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Studying for a test? Prepare with this lesson on Decimals.

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# Rewriting a fraction as a decimal: 6/12

Video transcript

Let's see if we can
rewrite 6/12 as a decimal. And once again, I encourage
you to pause this video and try this on your own. And I'll give you a little hint. See if you can rewrite
this fraction, not in terms of 12ths,
but in terms of 10ths. Well, let's just
visualize this thing. So let's say that this
right over here is a 12th. So that is a 12th. And so let me try
to make 12 12ths. So copy and paste that,
so that's two 12ths. And that is three 12ths. And that is-- actually
let me just copy and paste the three 12ths. So copy and paste. So now we have six 12ths, which
I'll color it in a second. And now we have 9/12, and now we
have 12 12ths right over there. And we care about
six of these 12ths, so this is representing
six of these 12ths. So let me see if I can
color in six of them. So let me go to-- let me
see if I can pull this off. So this is going to be 1. Let me do a bigger paint brush. So 1, 2, 3, 4, 5, 6. That's right. That's 6/12. I'm just going to color
all of this business in. So there you have. We have represented
our fraction. Now, how do we represent
this thing right over here in terms of 10ths? So the one thing that
I might want to do is well look, 6 and 12
are both divisible by 6. So what if we divide this, not
if we rewrite this whole, not in terms of 12ths, but we
write it in terms of halves? Well, how would we do that? Well, we could
say-- we could call all of this stuff-- this is
1/2, and this is another 1/2. Or another way of
thinking about it is we're taking six of our
12ths together, and then we're
putting them together, and we're turning
them into a 1/2. So in terms of the
number of sections we have, we're
dividing the number of sections we have by 6. So let's do that. So let's divide the
number of sections by 6. So now we're only going
to have two sections. We're only going
to have two halves. That right over there is 1/2,
and that right over there is the other 1/2. Notice we had 12/12. Now we're taking 6 of those at
a time putting them together, so now we only have two
sections instead of 12 sections. But those 6/12, what are
they going to be in halves? Well, once again, where we're
taking six of the things and putting them
together into one. So we're going to divide
that by 6 as well. And so this is going to
be the same thing as 1/2. And you see this
1/2 right over here. And notice, all we
did in the past, we had multiplied
and divided-- sorry, in the past we had
multiplied the numerator and the denominator
by the same quantity to get an equivalent fraction. Now, we're dividing the
numerator and the denominator by the same quantity to
get the same fraction. Hopefully, this makes sense,
that 1/2 is equivalent to 6/12. Now, why did I do that? Didn't I say that I wanted to
get this in terms of 10ths? And yes, I do want to
get it in terms of 10ths, but 1/2 is fairly easy to
rewrite in terms of 10ths. So let me re-express 1/2. So 1/2, let me
write it like this. So 1/2, I could
represent 1/2 again. I'm going to re-represent 1/2. So let's say this right
over here is clearly 1/2, so I'm just representing it. So I'm taking a whole,
dividing it into 2, and 1/2-- let me
just color it in-- would be that right over there,
which as we already seen, it's equivalent to the 6/12. Now, I want to
write this as 10ths. So what if I take
each of those halves, and I turn it into five
times as many pieces? So let me do that. So I'm going to do it into
1, 1, 2, 2, 3, 4, and 5. So what did I just do? I multiplied. I now have five
times as many pieces and the 1/2 is
going to represent five times as many 10ths. So this is going to
be equal to 5/10. Let me do it in a
green color, 5/10. Notice, 6/12 is the
same thing as 1/2, which is the same thing as 5/10. All I did here is I
multiplied the numerator and the denominator by
the same quantity 5, so I could get 10
in the denominator. And 5/10, well that's the
same thing as 5 times 1/10. It's literally 5/10, and we can
represent this as a decimal, or you could say in
decimal notation. 5/10, we know that-- let's say
that that is the ones place, and if we go one place to the
right of the decimal, that is the tenths place. That right over there
is the tenths place. And we have 5/10, so we would
put a 5 right over there. So this could be rewritten
as the decimal, 0.5. Now, there's other ways you
could have thought about it. You could say hey, look. 6 is half of 12, and
so what is half of 10? Well, 5 is half
of 10, and so 5/10 is the same thing as 5/10,
which is the same thing as 5/10 written as a decimal.