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# Adding fractions (denominators 10 & 100)

Sal adds 3/10+7/100 by finding a common denominator. Created by Sal Khan.

Video transcript

Let's see if we can
add 3/10 to 7/100. And I encourage you to
try adding these two fractions on your own first
before I work through it, and I'll give you one hint. Right now, it's very hard
to add these fractions. You're adding 3/10 to 7/100. You're adding two
different fractions with two different denominators. So what I would
encourage you to do is try to rewrite
3/10 in a way that it has 100 as a
denominator, or so it's expressed in terms
of hundredths, and then see if
you can add them. Well, I'm assuming
you've given a go at it. Let's see how we
can rewrite 3/10, and I'll try to visualize it. So what I've done here, so this
you could consider a whole, and this is a whole as well. And this whole is divided into
tenths-- 1,2, 3, 4, 5, 6, 7, 8, 9, 10. So what would 3/10 look like? Well, it would be one, two,
and three of the tenths. Now, what would happen if
you took each of those tenths and you divided them
into 10 more sections? So you're essentially
taking each of those tenths and you're dividing
them into 10 sections. Well, you have 10 sections
and then each of them will have 10 subsections in it. So you're going to
have hundredths. Then the sections are going
to describe hundredths. So 10-- let me
write it this way. 10 times 10. You are then going
to have hundredths. And 3/10 would be equivalent to
how many of these hundredths? Well, each of these
tenths will now become 10. So you're going to
have 10, 20, and-- let me color them in better. So that's 10, 20, and
then 30 hundredths. So this part right over here. This-- let me get my tool
right-- this part right over here, this is going
to be 3 times 10, which is going to be equal to 30. 10 times 10 is equal to 100. So this is how we're going
to change the denominator. Instead of thinking
in terms of tenths, we're going to think
in terms of hundredths. And now our numerator, 3/10,
is equivalent to 30 hundredths so we can rewrite this fraction. We essentially multiplied
the numerator by 10, and we multiplied
the denominator by 10, which didn't change
the value of the fraction. It still represents
the same-- it still represents 3/10 of the whole. So when you do
that, you end up-- we can rewrite this
thing as 30 over 100. Three tenths is
equivalent to 30 over 100. We add that to 7 over 100. Or another way of thinking
about it, three tenths is the same thing
as 30 hundredths. And we add that to 7 hundredths. Well, now we're going to
have 30 plus 7 hundredths. So now, we're going to
have 30 plus 7 hundredths. Or we could say that this is
now going to be 37 hundredths. So this extra 7 that we're
adding here-- maybe I'll do this in-- that's
the same color. This extra sevenths-- let
me do this in a new color. This 7 hundredths that we're
adding, that's going to be one, two-- let me paint that
in a little bit clearer. So that's 1, 2, so it
gets us all the way to 7. Let's see, 1, 2, 3, so 7
hundredths is right over there. So let me get back to my pen. So that, whoops, this right
over here is 7 out of the 100 so 30/100 plus 7/100 is
going to get us to 37/100.