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- [Voiceover] We are asked,
"What numbers should replace
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"the A and B in the multiplication table?"
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So let's just make sure we can read
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this multiplication table.
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The way you think about it is,
if you wanted to figure out--
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It goes up to six.
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So if you want to figure
out what any number
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up to six times another
number up to six is,
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this table will tell you.
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So for example, if you
wanted to figure out
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what three times two is, you say,
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"Ok, three. Let me take the
row that has this three in it.
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"And then the column for the two.
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"So three times two."
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So if you're in this row, the three row,
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and you're in the two column,
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three times two is going to be six here.
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Or you could go the other way around.
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This 12, this means
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that 3 times 4 is 12.
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Or right over here, this 25.
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Notice, this is the same row as this five
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and the same column as that 5.
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So it's saying that five times five is 25.
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And so you notice that
if you go in any row,
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you're counting by that number
and if you go in column,
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you're also counting by that number.
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So for example, in this
two's column right over here
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you're counting by twos.
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Two, four, six, eight.
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In this five column,
you're counting by fives.
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Five, 10, 15, 20.
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And that makes sense because
five times one is five.
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Five times two is 10.
Five times three is 15.
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Five times four is 20.
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And the same thing is
happening as you go up a row.
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Two, four, six, eight.
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Because two times one is
two. Two times four is four.
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On and on and on, you're counting by twos.
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Here you're counting by sixes.
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Six times one is six. Six times two is 12.
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Six times three is 18.
Six times four is 24.
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So hopefully now we understand
the multiplication table.
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And it is actually pretty cool
to just keep looking at it
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and thinking about how it works.
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But let's answer their
question, what would A and B be?
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Well we have this A right over here.
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So one way to think about it,
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it needs to be whatever
four times four is.
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And you might know that
four times four is 16.
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Four times four is 16.
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Or another way is, you could just go down
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this column and count by fours.
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Four, eight, 12 and
then you add four again.
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12 plus four is 16.
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Now let's figure out what B is.
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And actually, let's do it that way.
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B is in this column so
we can count by threes.
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Three, six, nine. Add three
to that and you get to 12.
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So b could be 12.
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Or you could go from the row.
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You could go four, eight, add
four to that and you get 12.
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And that makes sense
because this, where B is,
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that should be whatever
four times three is.
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Cause four times three is 12.
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Then they say, "Complete the inequalities
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"with the greater-than,
less-than or equal symbol."
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So A is greater than B. Greater than.
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And I always remember
the greater than symbol
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because it is opened
to the number on left.
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The number on the left is greater than,
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it's opened to larger number.
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A is greater than B
because four times four
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is going to be greater
than four times three.
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Is greater than four times three.
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All right, four times four is
greater than four times three.
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It makes sense.
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If four times four is four fours
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and if four times three is three fours,
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you have more fours here.
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So hopefully that makes sense.
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Let's do a couple more of these.
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So now what number should replace A and B
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in the multiplication table?
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So same idea.
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So A should be whatever
four times five is.
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So it should be 20.
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Or you could look at whatever
row or column it's in.
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If you look at its
column, five, 10, 15, 20.
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Now let's do the same thing for B.
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B should be whatever five times four is.
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Well that's going to be 20 as well.
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That's going to be 20.
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And you could say, "Well
look, A is gonna be
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"four times five which is 20.
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"And B is gonna be five
times four which is 20."
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So either way you look
at it, they are the same.
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So, complete the inequalities?
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Well, A is equal to B
because four times five
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is the same thing as five times four.
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It doesn't matter what
order you multiply them in.
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Let's do one more of these.
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I think you're getting the sense of it.
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So what is A?
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So we see where it's located,
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it's in this row for this two
and the column for the six.
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So it needs to be
whatever two times six is.
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Which is 12.
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And you could count by sixes. Six, 12.
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Or you could count by twos.
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Two, four, six, eight, 10, 12 to get to A.
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Now B, this is going to be
whatever six times 2 is.
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Well, that's gonna be 12 again.
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And so it's just like the last one we saw.
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A is gonna be equal to B
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because two times six is
equal to six times two.
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Let's do one more, this
is actually a lot of fun.
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All right, so A is
whatever four times one is
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which we know is gonna be four.
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B is gonna be whatever one times four is
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which is also gonna be four.
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And I think you see a pattern here.
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A equals B because four times one
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is the same thing as one times four.