 # First Day of Math! Numbers are like people, torture them and they will give you answers.

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First Day of Math! Numbers are like people, torture them and they will give you answers

2. PENCIL 1.NOTEBOOK Algebra2 ‘Must Haves’

Diagnostic Test Let’s see how much you know about Algebra1 and Geometry

More on factoring

Properties of REAL NUMBERS

Subsets of Real Numbers

Opposites Two real numbers that are the same distance from the origin of the real number line are opposites of each other. Examples 2 and -2-100 and 100

Reciprocals Two numbers whose product is 1 are reciprocals of each other. Examples

Absolute Value The absolute value of a number is its distance from 0 on the number line. The absolute value of x is written. Examples

Commutative Property of Addition a + b = b + a When adding two numbers, the order of the numbers does not matter. Examples 2 + 3 = 3 + 2(-5) + 4 = 4 + (-5)

Commutative Property of Multiplication a  b = b  a When multiplying two numbers, the order of the numbers does not matter. Examples 2  3 = 3  2(-3)  24 = 24  (-3)

Associative Property of Addition a + (b + c) = (a + b) + c When three numbers are added, it makes no difference which two numbers are added first. Examples 2 + (3 + 5) = (2 + 3) + 5 (4 + 2) + 6 = 4 + (2 + 6)

Associative Property of Multiplication a(bc) = (ab)c When three numbers are multiplied, it makes no difference which two numbers are multiplied first. Examples –2  (3  5) = (2  3)  5 (4  2)  6 = 4  (2  6)

Distributive Property a(b + c) = ab + ac Multiplication distributes over addition. Examples 2 (3 + 5) = (2  3) + (2  5) (4 + 2)  6 = (4  6) + (2  6)

Identity Property of Addition This property states that if 0 is added to a number, the result is that number. Example: 3 + 0 = 0 + 3 = 3

Identity Property of Multiplication This property states that if a number is multiplied by 1, the result is that number. Example: 5  1 = 1  5 = 5

Inverse Property of Addition This property states that opposites add to zero. 7 + (-7) = 0 and -4 + 4 = 0

Inverse Property of Multiplication This property states that reciprocals multiply to 1.

LET’S SEE IF YOU CAN IDENTIFY THE PROPERTY USED IN EACH EQUATION

Identify which property that justifies each of the following. 4  (8  2) = (4  8)  2

Identify which property that justifies each of the following. 4  (8  2) = (4  8)  2 Associative Property of Multiplication

Identify which property that justifies each of the following. 6 + 8 = 8 + 6

Identify which property that justifies each of the following. 6 + 8 = 8 + 6 Commutative Property of Addition

Identify which property that justifies each of the following. 12 + 0 = 12

Identify which property that justifies each of the following. 12 + 0 = 12 Identity Property of Addition

Identify which property that justifies each of the following. 5(2 + 9) = (5  2) + (5  9)

Identify which property that justifies each of the following. 5(2 + 9) = (5  2) + (5  9) Distributive Property

Identify which property that justifies each of the following. 5 + (2 + 8) = (5 + 2) + 8

Identify which property that justifies each of the following. 5 + (2 + 8) = (5 + 2) + 8 Associative Property of Addition

Identify which property that justifies each of the following.

Identify which property that justifies each of the following. Inverse Property of MULTIPLICATION

Identify which property that justifies each of the following. 5  24 = 24  5

Identify which property that justifies each of the following. 5  24 = 24  5 Commutative Property of Multiplication

Identify which property that justifies each of the following. 18 + -18 = 0

Identify which property that justifies each of the following. 18 + -18 = 0 Inverse Property ADDITION

Identify which property that justifies each of the following. -34  1 = -34

Identify which property that justifies each of the following. -34  1 = -34 Identity Property MULTIPLICATION

Classwork

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