Adding Integers

1
Adding Integers
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2
The integers are
the whole numbers
their opposites
and zero
1, 2, 3, 4, 5, 6, 7, 8, and so on
no os dna -8, -7, -6, -5, -4, -3, -2, -1
, 0,
These are negative numbers.
These are positive numbers.
Click when ready.
3
One way to make sense of adding integers is to
think about money.
Positive numbers are gains of money.
5 means I gained 5.
Negative numbers are losses of money.
-5 means I lost 5.
Whats with the colors?
Being in the black means you have money.
Our positive dollars (gains) will be shown in
black.
1
Being in the red means you owe money.
Click when ready.
Our negative dollars (losses) will be shown in
red.
1
4
There are only four possibilities in adding
integers. Here is the first.
5 4
Both numbers are positive.
Of course, you know this already, but lets do it
with the money.
1
1
1
1
1
You gain five dollars.
1
1
1
1
Then you gain four more dollars.
Altogether you have a gain of nine dollars.
So, 5 4 9
Click when ready.
Positive five plus positive four equals positive
nine.
5
Try this. Negative four plus negative three.
-4 (-3)
Both numbers are negative.
1
1
1
1
You lose four dollars.
1
1
1
Then you lose three more dollars.
Altogether you have a loss of seven dollars.
So, -4 (-3) -7
Click when ready.
Negative four plus negative three equals negative
nine.
6
If you have four negatives (-4) and then you add
in three more negatives (-3), you end up with
seven negatives (-7).
This should make sense!
Click when ready.
7
Now try adding where the signs are different.
Five plus negative three.
5 (-3)
One number is positive. The other is negative.
The 5 is a gain. The -3 is a loss.
1
You gain five dollars.
1
1
1
1
Then you lose three dollars.
1
1
1
Each loss of 1 cancels out one gain of 1.
You have a net gain of two dollars.
So, 5 (-3) 2
Click when ready.
Positive five plus negative three equals positive
two.
8
Try this. Two plus negative six.
2 (-6)
One number is positive. The other is negative.
The 2 is a gain. The -6 is a loss.
1
You gain two dollars.
1
Then you lose six dollars.
1
1
1
1
1
1
Each loss of 1 cancels out one gain of 1.
You have a net loss of four dollars.
So, 2 (-6) -4
Click when ready.
Positive two plus negative six equals negative
four.
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If you have a positive number and a negative
number to add, you are finding out which you have
more of. If there are more positives, the answer
is positive. If there are more negatives, the
answer is negative.
Here there are two more positives than negatives.
5 (-3) 2
2 (-6) -4
Here there are four more negatives than positives.
Click when ready.
Again, it should make sense!
10
Practice by first stating the problem and then
the sum.
Please click for your first problem.
7 (-3)
4
seven plus negative three
equals four.
If you gain 7 and then lose 3, you will have
gained 4.
Click for another problem.
Click when ready.
-8 2
-6
negative eight plus two
equals negative six.
If you lose 8 and then gain 2, you will have
lost 6.
Click for another problem.
Click when ready.
-4 (-1)
-5
negative four plus negative one
equals negative five.
If you lose 4 and then lose 1, you will have
lost 5.
Click for another problem.
Click when ready.
11
Practice by first stating the problem and then
the sum.
5 (-8)
-3
five plus negative eight
equals negative three.
If you gain 5 and then lose 8, you will have
lost 3.
Click for another problem.
Click when ready.
-4 (-2)
-6
negative four plus negative two
equals negative six.
If you lose 4 and then lose 2, you will have
lost 6.
Click for another problem.
Click when ready.
-2 9
7
negative two plus nine
equals seven.
If you lose 2 and then gain 9, you will have
gained 7.
Click for another problem.
Click when ready.
12
More practice. Please read new explanations as
they appear.
-2 (-8)
-10
negative two plus negative eight
equals negative ten.
Add up how many negatives you have. The sum is
negative ten.
Click for another problem.
Click when ready.
-6 2
-4
negative six plus positive two
equals negative four.
You have four more negatives than positives. The
sum is negative four.
Click for another problem.
Click when ready.
-3 8
5
negative three plus positive eight
equals five.
You have five more positives than negatives. The
sum is positive five.
Click for another problem.
Click when ready.
13
More practice. Please read new explanations as
they appear.
8 (-11)
-3
positive eight plus negative eleven
equals negative three.
You have three more negatives than positives.
The sum is negative three.
Click for another problem.
Click when ready.
-1 (-5)
-6
negative one plus negative five
equals negative six.
Add up how many negatives you have. The sum is
negative six.
Click for another problem.
Click when ready.
7 (-6)
1
positive seven plus negative six
equals positive one.
You have one more positive than negative. The
sum is positive one.
Click for another problem.
Click when ready.
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If you are not getting them all correct, go back
to the beginning and go through slowly. Be
patient with yourself until it begins to make
sense. Make sure that you practice to put this
in your long term memory.
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