Integers
Integers

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

 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

Email me if you think of others!