -(-e)/f is equal to e/f.(2 votes)
- When there are 2 negatives, it equals to a positive. When someone says "Jump", it's a positive. When someone says "Don't eat", it is negative. Meanwhile, if someone says "Don't not eat", that's back to saying "Eat" which is a positive.(8 votes)

- just wondering is -6 / (-2) = 6 / 2?(4 votes)
- Yes, in multiplying/dividing positive and negative numbers, count number of - signs. If it is 0,2,4 or even numbers, answer is positive, and if 1,3,5,odd answer is snegative.

You have 2 negatives, so answer is positive. If you have (-6)^2/(-2) you end up with 3 negatives, so answer is -36/2=-18.(2 votes)

- why are there so many combinations(2 votes)
- There are a lot of places to put the negative sign, if that's what you mean! They're all just ways of showing whether or not the number is negative. Depending on how you work with an operation, the negative number may end up in different spots.

Needless to say, sometimes I get mixed up as well. I just count the number of negative signs applying to the fraction and decide if it's a negative number with the rule that if there's an even number of "-" signs it's a positive; if there's an odd number, it's negative.(3 votes)

- Why did we learn this AFTER lessons that needed it?(2 votes)
- I am currently very confused.(3 votes)
- It's ok, everyone gets confused sometimes!(1 vote)

- This helped me understand this better.(2 votes)
- can anyone pls help me of summarising the whole thing in one sentence?(2 votes)
- I will put them into examples so that it will make sense.

Positives and negatives: fractions

1. -1/2 = Negative

2. -(-1/2) = Positive because: n / n = p and if part of fraction is negative, then it would be positive.

3. 1/2 = Positive

And that's all I can think of for now. Please use this information for help in case you are stuck. remind me if you still need any help.(1 vote)

- i dont understand ?(2 votes)
- It seems like conflicting information to say that you can multiply the negative sign that's in FRONT of an entire fraction by either the numerator (at2:03) or the denominator (at4:35). The contradiction is confusing.(2 votes)

## Video transcript

- We already know a good
bit about negative numbers. And we know a good bit of fractions. So you can imagine we're
going to start seeing negatives and fractions together a lot. What I want to do in this video is just make sure we have
a decent understanding how to manipulate negative signs when we see them in fractions. For example, if I have
the fraction negative 1/2. Here I have the negative out
in front of the entire 1/2. This is the same thing
as negative one over two. And it's going to be the same thing as one over negative two. Now I could also think
about something like negative one over negative two. Now it's important to realize
one way to think about this as a fraction is you could view this as negative one divided by negative two. And we already know, if
you divide a negative by a negative it would be a positive. So this right over here is going to be the same thing as 1/2. This is going to be the
same thing as positive 1/2. Now with that out of the way,
let's think a little bit. Let's do some example
problems that might push our thinking on this a little bit more. So this first question. Which of the following expressions are equivalent to negative g over h? Negative G over H. Select all that apply. All right, so this has all
sorts of negatives here. So at first it looks a little bit unusual. But then we need to just
realize that this part. Actually, let me just square this off in blue right over here. Negative g over negative h. We've already figured that out. We actually looked at
that right over here. If you have a negative
divided by a negative, that's the same thing as a positive value divided by the positive value. So negative g over negative h, is the same thing as g over h. And then you still have
this negative out front. You still have that negative out front. So this one right over here is actually equal to negative g over h. When we think about it,
negative divided by a negative is a positive and you still
have this negative out here. So that's the same thing. And this right over
here, negative in front. And then you have g over negative h. This is going to be the same thing. You could rewrite this, you
could put the negative on top as negative g over negative h. And then this would be equal to g over h, which is different. This is positive g over h. This is negative g over h. So we wouldn't select that. And of course we wouldn't
select "None of the above." Cause we found a choice that we liked. All right. Which of the following
expressions are equivalent to five over b. Select all that apply. All right, so this one over here. Negative five over negative b. Well we could remember that this negative, we could write this is the
same thing as negative five over negative b. And I just want to make it
clear we're that negative. So this is negative Instead of writing it negative in front of the entire fraction, I could essentially
multiply the negative one times just the numerator. So you could write this as
negative five over negative b. And negative divided by a negative is going to be a positive. So this actually is going to be equal to positive five over b, which
is what we're looking for. So this is going to be right. Now this one, negative
divided by a negative, well that's just going to be positive. So that's the same thing as five over b. One way to think about it
is that well the negatives kind of cancel each other out. So five over b, that looks good too. And of course I won't
select none of the above because I found two choices that worked. All right, let's do one more. Which of the following expressions are equal to negative e over negative f? And remember we just have to
take this step by step here. Actually let's try to just
simplify this directly. So negative e over negative f. Well we just need to remind ourselves that this part right over here. Negative e over negative f. Let me write an equal sign. Negative e over, and I'm
gonna put this negative. Let me do this in a different color. Let me do this in purple. So we have this purple. So we have that purple
negative right over there. And negative e over negative f. We've already talked
about this multiple times. That's the same thing as negative's divided by a negative is a positive. That's the same thing as e over f, as positive e over f. So this whole thing will simplify to negative e over f. So let's see which of
these choices are that. Well this right here is positive e over f. So that's not the choice. This one over here. This one we could write
it several ways actually. We could write it negative
negative e over f. Which of course is equal
to positive e over f. We could also write this. We could put the negative
in the denominator. We could say that this thing. Actually let me write it over here as negative e over negative f. This is also a legitimate thing to do. You could take this negative and multiply it times the denominator. Right over here. But either way it's going to
be equal to positive e over f. These two are actually evaluate
to the same expression. So here, I would select. Finally, I would select. I've been waiting to
select "None of the above." All right, hopefully that helps.