Kayla's Great Big Book of Integers

Chapter 1:
grade 7 Integer Review
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With integers, you have zero pairs.

zero pairs are when you have the same number of positive integers that you do negative, and they cancel themselves out.

ex. (+3) + (-3) = 0

There doesn't have to be brackets, but for beginners, it becomes useful when you have a longer equation to solve. Standard form is what people usually use.

ex.
+4 -4
4-4 <---that is standard form.

SIGN RULE:
When you have an even number of negative factors, the product is always a POSITIVE.
When you have odd number of negative factors, the product is always a NEGATIVE.


Chapter 2:
Multiplying Integers
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(+3) x (+8)
(+3)(+8)
3(+8)

(+3) x (+3) <--- that means ' three groups of plus three'
+++ +++ +++ <--- three groups of plus three
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MULTIPLYING IS REPEATED ADDITION!!!
ex.
(+1) + (+1) + (+1) =
3 x (+1) =
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(+2) x (+3)
The 'x' means 'groups of.'

(-2) x (-3)
This means remove 2 groups of -3

1. (4) x (+2) = ++ ++ ++ ++
2. (5) x (-2) = -- -- -- -- --
3. (-4) x (2) = ---- ----
4. (-6) x (-1) = ++++++


Chapter 3:
Dividing Integers
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Partitive Division: How many parts
ex. 15 ÷ (-3) = 5
There are 5 parts of 3 in 15.

Quotative Division: Sharing in groups
15 ÷ 3 = 5
There are 3 groups of 5 in 15.

When both integers are the same, you can use both Partitive or Quotative Division.
ex.
(+15) ÷ (+3)
or
(-15) ÷ (-3)


Chapter 4:
Order of Operations
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When you use the order of operations, you use BEDMAS.

Brackets [and square brackets]
Exponents
Division
Multiplication
Addition
Subtraction

Square Brackets [ ], come first in the order of operations. If you see brackets in the equation, but there are also square brackets, do the square brackets first.

To solve this problem, you would use BEDMAS to get the answer.
ex.
(+5) x (-3) + (-6) ÷ (+3)=
(-15) + (-2)=
= -17

REMEMBER: two Negatives equal a Positive.