Transcript Adding and Subtracting Signed Integers The Number Line -7 -10 -5 +7  Previously, we learned that numbers to the right of zero are positive and numbers.

Adding and Subtracting
Signed Integers
The Number Line
-7
-10
-5
+7
0
5
10
 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.
Adding Integers - Same Sign
We can show addition using a number line.
9
-10
-5
0
5
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.
10
Adding Integers - Same Sign
Now add two negative numbers on a number line.
-9
-10
-5
0
5
10
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.
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?
1
1
1
1
1
+
1
5
1
1
1
+
1
1
=
1
7
=
What is –5 + –7?
-1
-1
-1
-1
-5
-1
-1
+
+
-1
-1
-1
-7
-1
-1
=
-1
=
1
1
1
1
1
1
1
1
1
1
1
1
12
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-12
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
1.
15  12
2.
 14  (33)
 47
3.
 4x  (12x)
 16x
27
Additive Inverse
What is (-7) + 7?
-10
-5
0
5
10
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.
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
1 + (-1) = 0.
This also represents a zero pair.
x
-x
x + (-x) = 0
Adding Integers - Different Signs
Add the following integers:
-10
-5
(-4) + 7.
0
5
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.
10
Adding Integers - Different Signs
Add (-9) + 3
-10
-5
0
5
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.
10
Adding Integers - Different Signs
Add 7 + (-3)
-10
-5
0
5
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.
10
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?
-1
-1
-1
1
+
-1
-4
1
1
1
+
1
1
1
=
1
7
1
=
1
3
What is 4 + (-7)?
1
1
1
1
4
-1
+
+
-1
-1
-1
-7
-1
-1
-1
=
-1
-1
=
-1
-3
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
12  15
15  12
3
17  (25)
25  17
8
Subtracting Integers
Subtraction is defined as addition:
a - b = a + (-b).
To perform subtraction, remember this rule:
Keep-Change-Change.
12 - 9 = 12 + (-9) = 3
Keep the 1st
# the same.
Change the
minus to a plus.
Change the sign
of the 2nd #.
4 - 13 = 4 + (-13) = -9
Keep the 1st
# the same.
Change the
minus to a plus.
Change the sign
of the 2nd #.
Subtracting Integers
Keep-Change-Change doesn’t mean the 2nd number always
ends up being negative:
4 - (-3) = 4 + (3) = 7
Keep the 1st
# the same.
Change the
minus to a plus.
Change the sign
of the 2nd #.
-4 - (-2) = -4 + (2) = -2
Keep the 1st
# the same.
Change the
minus to a plus.
Change the sign
of the 2nd #.
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
9c – (-12c)
Simplify each expression.
7.
18r – 27r
8.
9.
-7x + 45x
10. -3y + (-7y)
Solutions
1.
-24 – 11
= -24 + (-11) = -35
2.
18 + (-40)
= -22
3.
-9 + 9
=0
4.
-16 – (-14) = -16 + (14) = -2
5.
13 – 35
= 13 + (-35) = -22
6.
-29 + 65
= 36
Solutions
7.
18r – 27r
8.
9c – (-12c) = 9c + (12c) = 21c
9.
-7x + 45x
= 18r + (-27r) = -9r
= 38x
10. -3y + (-7y) = -10y