Algebra I – Chapter 2

Integers and Properties

Integer Rules• Adding:–Different signs: Find the difference

and keep the sign of the larger number–Ex: (-3) + (6) = (3)

–Same signs: Add and keep the signs–Ex: (-3) + (-6) = (-9)

Integer Rules

• Subtracting:

–Add the Opposite

Integer Rules• Multiplying and Dividing:

–Different Signs: The answer is negative• Ex: (-6)(3) = (-18)

–Same Sign: The answer is positive• Ex: (-4)(-5) = 20

Property Addition Multiplication

Commutative a + b = b + a Ab = ba

Associative (a+b) + c = a + (b+c) abc = cba

Identity a + 0 = a a (1) = a

Inverse a + (-a) = 0 a (1/a) = 1

Distributive a (b+c) = ab +ac and a (b-c) = ab - ac

Property Symbols Examples

Reflexive a = a 8 – n = 8 – n

Symmetric If a = b then b = a 3x = 2 then 2 = 3x

Transitive If a = b and b = c then a = c

If 2x = 8 and 8 = 5x – 3 then 2x = 5x - 3

Substitution If a = b then a can be replaced by b and b can be replaced by a

Reflection:• What will the answer be when you multiply

two numbers with the same signs?

• What about when you divide two numbers with different signs?

• When can associative property work?

Tonight’s Homework:

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