Tip:
Highlight text to annotate it
X
1.2d: Operations with Integers –
Add with the Same Sign Adding and subtracting integers.
You keep the sign with the number becomes after it.
What this means is that the sign in front of a number such as
dash 3 or -3 means we keep this negative with the 3.
One thing to address at the beginning
is what happens if there are double signs.
By a double sign,
we mean somewhere that has two signs separated by a parenthesis.
When there are two signs,
it may be confusing as to what the question is asking.
Therefore, we have a way of addressing this.
When there are double signs,
we get rid of them using the rules that we use for multiplication.
Therefore, if I have a positive and a negative next to each other,
I turn this into a negative because a positive times a negative is a negative.
I therefore can rewrite this problem as 3 minus 4.
In the second example shown here, we see that there are two negative symbols.
When I have two negative symbols, remember, that it becomes a positive.
This means I can rewrite this problem as 3 + 4.
The thing to remember is that if there are double signs, you must first clear
those before moving on with the problem.
To visualize this, you can think of the idea that
the -2 is literally two negative symbols
and that the -3 is three negative symbols.
The sign in the center is asking us to add these two together.
If I add up all of these symbols, I would have a total of 5 negative symbols,
therefore, giving me the answer -5.
When I add with the same sign, sometimes the thing can help with the problem.
The same used here is same sign, add and keep.
What this is saying is that the two numbers such as -2 and -3
have the same sign being that they are both negative,
we add those two numbers together,
the 2 and the 3 making 5 and keep the sign that they had which was negative.
Example 1 asks us -7 + -4,
as you can see there is a double sign.
We must address this before going further.
When there is a positive and a negative, remember that it becomes a negative.
This means that we can rewrite this as -7 minus 4.
These two numbers have the same sign being that there are both negative.
We therefore add the two numbers together making 11
and keep the sign which was negative.
Therefore, the answer is -11.
In the second example, we once again have
two symbols together or a double sign.
When we have the double sign, remember, we must eliminate that sign.
Therefore, we would then have -6 minus 8
because a positive and a negative results in a negative.
We now can do our addition or combining problem
in which we add the two numbers and keep the sign.
Since 6 and 8 add to 14, the answer is 14.
We then look at their sign and see that it was negative.
As we saw in these two examples,
you must eliminate the double sign before doing the problem
and assessing if they have the same sign or different.
After eliminating the double sign, if they result in the same sign,
you add the two numbers together and keep the sign on the number.