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Studying for a test? Prepare with these 8 lessons on Module 4: Multiplication and division of fractions and decimal fractions.

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# Rewriting a fraction as a decimal: 21/60

Video transcript

Let's see if we can
write 21/60 as a decimal. And I'll give you a little hint. See if you can rewrite
this as a fraction with 100 as the denominator. Or another way to say it is
see if you can rewrite this so it's a certain
number of hundredths, and then you can represent
that as a decimal. So we've done this before. We can rewrite a fraction. We can get an
equivalent fraction if we either multiply the
numerator and the denominator by the same quantity
or we divide the numerator and
the denominator by the same quantity. And this numerator and
this denominator, it looks pretty clear. 21 is divisible by 3
and 7 and 1 and 21. And 60 is clearly
divisible by 3 as well. It's not divisible by 7 or 21. Well, of course,
it's divisible by 1, but that doesn't
really help you much. So let's see if we can
rewrite this, maybe with lower numbers,
where we divide both the numerator and
the denominator by that common factor of 3. So we're dividing by 3. So I'm just rewriting this as
an equivalent fraction that might make it a little
bit easier for our heads to get around it. So 21 divided by
3 is equal to 7. And 60 divided by
3 is equal to 20. So we've rewritten
21/60 as 7/20. So you might be saying, Sal,
why did you even do this? Aren't we trying to get
it in terms of hundredths? Well, this one helps simplify
it in my brain a little bit. And what's extra good
about writing it as 7/20 it is that it's easier
to go from 20 to 100. To go from 20 to 100 we
just have to multiply by 5. Well, if each section is going
to be five times as many then these seven sections are going
to be five times as many. So, once again, we're
multiplying the numerator and the denominator
by the same thing. And so this is going to be
equal to 35 over 100, or 35/100. 35-- let me write it
a little bit-- 35/100, which is what we wanted to do. We wanted to rewrite this
in terms of hundredths. And what is 35/100? Well, let's just
remind ourselves when we're writing a decimal,
that's the ones place. This right over here, this next
place, is the tenths place. And the next place is
the hundredths place. And so 35/100, well, you
could write that like this. You could write that
as 35 hundredths. So you could literally
write this as 0.35. And you might say, wait, you
put a 3 in the tenths place. Why is this 35 hundredths? I get that this is 5 hundredths,
but why is this 35 hundredths? Well, 3/10 is 30/100. So this is 35/100. Or another way of
thinking about it, you could rewrite
this right over here. You could rewrite this as being
equal to 30/100 plus 5/100. And what is 30 over
100 if you wanted to rewrite it in
terms of tenths? Well, you could just divide the
numerator and the denominator by 10, and you would
get 3/10 plus 5/100. And we see that right
over here, 3/10, that's the tenths place, plus
5/100, that's hundredths place. Or this is sometimes
referred to as 35/100.