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## Adding & subtracting rational numbers

## Video transcript

So we have 0.79 minus
4/3 minus 1/2 plus 150%. So we have four
different numbers written in different formats. Here it's a decimal, here
we have two fractions, and then here we
have a percentage. So the easiest
thing to do would be to write all of these
in the same format. And for me, the easiest format
to do this computation in would be to write
them all as fractions. And the reason why I want to
do that, in particular, is because 4/3, when you divide
by 3, when you divide 1/3, 2/3, 4/3, you're going to
have a repeating decimal. So to avoid that,
I want to put all of these-- I want to rewrite
all of these as fractions. So let's do them one at a time. So 0.79, this is the
same thing as 79/100, so I'll just write it that way. So this is the same
thing as 79 over 100. Then of course,
we have minus 4/3. Then we have minus 1/2. And then finally,
we have-- I don't want to run out of colors here. Finally we have 150%. Well, 150%, percent literally
means per cent, per hundred. So this is plus 150 per 100. So now we've written
them all as fractions. And in order to do all the
subtraction and addition, we have to find a
common denominator. So what's the least common
multiple of 100, 3, 2, and 100? Well, 100 is divisible
by 2, so 100 is actually the least common
multiple of 102. So we really have to just
find the least common multiple between 100 and 300. And that's just going to be 300. There's no other common
factors between 100 and 3. So let's write all of them with
300 as the common denominator. So let me do this in
this reddish color. So 79 over 100 is
the same thing. If I were to write it over
300, to go from 100 to 300 in the denominator,
I'm multiplying by 3, so I have to multiply the
numerator by 3 as well. So I'm going to multiply
it by 3 as well. Let's see, 80 times
3 would be 240. So it's going to be
3 less than that. So 240 minus 3 is 237. Now 4/3. Well, to get the
denominator to be 300, we have to multiply
the denominator by 100, so we have to multiply the
numerator by 100 as well. 1/2, if our denominator is 300,
we multiplied the denominator by 150 to go from
200 to 300, so we have to multiply the
numerator by 150. And then finally, 150
over 100, well, we're multiplying the
denominator by 3 to get to 300, to go from 100 to 300. So we have to do the same
thing in the numerator. So 3 times 150 is 450. So now we have the
same denominator, and we can now add
our numerators. So this is going to be
equal to-- actually, I could just do it right over
here on the right-hand side. This is going to be equal
to some stuff over 300. So it's going to be 237
minus 400 and minus 150 and-- this actually should
be a plus right over here. This should be plus 450. And so let's see if we could
simplify this a little bit. We're subtracting 400,
and we're subtracting 150. So these two would be the
same thing as subtracting 550. And then we have a
positive 237, and we're adding it to a positive 450. Or actually, maybe
another easier way to think about this is
negative 550 plus 450 is going to get us negative 100. And so this simplifies
things a good bit. Now we have 237 minus
100 is going to be 137. So it equals 137 in
the numerator over 300. And this is about as simplified
as I can think of making it. And so this is our
final answer, 137/300.