**Chapter 1**

**Integers Review**

Zero pairs

- a pair of integer chips with one chip representing +1 and one chip representing -1

eg. -+

- the pair represents zero because

(+1)+(-1)=0

Find zero pairs for following integers.

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

Answers:

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

Integers from Grade 7

(+4) + (-4) = 0

(+4) have 4

(-4) owe 4

(Brackets are training wheels)

Standard form

4 - 4 = 0

+ positive = red

- negative = blue

Integer Questions

-3 - (-7) = +4

- 3 - 7 = -10

3 - 7 = -4

3 + 7 = +10

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**Chapter 2**

**Multiplying Integers**

-repeated addition

if you need to remove something that isn't there, use a zero pair

Examples

1. (+2) x (+3) = +6

Means: 2 groups of positive 3

2. (+2) x (-3) = -6

Means: 2 groups of negative 3

3. (-2) x (+3) = -6

Means: Remove 2 groups of positive 3

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

Means: Remove 2 groups of negative 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

*negative*factors the product is NEGATIVE.

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**Chapter 3**

**Dividing Integers**

Partitive Division

-making parts

6 ÷ 2 = +3

-6 ÷ (-2) = +3

Quotative Division

-sharing with groups

(-6) ÷ 2 = -3

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

6 ÷ (-2) = -3

6 ÷ (-3) = -2

**Sign Rule for Division**

The quotient of two integers with the same sign is positive.

The quotient of two integers with different signs is negative.

6 ÷ 2 = +3

They both have the same sign so it is positive.

-6 ÷ (-2) = +3

They both have that same sign so it is positive.

(-6) ÷ 2 = -3

They have different signs so it is negative.

6 ÷ (-2) = -3

They have different signs so it is negative.

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**Chapter 4**

**Order of Operations with Integers**

B.E.D.M.A.S

-Brackets

-Exponents

-Division

-Multiplication

-Addition

-Subtraction

Square brackets to box off division and multiplication.

(+5) x (-3) + (-6) ÷ (+3)=

[(+5) x (-3)] + [(-6) ÷ (+3)]=

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

Here is a link to help you.

Here is a video to help.

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