## Monday, March 7, 2011

### Glenesse's Great Big Book Of Integers

Chapter 1
Integers Review

Zero pairs
- a pair of integer chips with one chip representing +1 and one chip representing -1
eg. -+
- the pair represents zero because
(+1)+(-1)=0

Find zero pairs for following integers.
-6 +10 19 -16 -11 +14 63
+6 -10 -19 +16 +11 -14 -63

(+4) + (-4) = 0
(+4) have 4
(-4) owe 4
(Brackets are training wheels)

Standard form
4 - 4 = 0

+ positive = red
- negative = blue

Integer Questions
-3 - (-7) = +4
- 3 - 7 = -10
3 - 7 = -4
3 + 7 = +10

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Chapter 2
Multiplying Integers
if you need to remove something that isn't there, use a zero pair

Examples
1. (+2) x (+3) = +6
Means: 2 groups of positive 3

2. (+2) x (-3) = -6
Means: 2 groups of negative 3

3. (-2) x (+3) = -6
Means: Remove 2 groups of positive 3

4. (-2) x (-3) = +6
Means: Remove 2 groups of negative 3

Sign Rule (negative sign)
Even: When you have an even number of negative factors the product is POSITIVE.
Odd: When you have an odd number of negative factors the product is NEGATIVE.

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Chapter 3
Dividing Integers

Partitive Division
-making parts

6 ÷ 2 = +3

-6 ÷ (-2) = +3

Quotative Division
-sharing with groups

(-6) ÷ 2 = -3

The multiplicative inverse can help me solve 6 ÷ (-2) = by doing the question and the quotient is -3. -3 will be part of the question when the answer is -2.
6 ÷ (-2) = -3
6 ÷ (-3) = -2

Sign Rule for Division
The quotient of two integers with the same sign is positive.
The quotient of two integers with different signs is negative.

6 ÷ 2 = +3
They both have the same sign so it is positive.
-6 ÷ (-2) = +3
They both have that same sign so it is positive.
(-6) ÷ 2 = -3
They have different signs so it is negative.
6 ÷ (-2) = -3
They have different signs so it is negative.

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Chapter 4
Order of Operations with Integers

B.E.D.M.A.S
-Brackets
-Exponents
-Division
-Multiplication
-Subtraction

Square brackets to box off division and multiplication.

(+5) x (-3) + (-6) ÷ (+3)=
[(+5) x (-3)] + [(-6) ÷ (+3)]=
(-15) + (-2) = -17