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## 7th grade

### Course: 7th grade > Unit 2

Lesson 4: Multiply & divide negative fractions# Dividing negative fractions

Created by Sal Khan.

## Want to join the conversation?

- why can you muliply a negative number by a negative number and make it a positive number?(112 votes)
- The two negative numbers cancel each other out, so if you have -1 * -2 you get 2, the same thing as 1 * 2. Hope this answers your question!(62 votes)

- HOw do I divide two negative fractions?(12 votes)
- Start by flipping the second fraction, so you are multiplying two negative fractions instead of dividing. Any time you multiply two negative numbers the negatives cancel each other out, so you can multiply the fractions as though they were both positive (the product of the numerators over the product of the denominators)(23 votes)

- With negative fractions, when someone writes this: -1/2, does that mean only the 1 is negative, or are both the 1 and the 2 negative?(6 votes)
- The expression -1/2 is going to be negative. It doesn't matter if you treat it like a fraction (minus one half) or like division (minus one divided by two). The 2 can also be negative instead (as in 1/-2) and it'll still be fundamentally the same. If you had -1/-2, that would actually be a positive number. If you had -(-1/2), that would also be a positive number. If you had -(-1/-2), that would actually be negative.(12 votes)

- What's another word for reciprocal?(7 votes)
- The best word to replace reciprocal is "complementary". But I think it is better to use reciprocal.(9 votes)

- What about 4/5 divided by 8/15 In simplest form?(8 votes)
- 4/5 divided by 8/15 is the same as 4/5*15/8 (not sure why). The numerators multiply 4*15 which is 60 and the denominator also does 5*8=40. This gives us 60/40 which is the same as 6/4 which is the same as 3/2 or 1.5.(7 votes)

- Could we have a round of applause for Sal he helps many people to get better at math and more!(10 votes)
- Pls up vote this if you agree(1 vote)

- wow all these comments from years ago.. but im in 7th grade and u guys are like in college or highschool now have fun guys!! stay safe all of you/(7 votes)
- Oh my goodness, same! I'm currently in 7th and all the comments are like 8-7 years ago!(2 votes)

- couldn't Sal cross multiply(4 votes)
- Yep, he could but not necessary since its just for beginners to learn the concept(8 votes)

- i swear as soon as i get done with college and a job I am going to donate my first paycheck to this website(5 votes)

## Video transcript

Let's do some examples
dividing fractions. Let's say that I have negative
5/6 divided by positive 3/4. Well, we've already talked about
when you divide by something, it's the exact same thing as
multiplying by its reciprocal. So this is going to be the
exact same thing as negative 5/6 times the reciprocal
of 3/4, which is 4/3. I'm just swapping the
numerator and the denominator. So this is going to be 4/3. And we've already seen lots of
examples multiplying fractions. This is going to be the
numerators times each other. So we're going to multiply
negative 5 times 4. I'll give the
negative sign to the 5 there, so negative 5 times 4. Let me do 4 in
that yellow color. And then the denominator
is 6 times 3. Now, in the numerator here, you
see we have a negative number. You might already know
that 5 times 4 is 20, and you just have to
remember that we're multiplying a negative
times a positive. We're essentially going to
have negative 5 four times. So negative 5 plus negative 5
plus negative 5 plus negative 5 is negative 20. So the numerator
here is negative 20. And the denominator here is 18. So we get 20/18, but
we can simplify this. Both the numerator
and the denominator, they're both divisible by 2. So let's divide them both by 2. Let me give myself
a little more space. So if we divide both the
numerator and the denominator by 2, just to
simplify this-- and I picked 2 because
that's the largest number that goes
into both of these. It's the greatest common
divisor of 20 and 18. 20 divided by 2 is 10,
and 18 divided by 2 is 9. So negative 5/6 divided
by 3/4 is-- oh, I have to be very careful here. It's negative 10/9, just
how we always learned. If you have a negative
divided by a positive, if the signs are
different, then you're going to get a negative value. Let's do another example. Let's say that I have negative
4 divided by negative 1/2. So using the exact
logic that we just said, we say, hey look,
dividing by something is equivalent to multiplying
by its reciprocal. So this is going to be
equal to negative 4. And instead of writing
it as negative 4, let me just write
it as a fraction so that we are clear
what its numerator is and what its denominator is. So negative 4 is the exact
same thing as negative 4/1. And we're going to multiply
that times the reciprocal of negative 1/2. The reciprocal of negative
1/2 is negative 2/1. You could view it
as negative 2/1, or you could view it as
positive 2 over negative 1, or you could view
it as negative 2. Either way, these are
all the same value. And now we're ready to multiply. Notice, all I did here,
I rewrote the negative 4 just as negative 4/1. Negative 4 divided
by 1 is negative 4. And here, for the negative
1/2, since I'm multiplying now, I'm multiplying
by its reciprocal. I've swapped the denominator
and the numerator. Or I swapped the denominator
and the numerator. What was the denominator
is now the numerator. What was the numerator
is now the denominator. And I'm ready to multiply. This is going to be equal to--
I gave both the negative signs to the numerator
so it's going to be negative 4 times negative
2 in the numerator. And then in the denominator,
it's going to be 1 times 1. Let me write that down. 1 times 1. And so this gives us,
so we have a negative 4 times a negative 2. So it's a negative
times a negative, so we're going to get
a positive value here. And 4 times 2 is 8. So this is a positive 8 over 1. And 8 divided by 1
is just equal to 8.