>> Welcome back to another video on adding integers.
This video uses the formal rules for adding integers.
I do have other videos that show other techniques
for adding integers.
Let's first start off by reviewing what an integer is.
Integers are the numbers that can be written
without a fractional or decimal component and they fall
within the set listed here.
So let's go over the formal rules for adding integers.
When adding two integers, it will fall
in to one of two conditions.
Either we're adding two integers with the same sign
or we're adding two integers with different signs.
If we're adding integers with the same sign,
we add the absolute values of the numbers
and then keep the sign of the original integers.
However, if we're adding two integers with different signs,
we take the absolute value of both,
we subtract the smaller value from the larger value,
and then the sign of the answer is the original sign
of the number with the larger absolute value.
So let's go ahead and see how this works out.
So for example number one, we have negative 5 plus 6.
So we have two integers with different signs.
So we take their absolute value, the absolute value
of negative 5 would be 5.
The absolute value of 6 would be 6.
And because they have signs,
we subtract the smaller from the larger.
Well, 6 minus 5 would be 1 and then to determine the sign
of the sum, we take the sign of the number
that had the larger absolute value.
Well, 6 had the larger absolute value, 6 is positive,
so the sum is positive.
On number two, we have two integers with the same sign,
they're both negative.
So the formal rules say, take the absolute value of both.
That would be 8 and 3 and because they have the same sign,
we add them this time.
That would be 11, but then we keep the sign
of divisional numbers.
So instead of positive 11, it will be negative 11.
So the big difference here is,
if the two integers have different signs,
we subtract the smaller from the larger
after we take their absolute values, and if they're the same,
we find the sum after we determine the absolute values.
So on number three, we have different signs,
one's positive, one's negative.
So we take the absolute value of both
and then subtract the smaller from the larger.
So the absolute value of 1 is 1.
Absolute value of negative 7 is 7.
We subtract because the original sum had different signs.
Well, 7 minus 1 is 6.
However, since the 7 was a larger number,
and its original sign was negative,
our sum will be negative 6.
Let's try a few more.
Negative 25 plus 63.
One's negative and one's positive.
So once we find the absolute values, we'll have to substract.
The absolute value of negative 25 would be 25.
The absolute value of 63 is 63.
Notice how I always write the larger number on top
because I know since they have different signs,
I will have to subtract.
So borrow, so 13 minus 5 would be 8, 5 minus 2 would be 3.
So our sum will be 38.
And it will be positive 38
because 63 is the bigger number and it's positive.
Number two, we have negative 31 plus negative 84.
Again, we'll take the absolute value of both,
which will be 31 and 84.
But since they have the same sign, we'll add them this time.
So we have 5 and 11, 115.
And since both integers were negative,
our sum will be negative 115.
And the last example, again,
we have two integers with different signs.
So we'll take the absolute values and then subtract.
The absolute value of 15 is 15.
The absolute value of negative 47 is 47.
Again, notice I always get in the habit
of writing the larger number first just in case we do have
to subtract like we do here
because they have different signs.
So we'll subtract 7 minus 5 is 2, 4 minus 1 is 3.
So our sum is 32, but since the 47 had the larger absolute value
and the 47 is negative, our sum is negative.
Okay. So that's how you can add integers using the formal rules,
but again, if this seems difficult, you may want
to watch the video on using the number line to add integers
as well as using the money analogy.
Thank you for watching.