Adding and Subtracting Signed Integers

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Adding and Subtracting Signed Integers
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The Number Line
7
-7

• Previously, we learned that numbers to the right
  of zero are positive and numbers to the left of
  zero are negative. By putting points on the
  number line, we can graph values.

• If one were to start at zero and move seven
  places to the right, this would represent a value
  of positive seven.

• If one were to start at zero and move seven
  places to the left, this would represent a value
  of negative seven.

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Adding Integers - Same Sign
We can show addition using a number line.
What is 5 4?
Start at five (5 units to the right from zero).
Move four units to the right.
The final point is at 9 on the number line.
Therefore, 5 4 9.
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Adding Integers - Same Sign
Now add two negative numbers on a number line.
What is -5 (-4)?
Start at 5 (5 units to the left from zero).
Move four units to the left. Go left since we
are adding a negative number.
The final point is at -9 on the number line.
Therefore, -5 (-4) -9.
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Adding Integers - Same Sign
We can also show how to do this by using algebra
tiles. Each dark tile is a positive 1, each light
tile is a negative 1
What is 5 7?


5

7

12
What is 5 7?


-12


-7
-5
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Adding Integers - Same Sign
RULE To add integers with the same sign, add
the absolute values of the integers. Give the
answer the same sign as the integers.
Solution
Examples
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Additive Inverse
What is (-7) 7?
To show this, start at the value -7 (seven units
left of zero).
Now, move seven units to the right (adding
positive seven).
Notice, we are back at zero (0).
For every positive integer on the number line,
there is a corresponding negative integer. These
integer pairs are opposites or additive inverses.
Additive Inverse Property For every number a, a
(-a) 0.
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Additive Inverse
When using algebra tiles, the additive inverses
make what is called a zero pair. For example, the
following is a zero pair, the two tiles cancel
each other out.
1 (-1) 0.
This also represents a zero pair.
x (-x) 0
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Adding Integers - Different Signs
Add the following integers (-4) 7.
Start at the value -4 (four units to the left of
zero).
Move seven units to the right (because we are
adding a positive number.
The final position is at 3. Therefore, (-4) 7
3.
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Adding Integers - Different Signs
Add (-9) 3
Start at the value -9 (nine places to the left of
zero).
Move three places to the right (adding a positive
number).
The final position is at negative six,
(-6). Therefore, (-9) 3 -6.
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Adding Integers - Different Signs
Add 7 (-3)
Start at the value 7 (seven places to the right
of zero).
Move three places to the left (adding a negative
number).
The final position is at positive four,
(4). Therefore, 7 (-3) 4.
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Adding Integers - Different Signs
Each dark tile is a positive 1, each light tile
is a negative 1. One 1 and one - 1 make a zero
pair, they cancel each other.
What is (- 4) 7?


-4

7

3
What is 4 (-7)?


-3


-7
4
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Adding Integers - Different Signs
RULE To add integers with different signs
determine the absolute value of the two numbers.
Subtract the smaller absolute value from the
larger absolute value. The solution will have
the same sign as the number with the larger
absolute value.
Solution
Example
Subtract
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Subtracting Integers
Subtraction is defined as addition a - b a
(-b). To perform subtraction, remember this
rule
Keep-Change-Change.
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-9
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Subtracting Integers
Keep-Change-Change doesnt mean the 2nd number
always ends up being negative
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-2
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You Try It!
Find each sum or difference.
1. -24 11 2. 18 (-40) 3.
-9 9 4. -16 (-14) 5.
13 35 6. -29 65
Simplify each expression.
7. 18r 27r 8. 9c (-12c)
9. -7x 45x 10. -3y (-7y)
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Solutions
-24 (-11) -35
1. -24 11 2. 18 (-40) 3.
-9 9 4. -16 (-14) 5. 13
35 6. -29 65
-22
0
-16 (14) -2
13 (-35) -22
36
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Solutions
7. 18r 27r 8. 9c (-12c) 9.
-7x 45x 10. -3y (-7y)
18r (-27r) -9r
9c (12c) 21c
38x
-10y