## Multiplying and dividing negative numbers

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

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