## Tuesday, March 15, 2011

### Patrick's Great Big Book of Integers

Chapter 1 - Integers Review

Zero Pair:
A pair of integer chips with one chip representing +1 and one chip representing -1
Example: (+10) + (-10) = 0

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

If a number doesn't have a positive or negative sign on it, that means it is automatically a positive integer.

(+4) + (-4) = 0

(+4) is how much pencils you have
(-4) is how much pencils you owe Mrs. Wilson because you borrowed some and forgot to give
them back

Brackets for integers are kind of like the training wheels for a bike.

Grade 7 form : (+5) + (-5) = 0
Standard form :5 - 4 = 0

Positive = RED (+)
Negative = BLUE (-)

Questions:
-3 - (-7) = +4

-3 - 7 = -10

3 - 7 = -4

3 + 7 = 10

Chapter 2 - Multiplying integers
Multiplying integers - Repeated addition if you need to remove something that isn't there. We use zero pairs.

Examples:
1. (+2) x (+3) = +10 (2 groups of +3)
2. (+2) x (-3) = -6 (2 groups of -3)
3. (-2) x (+3) = -6 (Remove 2 groups of +3)
4. (-2) x (-3) = +6 (Remove 2 groups of -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 a negative factors the product is negative.

Chapter 3 - Dividing Integers

Partitive Division means to make parts of.

6 ÷ 2 = +3
-6 ÷ (-2) = +3

Quotative Division means to share with groups.
(-6) ÷ 2 = -3

The multiplicative inverse can help solve 6 ÷ (-2) by doing the question . The quotient is -3 and it will be a part of the question when the answer is -2.
6 ÷ (-2) = -36 ÷ (-3) = -2

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

6 ÷ 2 = +3
-6 ÷ (-2) = +3

They both have the same sign so it is positive.

(-6) ÷ 2 = -3
6 ÷ (-2) = -3

They both have different signs so it is negative.

Chapter 4 - Order of Operations with Integers

(+5) x (-3) + (-6) ÷ (+3) =
To solve this question, we will be using BEDMAS

We need to add square brackets to this problem, to make it easier.
SQUARE BRACKETS = KING OF BRACKETS.

[(+5) x (-3)] + [(-6) ÷ (+3)] =
(-15) + [(-6) ÷ (+3)] =
(-15) + (-2) = -13