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- [Voiceover] Let's say that
we have the fraction 9/10,

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and I want to add to
that the fraction 1/6.

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What is this, what is this going to equal?

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So when you first look at this, you say,

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"Oh, I have different denominators here.

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It's not obvious how I add these."

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And you'd be right and the way to actually

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move forward is to find
a common denominator,

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to convert both of these fractions into

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fractions that have a common denominator.

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So how do you think about
a common denominator?

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Well, a common denominator's
gonna have to be

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a common multiple of these two
denominators of 10 and six.

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So what's a common multiple of 10 and six?

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And it's usually simplest to
find the least common multiple,

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and a good way of doing that
is start with the larger

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denominator here, 10, and say,
okay is 10 divisible by six?

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No. Okay, now, is 20 divisible by six?

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No. Is 30 divisible by six?
Yes. 30 is divisible by six.

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So I'm just going through
the multiples of 10

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and saying, "Well what is
the smallest multiple of 10

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that is divisible by six?"
And that's going to be 30.

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So I could rewrite both of these fractions

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as something over 30.

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So nine over 10. How would I write that as

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something over 30? Well I multiply

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the denominator, I'm multiplying
the denominator by three.

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So I've just multiplied
the denominator by three.

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So if I don't want to change
the value of the fraction,

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I have to do the same
thing to the numerator.

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I have to multiply that by three as well

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because now I'm just multiplying
the numerator by three

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and the denominator by three,
and that doesn't change

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the value of the fraction.

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So nine times three is 27.

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So once again, 9/10 and 27/30

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represent the same number.

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I've just written it now
with a denominator of 30,

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and that's useful because
I can also write 1/6

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with a denominator of 30. Let's do that.

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So 1/6 is what over 30?

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I encourage you to pause the video

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and try to think about it.

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So what did we do go from six to 30?

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We had to multiply by five.

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So if we multiply the denominator by five,

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we have to multiply the
numerator by five as well,

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so one times five, one times five is five.

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So 9/10 is the same thing as 27/30,

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and 1/6 is the same thing as 5/30.

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And now we can add, now we can add

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and it's fairly straightforward.

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We have a certain number of 30ths,

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added to another number of 30ths,

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so 27/30 + 5/30, well that's going to be

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27, that's going to be 27 plus five,

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plus five, plus 5/30,

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plus 5/30, which of course

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going to be equal to 32/30.

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32 over 30, and

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if we want, we could try
to reduce this fraction.

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We have a common factor of 32 and 30,

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they're both divisible by two.

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So if we divide the numerator
and the denominator by two,

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numerator divided by two is 16,

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denominator divided by two is 15.

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So, this is the same thing
as 16/15, and if I wanted

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to write this as a mixed
number, 15 goes into 16 one time

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with a remainder one.

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So this is the same thing as 1 1/15.

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Let's do another example.

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Let's say that we wanted
to add, we wanted to add

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1/2 to

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to 11/12, to 11 over 12.

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And I encourage you to pause the video

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and see if you could work this out.

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Well like we saw before, we wanna find

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a common denominator.

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If these had the same denominator,

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we could just add them immediately,

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but we wanna find a common denominator

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because right now they're not the same.

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Well what we wanna find is a multiple,

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a common multiple of
two and 12, and ideally

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we'll find the lowest common
multiple of two and 12,

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and just like we did before,
let's start with the larger

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of the two numbers, 12.

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Now we could just say
well 12 times one is 12,

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so that we could view that
as the lowest multiple of 12.

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And is that divisible by two? Yeah, sure.

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12 is divisible by two.

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So 12 is actually the least
common multiple of two and 12,

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so we could write both of these

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fractions as something over 12.

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So 1/2 is what over 12?

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Well to go from two to
12, you multiply by six,

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so we'll also multiply
the numerator by six.

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Now we see 1/2, and 6/12,
these are the same thing.

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One is half of two, six is half of 12.

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And how would we write
11/12 as something over 12?

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Well it's already written
as something over 12,

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11/12 already has 12 in the denominator,

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so we don't have to change that.

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11/12, and now we're ready to add.

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So this is going to be equal to six,

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this is going to be equal to six plus 11,

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six plus 11 over 12.

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Over 12. We have 6/12 plus 11/12,

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it's gonna be six plus 11 over 12,

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which is equal to, six plus 11 is 17/12.

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If we wanted to write
it as a mixed number,

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that is what, 12 goes
into 17 one time with

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a remainder of five, so 1 5/12.

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Let's do one more of these.

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This is strangely fun. Alright.

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Let's say that we wanted to add,

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We're gonna add 3/4 to,

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we're gonna add 3/4 to 1/5.

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To one over five.

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What is this going to be?

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And once again, pause the video and

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see if you could work it out.

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Well we have different denominators here,

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and we wanna find, we wanna rewrite these

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so they have the same denominators,

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so we have to find a common multiple,

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ideally the least common multiple.

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So what's the least common
multiple of four and five?

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Well let's start with the larger number,

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and let's look at its
multiples and keep increasing

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them until we get one
that's divisible by four.

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So five is not divisible by four.

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10 is not divisible by four,
or perfectly divisible by four

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is what we care about.

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15 is not perfectly divisible by four.

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20 is divisible by four, in
fact, that is five times four.

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That is 20. So what we
could do is, we could write

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both of these fractions as
having 20 in the denominator,

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or 20 as the denominator.

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So we could write 3/4
is something over 20.

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So to go from four to
20 in the denominator,

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we multiplied by five.

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So we also do that to the numerator.

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We multiply by three times five to get 15.

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All I did to go from four
to 20, multiplied by five.

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So I have to do the same
thing to the numerator,

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three times five is 15.

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3/4 is the same thing
as 15/20, and over here.

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1/5. What is that over 20?

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Well to go from five to 20,
you have to multiply by four.

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So we have to do the same
thing to the numerator.

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I have to multiply this
numerator times four to get 4/20.

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So now I've rewritten this
instead of 3/4 plus 1/5,

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it's now written as 15/20 plus 4/20.

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And what is that going to be?

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Well that's going to be
15 plus four is 19/20.

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19/20, and we're done.