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## 7th grade (Illustrative Mathematics)

### Unit 5: Lesson 11

Lesson 11: Dividing rational numbers# Dividing positive and negative numbers

Discover the basics of dividing with negative numbers. Created by Sal Khan.

## Want to join the conversation?

- is dividing positive and negative numbers like multiplying them?(15 votes)
- The rules are very much the same, if that's what you're asking. Like a negative divided by a negative will always be positive.(2 votes)

- if 5/0 is undefined,

and 0/0 is undefined,

how is 0/5 = 0?

0 has no value right?

So how can you divide a NON value thing by a number?(4 votes)- If you were solving 8 / 2, you would find the number that you can multiply by 2 to create the 8. The answer is 4 because 2*4 = 8.

Now, follow the same approach with 0 / 5. Find the number that you can mulitply with 5 to create 0. The answer is 0 because 5*0 = 0.

Hope this helps.(8 votes)

- In3:13He said "A negative divided by a negative is a positive"

That's the only part i don't understand.(1 vote)- since there are 2 negatives, they cancel each other out. So you get a positive. :)(12 votes)

- i dont understand the decimal fraction one.(6 votes)
- Someone please help me with 846w5xy3/765x2y4

That's a fraction, by the way.

Simplify, I need help with s I m p l I f y .(4 votes)- I guess you mean

846𝑤⁵𝑥𝑦³∕(765𝑥²𝑦⁴)

This can be written as

846∕765⋅𝑤⁵⋅𝑥∕𝑥²⋅𝑦³∕𝑦⁴

– – –

Now we simplify the rational expressions (fractions) one by one:

846∕765 = 2⋅3⋅3⋅47∕(3⋅3⋅5⋅17) [prime factorization]

= 2⋅47∕(5⋅17) = 94∕85

𝑥∕𝑥² = 1∕𝑥

𝑦³∕𝑦⁴ = 1∕𝑦

– – –

So, 846𝑤⁵𝑥𝑦³∕(765𝑥²𝑦⁴) = 94∕85⋅𝑤⁵⋅1∕𝑥⋅1∕𝑦

= 94𝑤⁵∕(85𝑥𝑦)(4 votes)

- how do you divide a positive fraction by a negative fraction?(4 votes)
- I think that 1/2 divided by -1/4=-2(3 votes)

- is it different when you multiply a positive, negative and positive?(2 votes)
- I dont understand why would 0 divided by 0 undefind why would it not be 0?(3 votes)
- you can't divide anything by zero because it has no value.(4 votes)

- 0x0 should be one because science proves this thus forth putting an example x/x is x but 0/0 is 1(3 votes)
- I am a bit confused on how the 0/5 is undefined but thank you for the explanation(2 votes)
- If you listen closely, Sal states that 0/5=0. He then states if you reciprocate it to 5/0, this is what is undefined - cannot divide by 0 or break a number into 0 parts.(3 votes)

## Video transcript

Now that we know a little bit about multiplying positive and negative numbers, Let's think about how how we can divide them. Now what you'll see is that it's actually a very similar methodology. That if both are positive, you'll get a positive answer. If one is negative, or the other, but not both, you'll get a negative answer. And if both are negative, they'll cancel out and you'll get a positive answer. But let's apply and I encourage you to pause this video and try these out yourself and then see if you get the same answer that I'm going to get. So eight (8) divided by negative two (-2). So if I just said eight (8) divided by two (2), that would be a positive four (4), but since exactly one of these two numbers are negative, this one right over here, the answer is going to be negative. So eight (8) divided by negative two (-2) is negative four (-4). Now negative sixteen (-16) divided by positive four (4)-- now be very careful here. If I just said positive sixteen (16) divided by positive four (4), that would just be four (4). But because one of these two numbers is negative, and exactly one of these two numbers is negative, then I'm going to get a negative answer. Now I have negative thirty (-30) divided by negative five (-5). If I just said thirty (30) divided by five (5), I'd get a positive six (6). And because I have a negative divided by a negative, the negatives cancel out, so my answer will still be positive six (6)! And I could even write a positive (+) out there, I don't have to, but this is a positive six (6). A negative divided by a negative, just like a negative times a negative, you're gonna get a positive answer. Eighteen (18) divided by two (2)! And this is a little bit of a trick question. This is what you knew how to do before we even talked about negative numbers: This is a positive divided by a positive. Which is going to be a positive. So that is going to be equal to positive nine (9). Now we start doing some interesting things, here's kind of a compound problem. We have some multiplication and some division going on. And so first right over here, the way this is written, we're gonna wanna multiply the numerator out, and if you're not familiar with this little dot symbol, it's just another way of writing multiplication. I could've written this little "x" thing over here but what you're gonna see in Algebra is that the dot become much more common. Because the X becomes used for other-- People don't want to confuse it with the letter X which gets used a lot in Algebra. That's why they used the dot very often. So this just says negative seven (-7) times three (3) in the numerator, and we're gonna take that product and divide it by negative one (-1). So the numerator, negative seven (-7) times three (3), positive seven (7) times three (3) would be twenty-one (21), but since exactly one of these two are negative, this is going to be negative twenty-one (-21), that's gonna be negative twenty-one (-21) over negative one (-1). And so negative twenty-one (-21) divided by negative one (-1), negative divided by a negative is going to be a positive. So this is going to be a positive twenty-one (21). Let me write all these things down. So if I were to take a positive divided by a negative, that's going to be a negative. If I had a negative divided by a positive, that's also going to be a negative. If I have a negative divided by a negative, that's going to give me a positive, and if obviously a positive divided by a positive, that's also going to give me a positive. Now let's do this last one over here. This is actually all multiplication, but it's interesting, because we're multiplying three (3) things, which we haven't done yet. And we could just go from left to right over here, and we could first think about negative two (-2) times negative seven (-7). Negative two (-2) times negative seven (-7). They are both negatives, and negatives cancel out, so this would give us, this part right over here, will give us positive fourteen (14). And so we're going to multiply positive fourteen (14) times this negative one (-1), times -1. Now we have a positive times a negative. Exactly one of them is negative, so this is going to be negative answer, it's gonna give me negative fourteen (-14). Now let me give you a couple of more, I guess we could call these trick problems. What would happen if I had zero (0) divided by negative five (-5). Well this is zero negative fifths So zero divided by anything that's non-zero is just going to equal to zero. But what if it were the other way around? What happens if we said negative five divided by zero? Well, we don't know what happens when you divide things by zero. We haven't defined that. There's arguments for multiple ways to conceptualize this, so we traditionally do say that this is undefined. We haven't defined what happens when something is divided by zero. And similarly, even when we had zero divided by zero, this is still, this is still, undefined.