Algebra I Sections 2.2, 2.3, 2.5, 2.7. Properties of Addition Commutative Property a + b = b +a a + b = b +a 3 + (-2) = -2 +3 3 + (-2) = -2 +3 Associative.

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Presentation transcript:

Algebra I Sections 2.2, 2.3, 2.5, 2.7

Properties of Addition Commutative Property a + b = b +a a + b = b +a 3 + (-2) = (-2) = Associative Property (a + b) + c = a + (b + c) (a + b) + c = a + (b + c) (-5 + 6) + 2 = -5 + (6 + 2) (-5 + 6) + 2 = -5 + (6 + 2) Identity Property a + 0 = a a + 0 = a = = -4 Property of Zero (Inverse Property) a + (-a) = 0 a + (-a) = (-5) = (-5) = 0

Definitions ORIGIN: The point labeled zero on the number line ABSOLUTE VALUE: The number in the absolute value brackets is always positive OPPOSITES: The same number with different signs

Example 1 Find the absolute value of each expression │2.3│ │2.3│ = 2.3 │ - ½ │ │ - ½ │= ½ -│-8│ -│-8│= -8

Example 2 Find the opposite of the following

Example 3 Find the sum (-9) (-9) (-4.1) (-4.1) (-3.0) (-3.0) (-3 ½) (-3 ½)-33

Subtraction Rules Subtracting is the same as adding the opposite a – b = a + (-b) a – b = a + (-b) 3 – 5 = 3 + (-5) 3 – 5 = 3 + (-5) -2 – 5 = -2 + (-5) -2 – 5 = -2 + (-5)

Example 4 Evaluate each expression 3 – (-4) – – (-4) – – 5 4 – 5 ½ - ¼ ½ - ¼¼ -2.4 – – │-2│ 6 - │-2│4

Multiplication Properties Commutative Property a b = b a a b = b a 3 (-2) = (-2) 3 3 (-2) = (-2) 3 Associative Property (a b) c = a (b c) (a b) c = a (b c) (-6 2) 3 = -6 (2 3) (-6 2) 3 = -6 (2 3) Identity Property 1 a = a 1 (-4) = -4 Property of Zero a 0 = = 0 Property of Opposites (-1) a = -a (-1) (-3) = 3

Example 5 Find the product (-8)(3) (-8)(3)-24 (-4)(-7)( 3 / 7 ) (-4)(-7)( 3 / 7 )12 (-11)( ¼ ) (-11)( ¼ )-11/4

Division Rules Division is the same as multiplication by a reciprocal a ÷ b = a 1 / b a ÷ b = a 1 / b -1 ÷ 2 = -1 ½ -1 ÷ 2 = -1 ½

Example 6 Find the quotient -51 ÷ (-17) -51 ÷ (-17)3 35 ÷ (-70) 35 ÷ (-70) - ½ -18 ÷ ⅜ -18 ÷ ⅜ ÷ (-2 4 / 7 ) 56 ÷ (-2 4 / 7 ) / 9

Helpful Hints (Addition and Subtraction) Two negatives next to each other make a positive 5 – (-2) 5 – (-2) A positive and a negative next to each other make a negative 3 + (-1) 3 + (-1) 3 – 1 3 – 1 2

Helpful Hints (Multiplication and Division) When multiplying or dividing like signs, the result is positive ÷ 2 12 ÷ ÷ ÷ -86 When multiplying or dividing unlike signs, the result is negative ÷ ÷ ÷ ÷ -4-6

Homework Order of Operations Worksheet