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## 7th grade

### Course: 7th grade > Unit 2

Lesson 3: Understanding multiplying and dividing fractions# 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).(6 votes)
- At4:35, I still don't get why -(-e)/f is equal to e/f.(1 vote)
- 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.(7 votes)

- just wondering is -6 / (-2) = 6 / 2?(3 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)
- 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)
- can anyone pls help me of summarising the whole thing in one sentence?(2 votes)
- Brother Emmet Fisher was a fine looking young man who lived in a tiny community on the Georgia coast. He was well respected in town for being an honest, hardworking fellow. Although he wasn’t wealthy, he made a nice-enough living doing handiwork for the local townspeople.

Emmet was getting close to marrying age, and every woman in town was jumping at the chance to be his chosen. He’d have unexpected visits from different women every day bearing gifts of fried chicken, gumbo, cakes, cookies and other delicacies.

But Emmet had his eyes set on a beautifully mysterious young woman who lived alone in a small cabin deep in the marsh. She was incredibly beautiful, with long dark hair, smooth skin and piercing green eyes. But word around town was that she was a little strange, and it was best to stay away from her.

Emmet, however, couldn’t get this mysterious woman out of his head. What made her even more intriguing was the fact that she would walk through town, turning heads with every step, but never did she acknowledge the admiring glances or catcalls from numerous, hopeful, would-be suitors. In fact, no one in town could ever remember this woman speaking a word to anybody.

Gullah Cabin in Hog Hammock Community, Sapelo Island, Georgia

After several months of watching this gorgeous beauty walk through town, Emmet finally worked up enough nerve to call on her at her marsh cabin. His plan was to go fishing one day in a tidal creek that just so happened to be near her home. While out fishing, he conveniently broke his water jug into a hundred little pieces. Brother Emmet walked up to the woman’s house and knocked on the door.

As the door slowly creaked open and the woman peeked out, Emmet nervously cleared his parched throat. “Excuse me, ma’am,” he stammered, “my name is Emmet Fisher, and I seem to have broken my water jug. Could you please spare me just a cup of water? I’m mighty thirsty.”

The woman smiled and invited him in without hesitation. Her voice was even more beautiful and silky than Emmet had imagined. She not only gave Emmet a cup of water, but to his surprise, asked him to stay for supper. The food was delicious, and the woman waited on Emmet hand and foot. Before he knew it, she invited him to stay for breakfast the next day, then lunch, then another dinner.

Suddenly, in the blink of an eye, Brother Emmet found himself married to the mysterious woman.

After their sudden marriage, Emmet and his bride got along reasonably well for a while. But after a few months, he began to notice that something peculiar was going on with his new wife. On certain nights, when the clock struck midnight, Emmet would sometimes wake up to find that his wife wasn’t in bed with him, nor could she be found anywhere in the house. Emmet began to get worried that she might be seeing someone else on the side, and confronted her about it. But she would just laugh and reassure him that she was, indeed, in the house, and that he must be having nightmares.

As his wife began to disappear more often, Emmet decided to confide in one of his best friends who had also just gotten married. After hearing Emmet’s story, his friend shook his head and said, “Emmet, I hate to say this, but it sounds to me like you might’ve married yo’self a boo-hag.”

“A boo-hag?” asked Emmet. “What’s a boo-hag?”

His friend went on to explain: “Well, a boo-hag is an evil spirit that wakes up at night, sheds her skin like a snake, and flies outside and sucks the blood out of victims from near and far. A boo-hag is an evil spirit that sits on your chest and steals your voice. A boo-hag is an evil spirit that sits on your back and rides you all night like a horse until you drop dead.”

Horrified, Emmet said, “Well, I sho’ don’t want to be married to no boo-hag, if that’s what she is. What am I gonna do about it?”

“The only way to get rid of a boo-hag is to make sho’ she can’t get back in her skin. When she’s gone, take a look in the closet. If you see her skin hanging in there, take it offa the hook, fill it with salt and pepper, put it back in the closet, then lie back and watch.”

Around midnight that very evening, Emmet rolled over in bed and found that his wife was gone. He did what his friend told him to do – he got up, went to the closet, and found his wife’s skin hanging there, cold and slimy to his touch like a lizard’s skin. He filled it with salt and pepper, hung it back in the closet, then went back to bed and waited for his wife to return.

Sure enough, as the sun was about to rise that morning, the door opened, and in walked his skinless wife. She opened the closet door, took her skin off the hook and spoke to it in a gravelly, witch-like hiss:

“I done been out and had my fun,

But I’m back now, and my work’s all done.

So let me in, skin, for the sun’s about to crest,

You knows I’m a boo-hag, and I needs my rest.”

She then stepped into her skin and fastened it around her body. But after a while, that salt and pepper started to itch and burn her real bad. She tried to yank the skin off, but the more she tried, the tighter the skin pressed against her body. She screamed and hollered and jumped around the room, her skin burning her alive.

With that, Emmet leapt out of bed and said, “I got you now, you ol’ boo-hag witch! You fooled me and tricked me into marrying you. So now I’m gonna kill you. Ain’t nothin’ else can be done!”

With that, he shoved the boo-hag into a large barrel of tar he had cooking on the hearth. And that boo-hag burned and melted, her screams filling the air for miles and miles.

After the boo-hag was dead, Emmet, being the handyman that he was, knew exactly what to do with that hot barrel of tar. As the sun rose that morning, he took that tar up to the top of his house, and p-(1 vote)

## 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.