Tip:
Highlight text to annotate it
X
Here we're going to add some signed numbers that have
different signs.
Now, when we were adding the ones that had same signs, we
looked at it and said, oh, we're adding two numbers that
have the same sign, we're going to get even
more of the same sign.
But here's something different happening, the two signs tend
to cancel each other out.
So if I have five positives, and it's helpful to look at
this visually first, and I'm combining that with or adding
it with two negatives.
If you take each plus and negative pair, they cancel
each other out.
And basically, we're left with three positives.
So, 5 plus negative 2, is going to leave me with
positive 3.
And we usually don't show the positive sign, so we just get
3 for an answer.
So that's one way you can do these, is to just look at
what's happening with positive and negative signs.
We can also think of it as a rule.
We can say, when we're adding signed numbers with different
signs, we're going to keep the sign of the larger absolute
value number.
So in this case, we have more positives because we have five
positives, so we'll keep that sign, and then we're going to
take the difference of the absolute
values of the numbers.
So we're going to say, OK, 5 minus 2, gives us a 3.
All right, so let's try another one.
And I'm gonna show you a couple different ways to think
about these, and just use whatever method makes the most
sense to you.
Negative 5 plus 2.
So again, we can look and say, all right, well, we are
starting off with more negatives because we have five
negatives and only two positives.
So that means the final answer is going to be negative.
And then ask yourself, well how many more
negatives do we have?
If we have five negatives and two positives, we have a total
of three more negatives.
So these tend to cancel each other out, leaving a leftover
of three negatives.
So our answer is negative 3.
And again, you can look at this with signs canceling out
like we did over here.
Another way that I want to show you is you can look at it
with the number line.
And if we start at negative 5, if we're adding positive 2,
that means positive 2 is going to the right two spaces, and
we see where we end up.
If this is negative 4--
or negative 5, then this is negative 4 and this is
negative 3.
So two spaces to the right, or plus 2, brings
us to negative 3.
And let's look at one more problem.
Now, it's hard to do the sign method or the number line
method when you have larger numbers.
So then you want to start thinking about it in terms of
a rule method, which is adding two signed numbers with
different signs, we're going to keep the sign of the number
with the larger absolute value.
So we have more positives, cause 64 is larger than 14.
Therefore, we're going to keep the positive.
And then, we're going to take the difference of the two
absolute values.
Which tells us how many more positives do
we have than negatives?
Well, we have 64 minus 14.
More positive than negative.
So if I do that out, I get 50.
So negative 14 plus 64 is equal to 50.
And we don't usually show the plus, so we'll just put 50 for
the answer.