## Tuesday, March 22, 2011

### Kim's Great Big Book Of Integers

Chapter 1: Grade 7 Integer Review

In Grade 7, I learned that integers were whole numbers that were positive and negative. They could be represented using integer chips and a number line.

Find zero pairs for the following integers.

-6 +6
+10 -10
19 -19
-16 +16
-11 +11
+14 -14
63 -63

have 4 owe 4
(+4) + (-4) = 0

Brackets are training wheels.

Standard form:

+4 -4

4-4 <--- pure standard form

Questions:

-3 - (-7) = +4

-3 - 7 = -10

3 - 7 = -4

3 + 7 = +10

-3 + 7 = +4

Chapter 2

Multiplying Integers

Sign Rule:
Even= when you have an even number of n
egative factors the product is POSITIVE.
Odd= when you have an odd number of negative factors the product is NEGATIVE.

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

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

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

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

Dividing Integers

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

Partative Division - making parts or groups

6 ÷ 2 = 3
How many groups of 2 are in 6?
How 2's go into 6?

-6 ÷ (-2) = 3
How many groups of (-2) are in -6?
How many (-2)'s go into -6?

Quotative Division - sharing with groups

(-6) ÷ 2 = -3
share groups

When both integers are the same you can use partative and quotative.
(+15) ÷ (+3) = (+5) or (-15) ÷ (-3) = (-5)

You can use multiplicative inverse to help solve 6 ÷ (-2) by finding the answer which is (-3) and switching it with (-2) making the question 6 ÷ (-3) and the answer would be (-2).

Order of Operations with Integers

Brackets
Exponents
Division
Multiplication
Subtraction

Solve this question:
(+5) x (-3) + (-6) ÷ (+3) =

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