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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