Lesson 1.4 add/subtract integers

1
Adding and Subtracting Integers
2
Absolute Value
7
-7
A number line has many functions. 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.
3
Absolute Value
7
-7
Both of these numbers, positive seven (7) and
negative seven (-7), represent a point that is
seven units away from the origin.
The absolute value of a number is the distance
between that number and zero on a number line.
Absolute value is shown by placing two vertical
bars around the number as follows ?5 ? The
absolute value of five is five. ?-3 ? The
absolute value of negative three is three.
4
Adding Integers - Same Sign
What is 5 7?
We can show how to do this by using algebra tiles.


5

7

12
What is 5 -7?


-12


-7
-5
5
Adding Integers - Same Sign
We can show this same idea using a number line.
What is 5 4?
Move five (5) units to the right from zero.
Now move four more units to the right.
The final point is at 9 on the number line.
Therefore, 5 4 9.
6
Adding Integers - Same Sign
What is -5 (-4)?
Move five (5) units to the left from zero.
Now move four more units to the left.
The final point is at -9 on the number line.
Therefore, -5 (-4) -9.
7
Adding Integers - Same Sign
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
8
Additive Inverse
What is (-7) 7?
To show this, we can begin at zero and move seven
units to the left.
Now, move seven units to the right.
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
9
Additive Inverse
When using algebra tiles, the additive inverses
make what is called a zero pair. For example, the
following is a zero pair.
1 (-1) 0.
This also represents a zero pair.
x (-x) 0
10
Adding Integers - Different Signs
Add the following integers (-4) 7.
Start at zero and move four units to the left.
Now move seven units to the right.
The final position is at 3. Therefore, (-4) 7
3.
11
Adding Integers - Different Signs
Add the following integers (-4) 7.
Notice that seven minus four also equals
three. In our example, the number with the larger
absolute value was positive and our solution was
positive.
Lets try another one.
12
Adding Integers - Different Signs
Add (-9) 3
Start at zero and move nine places to the left.
Now move three places to the right.
The final position is at negative six,
(-6). Therefore, (-9) 3 -6.
13
Adding Integers - Different Signs
Add (-9) 3
In this example, the number with the larger
absolute value is negative. The number with the
smaller absolute value is positive. We know that
9-3 6. However, (-9) 3 -6. 6 and 6 are
opposites. Comparing these two examples shows us
that the answer will have the same sign as the
number with the larger absolute value.
14
Adding Integers - Different Signs
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
15
Subtracting Integers
We can show the addition of numbers with opposite
signs by using algebra tiles. For example, 3
(-5) would look like this

Group the zero pairs.
Remove the zero pairs
16
Subtracting Integers
We can show the addition of numbers with opposite
signs by using algebra tiles. For example, 3
(-5) would look like this


Group the zero pairs.
Remove the zero pairs
The remainder is the solution. Therefore, 3
(-5) -2
17
Subtracting Integers
Lets see how subtraction works using algebra
tiles for 3 - 5.
Begin with three algebra tiles.
Now, take away or remove five tiles from these
three. It cant be done. However, we can add
zero pairs until we have five ones because adding
zero doesnt change the value of the number.
18
Subtracting Integers
Lets see how subtraction works using algebra
tiles for 3 - 5.
Begin with three algebra tiles.
Now remove the five ones.
19
Subtracting Integers
Lets see how subtraction works using algebra
tiles for 3 - 5.
Begin with three algebra tiles.
Now remove the five ones.
The remainder is negative two (-2). Therefore, 3
5 -2. This is the same as 3 (-5).
To subtract a number, add its additive
inverse. For any numbers a and b, a b a
(-b).
20
You Try It
Find each sum or difference.

• -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
Evaluate each expression.

• ?89 ? 11. ?-14 ?
  
• 12. - ?-7 ? 13. ?c 5 ? if
  c -19

21
Solutions
22
Solutions
23
Solutions
13. ?c 5 ? if c -19