Integers
Integers

Definition      Addition      Subtraction      Multiplication      Division       Real Life Situations






Integers are:
        -negative and positive numbers and zero
        -a number with a + or - sign
        -numbers with NO fraction or decimal part
        -the "opposite of"
 
 


Rules for ADDING INTEGERS
Rule
Rhyme
Symbols
Examples
If the signs are the same, add the numbers and keep the sign.
Same
Sign
Sum
m + n
-m + -n
3 + 6 = 9
-4 + -2 = -6
If the signs are different, subtract the numbers and keep the sign of the larger number.
Different
Sign
Difference
-m + n
m + -n
-2 + 8 = 6
(think 8-2=6 and 8 is bigger than 2, so keep the positive sign)

-7 + 3 = -4
(think 7-3=4 and 7 is bigger than 3, so keep the negative sign)

When adding more than two integers, add two at a time until all numbers have been used.  You can use the COMMUTATIVE PROPERTY (changing the order) and the ASSOCIATIVE PROPERTY (changing the grouping) to make it easier.  For example:
-2 + 3 + -6 + 10 =
(10 + 3) + (-2 + -6) =
     13    +    - 8       =
5


Rules for SUBTRACTING INTEGERS

Any subtraction problem involving integers can be rewritten as an addition problem.  Then, the rules listed above apply.  For example:

-64 - (-18) =
-64   +   18   =
-46
-154 - 83 =
-154 + (-83) =
-237

 

"Change the sign & the number behind"   ~   Two-stroke    ~    Eliminate "double signs"
 



Rules for MULTIPLYING INTEGERS
 
Rule
Symbol
Example
If the signs are the same, the answer will be positive.
 (m)(n)
(-m)(-n)
6 * 8 = 48
-8 * -6 = 48
If the signs are different, the answer will be negative.
(m)(-n)
(-m)(n)
4 * -5 = -20
-4 * 5 = -20

NOTE:  An EVEN number of negative signs will produe an POSITIVE answer.  An ODD number of negative signs will produce a NEGATIVE answer. (Every pair will "cancel" out.)



Rules for DIVIDING INTEGERS

Division follows the same odd/even rules as multiplication.  Note that when divison is written as a fraction, there are three locations for the negative sign (top, middle, bottom):
 

 - 2
  3
  2
  3
 2 
- 3



Real Life Situations
 
 
 
Situation
Zero
Positive
Negative
business
breaking even
profit
loss
temperature (Celsius)
zero degrees
warm 
cold (freezing)
elevation
sea level
mountains
valleys
time
today
tomorrow
yesterday
banking
no change
deposit
withdrawl
football
line of scrimage
gain yardage
loss of yardage

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