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## Adding & subtracting rational numbers

Current time:0:00Total duration:4:29

## Video transcript

79% minus 79.1
minus 58 and 1/10. And I encourage you
to pause this video and try to compute this
expression on your own. Well, the thing that
jumps out at you is that these are in
different formats. This is a percentage. These are different
representations. There's a percentage. This is a decimal. This is a mixed number. And so to make sense of it,
it's probably a good idea to get them all in
the same format. And it seems like
we could get all of these into a decimal
format pretty easily. So let's go that way. So 79%, that literally
means 79 per 100. If you wanted to write it as a
fraction, it would be 79/100. But if you wanted to
write it as a decimal, it's 0.79, which could be 0-- or
we would write it down a 0.79. Now, 79.1 is already
written as a decimal, so we'll just write it again. So minus 79.1. And then, 58 and 1/10. Well, 1/10 is the
same thing as 0.1. So you could view this as 58--
well, and literally as 1/10. So it's minus 58 and 1/10. Or, you could view this as 58.1. So now they're all
in the same format, let's actually do
the computation. Now, the first thing
that jumps out at you is you have a fairly
small number here. Small positive number. It's less than 1. And you're subtracting fairly
large numbers over here. So your whole answer is
going to be negative. And to make sense of
this a little bit, what I'm going to
do is I'm going to factor out a negative sign. And that'll make
the computation-- at least in my brain, it's going
to make it a little bit easier. So if we factor out
a negative sign, this becomes-- so we're
going to factor it out. Actually, let me
just do it this way. So if we factor out
a negative sign, then this will become negative. This would be positive. And this would be positive. And just to verify this,
imagine distributing this negative sign, or
if this was a negative 1. Negative 1 times
this is positive. Negative 1 times
this is negative. Negative 1 times
this is negative. So these two expressions
are the exact same thing. And the reason why
I did that is now we'll do the more
natural thing of we will add these two numbers. We'll get a positive number,
a larger positive number than what we're going to
subtract from it right over here. So we can use our
traditional method. Although, we can't forget
about this negative out here. So let's first do that. Let's add 79.1 plus 58.1. So 79.1 plus 58.1. So 0.1 plus a 0.1 is 0.2. 9 plus 8 is 17. So that's seven 1's and one 10. So one 10 plus seven 10's
is going to get us to 0.8. Plus 0.5 gets us to
thirteen 10's, or 130. So we have 137.2 is this
part right over here. So 100. Let me write this down. So we have 137.2. And then from that,
adding a negative 0.79 is equivalent of
subtracting 0.79. So let's do that. Let's subtract
0.79, making a point to align our decimal points
so that we're subtracting the right place from
the right place. And now let's do
our subtraction. So right now we're
subtracting 9 from nothing. We could write a
0 right over here, but we still face an issue
in the hundredths place. We're also subtracting
a 0.7 from 0.2. So we're going to have
to regroup a little bit in the numerator in
order to subtract. Or at least, in
order to subtract using the most
traditional technique. So let's take a tenth from the
2, so it's only one tenth now, and give it to the hundredths. So one tenth is ten hundredths. So we could subtract that
ten hundredths minus nine hundredths is one hundredth. Now in the tenths place. We don't have enough up
here, so let's take 1 from the one's place. So that becomes a 6. 1 is ten tenths. So now we have 11 tenths. 11 minus 7 is 4. Add our decimal place. 6 minus 0 is 6. And then we got our
13 just like that. So outside the parentheses, I
still have the negative sign. When I computed all of this
inside the parentheses, I got 136.41. And then we can't forget about
the negative sign out here. So this whole thing
computes to negative 136.41.