Albert's Great Big Book of Integers

Chapter 1:
Grade 7 Integer Review

Integers could be express using a number line or integer chips.







In integers, when adding both positive and negative with the same number they will cancel each other out making the answer a zero.

eg. (+5) + (-5) or (-5) + 5






The brackets for the integers are like training wheels for making equations more understandable
but mostly we need to use standard form.

eg. (+6) + (-6) In standard form 6 -6

Chapter 2:
Multiplying Integers

The Sign Rule:

When you have an even number of negative factors, the product will be POSITIVE.
eg. (-4) x (-4) = +16

When you have an odd number of positive factors, the product will be NEGATIVE.
eg. (+5) x (-4) = -20

Ways of showing how to multiply integers:

Positive x Positive = Positive: (+2) x (+3) = +6 , (2) x (3) = 6 , (2) (3) = 6
or
2(3) = 6
or
2 groups of (+3)

Negative x Positive = Negative: (-2) x (+3), remove 2 groups of (+3)

Negative x Negative = Positive: (-2) x (-3), remove 2 groups of (-3)


Chapter 3:
Dividing Integers

The way of reading the dividing integers is:
- How many groups of __ are in __?
- How many __'s go into __?

Partitive Division - The making of groups or parts.

Quotative Division - Sharing with groups.

The quotient of the two integers with the same sign is Positive.
The quotient of the two integers with the same sign is Negative.

Chapter 4:
Order of Operations with Integers

B.E.D.M.A.S. is used to do the order of operations for integers which stands for:

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

eg.
(+5) x (-3) + (-6) ÷ (+3) =

[(+5) x (-3)] + [(-6) ÷ (+3)] =

(-15) + (-2) = -17