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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