Multiplying and dividing negative numbers
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Multiplying Positive and Negative Numbers
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Why a Negative Times a Negative is a Positive
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Why a Negative Times a Negative Makes Intuitive Sense
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Dividing Positive and Negative Numbers
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Example: Multiplying numbers with different signs
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Multiplying and dividing negative numbers
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Negative number word problems
Multiplying and dividing negative numbers Multiplying and dividing negative numbers
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- Welcome to the presentation on multiplying and
- dividing negative numbers.
- Let's get started.
- I think you're going to find that multiplying and dividing
- negative numbers are a lot easier than it might
- look initially. You just have to remember a couple of rules.
- And I am going to teach probably in the future like I'm actually going
- to give you more intuition on why there rules work.
- So the basic rules are when you multiply two negative numbers,
- so let's say I had negative 2 times negative 2.
- First you just look at each of the numbers as if there
- was no negative sign.
- Well you say well, 2 times 2 that equals 4.
- And it turns out that if you have a negative times a
- negative, that that equals a positive.
- So let's write that first rule down.
- A negative times a negative equals a positive.
- What if it was negative 2 times positive 2?
- Well in this case, let's first of all look at the
- two numbers without signs.
- We know that 2 times 2 is 4.
- But here we have a negative times a positive 2, and it
- turns out that when you multiply a negative times a
- positive you get a negative.
- So that's another rule.
- Negative times positive is equal to negative.
- What happens if you have a positive 2 times a negative 2?
- I think you'll probably guess this one right, as you can tell
- that these two are pretty much the same thing by, I believe
- it's the transitive property -- no, no I think it's the
- communicative property.
- I have to remember that.
- But 2 times negative 2, this also equals negative 4.
- So we have the final rule that a positive times a negative
- also equals the negative.
- And actually these second two rules, they're kind
- of the same thing.
- A negative times a positive is a negative, or a positive
- times a negative is negative.
- You could also say that as when the signs are different and
- you multiply the two numbers, you get a negative number.
- And of course, you already know what happens when you have a
- positive times a positive.
- Well that's just a positive.
- So let's review.
- Negative times a negative is a positive.
- A negative times a positive is a negative.
- A positive times a negative is a negative.
- And positive times each other equals positive.
- I think that last little bit completely confused you.
- Maybe I can simplify it for you.
- What if I just told you if when you're multiplying and they're
- the same signs that gets you a positive result.
- And different signs gets you a negative result.
- So that would be either, let's say a 1 times 1 is equal to 1,
- or if I said negative 1 times negative 1 is equal to
- positive 1 as well.
- Or if I said 1 times negative 1 is equal to negative 1, or
- negative 1 times 1 is equal to negative 1.
- You see how on the bottom two problems I had two different
- signs, positive 1 and negative 1?
- And the top two problems, this one right here
- both 1s are positive.
- And this one right here both 1s are negative.
- So let's do a bunch of problems now, and hopefully it'll hit
- the point home, and you also could try to do along the
- practice problems and also give the hints and give you what rules to you so that should help you as well
- So if I said negative 4 times positive 3, well 4 times
- 3 is 12, and we have a negative and a positive.
- So different signs mean negative.
- So negative 4 times 3 is a negative 12.
- That makes sense because we're essentially saying what's
- negative 4 times itself three times, so it's like negative 4
- plus negative 4 plus negative 4, which is negative 12.
- If you've seen the video on adding and subtracting negative
- numbers, you probably should watch first.
- Let's do another one.
- What if I said minus 2 times minus 7.
- And you might want to pause the video at any time to see if you
- know how to do it and then restart it to see
- what the answer is.
- Well, 2 times 7 is 14, and we have the same sign here, so
- it's a positive 14 -- normally you wouldn't have to write the
- positive but that makes it a little bit more explicit.
- And what if I had -- let me think -- 9 times negative 5.
- Well, 9 times 5 is 45.
- And once again, the signs are different so it's a negative.
- And then finally what if it I had -- let me think of some
- good numbers -- minus 6 times minus 11.
- Well, 6 times 11 is 66 and then it's a negative and
- negative, it's a positive.
- Let me give you a trick problem.
- What is 0 times negative 12?
- Well, you might say that the signs are different, but
- 0 is actually neither positive nor negative.
- And 0 times anything is still 0.
- It doesn't matter if the thing you multiply it by is a
- negative number or a positive number.
- 0 times anything is still 0.
- So let's see if we can apply these same rules to division.
- It actually turns out that the same rules apply.
- If I have 9 divided by negative 3.
- Well, first we say what's 9 divided by 3?
- Well that's 3.
- And they have different signs, positive 9, negative 3.
- So different signs means a negative.
- 9 divided by negative 3 is equal to negative 3.
- What is minus 16 divided by 8?
- Well, once again, 16 divided by 8 is 2, but
- the signs are different.
- Negative 16 divided by positive 8, that equals negative 2.
- Remember, different signs will get you a negative result.
- What is minus 54 divided by minus 6?
- Well, 54 divided by 6 is 9.
- And since both terms, the divisor and the dividend, are
- both negative -- negative 54 and negative 6 -- it turns out
- that the answer is positive. Remember, same signs
- result in a positive sign.
- Let's do one more.
- Obviously, 0 divided by anything is still 0.
- That's pretty straightforward.
- And of course, you can't divide anything by 0
- -- that's undefined.
- Let's do one more.
- What is -- I'm just going to think of random numbers --
- 4 divided by negative 1?
- Well, 4 divided by 1 is 4, but the signs are different.
- So it's negative 4.
- I hope that helps.
- Now what I want you to do is actually try
- as many of these multiplying and dividing negative numbers as you can.
- And you click on hints
- and it'll remind you of which rule to use.
- In your own time you might want to actually think about
- why these rules apply and what it means
- to multiply a negative number times a positive number.
- And even more interesting, what it means
- to multiply a negative number times a negative number.
- But I think at this point,
- hopefully, you are ready to start doing some problems.
- Good luck.
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