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1.2 Integers_ Adding and Subtracting Integers

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									Problem of the Day
Copy and complete the magic square.
The magic sum is 0.


            +5    –8   +3

            –2    0    +2

            –3    +8   –5
Monday, November 19, 2012
Homework Answers
 -Integer, additive inverse, opposite, absolute value
15) -3 < 2, Mon, Thurs, Tues, Wed
                                           37)   -16, -12, 24
17)   -11,-5, 8                            39)   -45, -25, 35
19)   -2, -1, 4
                                           41)   50
21)   15                                   43)   1
23)   31                                   45)   72
25)   21                                   47)   6
27)   10
                                           49)   48
29)   <                                    51)   2
31)   =                                    55) The absolute value of a
33)   =                                          number is always positive.
35)   >                                    56) -7, -6, -5
Integers are the set of whole
numbers and their opposites. On a
number line, opposites, or additive
inverses, are numbers that are the
same distance from 0, but on
opposite sides of 0 on the number
line.
Remember!

Numbers on a number line increase
in value as you move from left to
right.



–5 –4   –3 –2   –1 0   1   2   3   4   5
What integer would represent each situation?

1) 160 ft below sea level
2) a gain of 13 yards
3) John earned $35
4) Alaska’s temperature was 5 below zero
5) a loss of 10 yards
6) Betsy spent $55
A number’s absolute value is its distance
from 0 on a number line. Absolute value is
always positive because distance is always
positive. “The absolute value of –4” is written
as –4 . Additive inverses have the same
absolute value.
          4 units            4 units


–5   –4   –3   –2   –1   0   1   2     3   4   5


–4 = 4 = 4.
Since absolute value is only concerned with
  distance, not direction, the absolute value of a
  number cannot be negative.
Examples:
7 = 7
-14= 14
-24 = 24
 10 - 8 = 2

Name two integers whose absolute value is 9.
WATCH: Evaluate each expression.



  A. –8   + –5
     –8 = 8       –8 is 8 units from 0.
     –5 = 5       –5 is 5 units from 0.
     8 + 5 = 13

  B. 5 – 6

      –1 = 1      –1 is 1 units from 0.
Evaluate each expression.



  A.    –4 +     6          B.   12       +    -8




   C.   5 + 10              D. -1     +       -11
Monday, November 19, 2012
EX. 1- Use a number line to find the sum.
(–6) + 2
             –6
     2


 –6 –5 –4 –3 –2 –1       0   1   2   3   4   5
   You finish at –4, so (–6) + 2 = –4.

  Helpful Hint
  To add a positive number move to the right.
  To add a negative number move to the left.
EX. 2- Use a number line to find the sum.
–3 + (–6)
            –6
                              -3


 –9 –8 –7 –6 –5 –4 –3 –2 –1 0             1   2

   You finish at –9, so –3 + (–6) = –9.
Rules for Adding Integers
 Same signs, find the SUM. The answer
 carries the same sign.
Example:                  Example:
18 + 4 = 22               (-18) + (-4) = -22

 Different signs, find the DIFFERENCE. The
 answer carries the sign of the number with
 the greater absolute value.
Example:                  Example:
(-8) + 4 = -4                 (-4) + 8 = 4
Melissa opened a new bank account. Find her
account balance after the first four transactions
listed below.
    Deposits: $200, $20 Withdrawals: $166, $38

200 + 20 + (–166) + (–38)             Use a positive sign for
                                      deposits and a negative
                                      sign for withdrawals.

        220 + (–204)

            16

Melissa’s account balance after the first four transactions is $16.
Note that each of the following statements is true:
                10 – 5 = 10 + (-5)
                 7 – 7 = 7 + (-7)
              25 – 10 = 25 + (-10)

What do you notice about the first expression in
 each equality and its relationship to the 2nd
                 expression?
Subtracting an integer is the same as adding its opposite.

 Change the subtraction sign to an addition
 sign and change the sign of the second number.



The rules for subtracting integers are:
*change subtraction to addition
*change the sign of the second integer
*now follow the rules for adding integers with
like or unlike signs
Subtracting an integer is the same as adding its opposite.


Change the subtraction sign to an addition
sign and change the sign of the second number.

 A. –7 – 4


 B. 8 – (–5)


 C. –6 – (–3)
Subtract
 Examples

 D. –7 – (–8)



 E. –4 – 1



 F. 3 – (–6)
The top of the Sears Tower in Chicago, is
1454 feet above street level, while the
lowest level is 43 feet below street level.
How far is it from the lowest level to the top?

1454 – (–43)   Subtract the lowest level from
               the height.
1454 + 43      Add the opposite of (–43).

= 1497         Same sign; use the sign of the
               integers.
The distance from the high dive to the
swimming pool is 10 feet. The pool is 12 feet
deep. What is the total distance from the high
dive to the bottom of the pool?
10 – (–12)   Subtract the depth of the pool from the
             height of the high dive.
10 + 12      Add the opposite of (–12).

= 22

It is 22 feet from the diving board to the bottom
of the pool.
Examples:

1)-4 – 2                          2) -4 – (-2)

3)-8 – 9                          4) 3 – (-2) – 4


5) - 2 – 4                     6) -2  -  4 

 7) Use algebra tiles to show a model of the result of #2.
 Be sure to write an addition problem first!!!
                   -4 – (-2)
Homework
Worksheet 1.2
Human Number Line
 Adding – face right
 Subtracting – face left
 Positive number – walk forward
 Negative number – walk backward
        3+6=                3 - 6=
        -3 + 6 =            -3 – 6 =
         3 + -6 =            3 - -6=
         -3 + -6 =           -3 - -6=

								
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