WEBVTT
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Let's add some rational
numbers.
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And I'm using that word because
that's the word that
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this book uses, but in more
popular terminology we'll be
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adding fractions.
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So let's just go through all
of these, actually, just to
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see all of the examples.
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So first we're going to
have 3/7 plus 2/7.
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Our denominators are the same,
so we can just add the
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numerators.
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So our denominator is
7, 3 plus 2 is 5.
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That is a.
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Let me do every other.
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It would take forever
to do all of them.
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Not forever, but just more time
than I want to spend.
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So c is 5/16 plus 5/12.
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Our denominators are
not the same.
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We have to find a common
denominator, which has to be
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the least common-- it actually
could be any common multiple
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of these, but for simplicity
let's do the
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least common multiple.
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So what's the smallest number
that's a multiple
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of both 16 and 12?
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So let's see, 16 times 2
is 32, not there yet.
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Times 3, 48.
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That seems to work.
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12 goes into 48 four times.
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So let's use 48 as our
common denominator.
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So we had to multiply 16 times 3
to get to 48, so we're going
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to have to multiply
this 5 times 3.
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We're just multiplying the
numerator and the denominator
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by the same number, so we're
not really changing it.
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So 5 times 3 is 15.
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And then to get from this 12 to
this 48 right there, we had
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to multiply times 4.
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So then to get to 5 to this
numerator over here, we have
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to multiply times 4.
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5 times 4 is 20.
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Now we have the same
denominator.
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So this is going to be equal
to, our denominator is 48.
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And so we can add 15 plus
20, which is 35.
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And can we reduce this?
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Let's see, 5 does
not go into 48.
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7 does not go into 48.
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It looks like we're all done.
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Let's do e right there.
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8/25 plus 7 over 10.
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Once again, we don't have
a common denominator.
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But we can solve that.
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Let's make, let's see, 50 is the
smallest number that both
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of these go into.
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25 times 2, so that's 50.
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8 over 25, to go to 50
we multiply by 2.
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So the 8, we're going to
have to multiply by 2.
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So it's going to
be 16 over 50.
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And then the 7 over 10,
we're going to want
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to put it over 50.
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We multiply the 10 times
5, so we have to
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multiply the 7 times 5.
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So it's going to
be 35 over 50.
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Now that our denominators are
the same, we have it over 50.
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16 plus 35, what is that?
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10 plus 35 is 45,
plus 6 is 51.
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So it is 51 over 50.
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Problem g.
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Let me do it in a new color.
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Problem g.
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So here we have 7 over 15-- I'll
write the second one in a
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different color--
plus 2 over 9.
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Once again, the denominators
are different.
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Find a common denominator.
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What is the smallest number that
both 15 and 9 go into?
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Let's see, 15 times 2 is 30.
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Nope, not divisible by 9.
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15 times 3 is 45, that works.
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45 is divisible by 9.
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So we use 45.
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15 times 3 is 45, so
7 times 3 is 21.
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These two fractions
are equivalent.
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Plus we're going over 45.
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To get from 9 to 45, we have
to multiply times 5.
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So to get our numerator
over here, we have to
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multiply it times 5.
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So 2 times 5 is 10.
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2/9 is the same thing
as 10/45.
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So now we can add.
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We're adding fractions of 45.
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21 plus 10 is 31,
and we are done.
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Let's do one more problem down
here, a word problem.
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Nadia, Peter and Ian are pooling
their money to buy a
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gallon of ice cream.
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Nadia's the oldest and gets
the greatest allowance.
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She contributes 1/2 the cost.
So Nadia is contributing 1/2
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the cost. So that is
Nadia right there.
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Ian is next oldest and
contributes 1/3 of the cost.
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So Ian contributes 1/3.
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That is Ian.
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Peter, the youngest, gets the
smallest allowance and
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contributes 1/4 of the cost.
So Peter gives 1/4 of the
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cost. Peter contributes
1/4 of cost.
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They figure that this will
be enough money.
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When they get to the checkout,
they realize that they forgot
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about sales tax and
worry there will
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not be enough money.
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Amazingly, they have exactly
the right amount of money.
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What fraction of the cost of
ice cream was added as tax?
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Well, let's see, if we add 1/2
plus 1/3, plus 1/4 of the
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cost, let's see what we get.
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So we have to find a common
denominator, some number that
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is the least common multiple
of 2, 3, and 4.
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And let's see, 4, it would
have to be 12, right?
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12 is divisible by 2, it's
divisible by 3, and it's
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divisible by 4.
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So 1/2 is the same
thing as 6/12.
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2 times 6 is 12.
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1 times 6 is 6.
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These are equivalent.
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6 is 1/2 of 12.
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1/3, if we use 12 as a common
denominator, to go from 3 to
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12 you have to multiply by 4.
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So you take that 4 and
you multiply it by 1.
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4/12 is the same thing as 1/3.
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And then 1/4, if you use your
denominator 12, to go from 4
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to 12 you have to multiply by
3, so multiply the numerator
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by 3 as well, you get 3.
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So let's add these.
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So 6/12 plus 4/12, plus 3/12 is
going to be equal to-- our
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denominator's going to be 12--
it's going to be 6 plus 4,
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plus 3, which is equal to 6 plus
4 is 10, plus 3 is 13.
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So it's going to be
equal to 13/12.
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And this is as an improper
fraction.
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Or we could say that this is the
same thing, this is equal
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to 12/12 plus 1/12, or we could
say the same thing as
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12/12 is just 1, right?
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12 divided by 12 is 1.
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So this is 1 and 1/12.
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So when they pool their money,
they get 1 and 1/12 of the
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price of the ice cream that
they want to buy.
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So they say what fraction of
the cost of ice cream was
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added as tax?
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This is the exact amount that
they needed to pay.
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So clearly, 1 is the non-taxed
price of the ice cream, so
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this 1/12 was the amount
added as tax.
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So the answer to the question
is 1/12 of the price
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was added as tax.
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