Integer Operations
Integers are the set of whole numbers
and their opposites.
The set of whole numbers starts with
zero! 0,1,2,3,4,5,…
Integers …-1,-2,0,1,2…
Adding Integers
= positive 1
= negative 1
+
+
=
+
+2
+
+
=
-5
Adding integers
If the colored chips are the same, then all you
have to do is add them together to get the sum.
Three red chips plus two red chips equals five red
chips.
+
-3
=
+
-2
=
-5
Adding integers
If the colored chips are the same, then all you
have to do is add them together to get the sum.
Three black chips plus two black chips equals five
black chips.
+
3
=
+
2
=
5
Opposites
Opposites are numbers that are the same
distance from zero. Distance from zero is called
absolute value. It is always positive.
The numbers –5 and 5 are both 5 units away
from zero, so they have the same absolute value.
Adding opposites gives a sum of zero!!!
5 units
-5
5 units
0
5
Absolute value is also shown with a
vertical line on either side of a number.
5
=
5
-5
=
5
Opposites have the same absolute value.
Adding on a number line.
Negatives Positives
•
0
When you add on a number line you
move to the right if you are adding
positives.
When you add negatives you go to
the left.
3 + -2 =
-2
+3
•
You end up
here at
positive 1
-6 + 9 =
9
-6
•
0
You end up
here at
positive 3
Adding integers with unlike
signs
 If one number is positive
and the other is negative,
you subtract the absolute
values and determine
whether your answer is
positive or negative
based on which number
has the largest absolute
value.
-5 + 11 = ? Positive 6
-5
+
11
-5 = 5
11
11
=
= 11
11 has the larger
absolute value and is
positive
5
_________
6
Therefore your
answer is
positive!
Subtracting Integers
 If the signs are the
same and there are
more of the first
number, you just
subtract and leave the
sign the same
-5 - -4 = -1
Your answer is –1!
What happens when you subtract
positives and negatives?
-3 - 2
You are trying to take away 2 black chips. You
don’t have any.
Remember that a red black pair is zero!
Since you need two black chips, you
have to add two zero pairs!
What happens when you subtract
positives and negatives?
-3 - 2
Your answer is
negative 5!
When you are trying to take
away something that isn’t
there; it is like adding more
of what you have!
-6 – (- 9) =
-(-9)
-6
•
0
You end up
here at
positive 3
Subtraction is the opposite of addition!
You can re-write subtraction as addition!
Change to the opposite! Then everything else changes to its
opposite!
-5 - 4
-5 + -4
Don’t mess with the original! Leave the
first integer alone.
-5 + -4 = -9!
Whenever you subtract a negative, it
is just like adding a positive.
8 – (-9) =
8 + +9 = 17
If you tried to subtract 9 red chips
from 8 black chips, you couldn’t
do it. You would need to add 9
pairs so you could remove the 9
red chips leaving you with 9 more
black chips!