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## Fractions with denominators of 10 and 100

# Adding fractions: 7/10+13/100

CCSS.Math:

## Video transcript

- [Instructor] So what we're
going to try to do in this video is add 7/10 to 13/100,
pause this video and see if you can figure what that is. Alright so despite being a
little bit intimidating at first because we're adding tenths
here, 7/10 and we're adding hundredths here 13/100, how
do I add a certain number of tenths to a certain
number of hundredths? The key idea is to re-express
7/10 as a certain number of hundredths, so how do we do that? Well let's just first visualize
each of these fractions. So 7/10 if we imagine this
square is a whole and that we've divided it into ten equal
sections I tried to hand draw it as best as I can, notice I
have filled in seven of those ten equal sections that we
have split the whole into. So this represents 7/10 and
13/100 you could split the whole into 100 equal sections and
I tried to hand draw it, let's assume that these
are 100 equal sections. And so notice this is a ten
by ten square, it's got 100 of these squares and notice we
have ten plus three 13 filled in so we want to add these
7/10 to these 13/100. Now how do we express 7/10
in terms of hundredths? Well visually you could take
each of your tenths and split them into ten equal sections,
now you have your whole split into hundredths and each of
your tenths is now a hundredth so you have ten times as many
things in the denominator and you also have ten times as
many things in the numerator. Before you had seven of the
tenths filled in, now you have 70 of the hundredths filled in. Or another way to think
about it, we multiplied the numerator by ten and the
we multiplied the denominator by ten. And if you do the same
thing to the numerator and the denominator, you
multiply or divide it by the same number, you're not changing
the value, think about it, ten over ten is the same thing
as one, so we're just taking one and multiplying it by
7/10 isn't going to change the value. But this is as we already
talked about this is equivalent to 70/100, so this is equal
to 70/100 which is this right over here plus 13/100, plus 13/100. Well now we're adding 100s
in both cases, if I have 70 of something and I add to
that 13 of the same somethings in this case the something
is hundredths, I'm going to have 83 of that so this is
going to be 70, get the same color, this is going to be equal
to 70 plus 13, plus 13/100. 70 plus 13/100 and what's 70
plus 13, well that of course is going to be 83/100. And we are done.