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Properties of Real Numbers

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2 PROPERTIES OF REAL NUMBERS COMMUTATIVE PROPERTY: Addition:a + b = b + a 5 + 7 = 7 + 5 1 + 6 = 6 + 1 3.6 + 1.1 = 1.1 + 3.6 Multiplication: 9 6 4 20 = 6 9 6.4 5.2 = 20 4 = 5.2 6.4 For any real numbers a, b, and c: a b = b a Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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3 PROPERTIES OF REAL NUMBERS ASSOCIATIVE PROPERTY: Addition:(a + b) + c = a + (b + c) (3 + 4) +1 = 3 + (4 + 1) (2 + 5) + 7 = 2 + (5 + 7) (6.2 + 4.1) +3.3 = 6.2 + (4.1 + 3.3) Multiplication: For any real numbers a, b, and c: 15 4 7 2 3 5 4 7 2 3 5 = 34 45 6 = 34 45 6 5.7 7.2 2.3 = a b c= a b c Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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4 PROPERTIES OF REAL NUMBERS IDENTITY PROPERTY: Addition:a + 0 = 0 + a=a 5 + 0 = 0 + 5 1 + 0 = 0 + 1 3.6 + 0 = 0 + 3.6 Multiplication: 9 1 4 1 = 1 9 6.4 1 = 1 4 = 1 6.4 For any real numbers a, b, and c: a 1 = 1 a = a = 9 = 4 = 6.4 = 5 = 1 = 3.6 Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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5 PROPERTIES OF REAL NUMBERS INVERSE PROPERTY: Addition:a + (-a) = (-a) + a=0 5 + (-5) = (-5) + 5 3 + (-3) = (-3) + 3 3.6 + (-3.6) = (-3.6)+ 3.6 Multiplication: For any real numbers a, b, and c: = 1 = 0 a = a = 1 1 a 1 a If a=0 then 3 5 5 3 1 5 5 1 2 2 = 2 1 2 = 5 3 3 5 1 5 = 5 Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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6 PROPERTIES OF REAL NUMBERS DISTRIBUTIVE PROPERTY: Distributive: For any real numbers a, b, and c: a(b+c) = ab + ac (b+c)a = ba + ca and 3(5+1) = 3(5) + 3(1) (5+1)3 = 5(3) + 1(3) and 4(2+6) = 4(2) + 4(6) (2+6)4 = 2(4) + 6(4) and Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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7 Name the property shown at each equation: 1 45 = 45 a) 56 + 34 = 34 + 56 b) (-3) + 3 = 0 c) 5(9 +2) = 45 + 10 d) (2 + 1) +b= 2 + (1 + b) e) -34(23) = 23(-34) f) Identity property (X) Commutative property (+) Inverse property (+) Distributive property Associative property (+) Commutative property (X) Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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8 Simplify 3(4c -7d) + 5(2c + 9c) 3(4c -7d) + 5(2c + 9d) = 3(4c) – 3(7d) +5(2c) +5(9d) =12c – 21d + 10c +45d = 12c + 10c – 21d + 45d = 22c +24d Use distributive property Multiply Use commutative property to group like terms Add like terms Simplify 1 4 (12-4x) 3 5 (15x-10) + 1 4 (12-4x) 3 5 (15x-10) + =( )(12) – ( )(4x) + ( )(15x) – ( )(10) 1 4 1 4 3 5 3 5 = 3 – x + 9x -6 = 3 -6 - x + 9x = 8x-3 Use distributive property Multiply Use commutative property to group like terms Add like terms and commutative property Standards 6, 25 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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