## Tuesday, March 22, 2011

### Jae Anne's Great Big Book of Integers

Chapter 1Here are some exercise we did in class.

Zero Pair is when the same negative (-1) and a positive (+1) number are combined, the result is zero.
example:  -6   +6        +10  -10       19 +19
-16  +16       -11   +11    +14  -14      63   -63
Brackets are training wheels.
example:  (+4) + (-4) = 0
(have 4) + (owe 4) = 0
4 - 4  <== pure standard form

examples:
-6 +2 = -4
-6 -2 = -8
-6 +10 = +4

Here are the * questions.
When subtracting something isn't there use zero pair.

-3 - (-7) = 4

-3 -7 = -10

3 -7 = -4

3 +7 = 10

-3 +7 = 4

Chapter 2
Multiplying Integers

Sign Rule (negative signs)
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.

(+2) x (+3) = 6
2 grops of (+3)

(+2) x (-3) = -6
2 groups of (-3)

(-2) x (+3)= -6
remove 2 groups of (+3)

(-2) x (-3) = 6
remove 2 groups of (-3)

Dividing Integers

How many groups of __ are in __?
How many __'s go into __?

Partitive Division - making parts or group

6 ÷ 2 = 3

-6 ÷ (-2) = +3

Qoutative Division - sharing with groups

(-6)    ÷       2       =
share        group

When both integers are the same you can use partitive or qoutative division.
(+15) ÷ (3) = (+5) or 15 ÷ 3 = 5

Multiplicative Inverse can help solve 6 ÷ (-2) by finding the answer which is (-3) and switch it places with (-2) that makes 6 ÷ (-3) and the answer is (-2).

﻿Sign Rule

When 2 integers have the same sign (+) ÷ (+) or (-) ÷ (-) the answer would be POSITIVE.
6 ÷ 2 = 3
-6 ÷ (-2) = +3
When 2 integers have different sign (+) ÷ (-) or (-) ÷ (+)the answer would be NEGATIVE.
(-6) ÷ 2 = -3
6 ÷ (-2) = -3

Order of Operations with Integers

(+5) x (-3) + (-6) ÷ (+3)

We can solve this problem by:
1) put brackets where you see multiplication and division happens
[(+5) x (-3)] + [(-6) ÷ (+3)]
2) solve the ones in brackets
(- 15) + (-2)