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\n" ); document.write( "Property (a, b and c are real numbers, variables or algebraic expressions)
\n" ); document.write( "Examples
\n" ); document.write( "Verbal hints
\n" ); document.write( "1.
\n" ); document.write( "Distributive Property
\n" ); document.write( "a • (b + c) = a • b + a • c
\n" ); document.write( "3 • (4 + 5) = 3 • 4 + 3 • 5
\n" ); document.write( "\"multiplication distributes across addition\"
\n" ); document.write( "2.
\n" ); document.write( "Commutative Property of Addition
\n" ); document.write( "a + b = b + a
\n" ); document.write( "3 + 4 = 4 + 3
\n" ); document.write( "\"commute = to get up and move to a new location : switch places\"
\n" ); document.write( "3.
\n" ); document.write( "Commutative Property of Multiplication
\n" ); document.write( "a • b = b • a
\n" ); document.write( "3 • 4 = 4 • 3
\n" ); document.write( "\"commute = to get up and move to a new location: switch places\"
\n" ); document.write( "4.
\n" ); document.write( "Associative Property of Addition
\n" ); document.write( "a + (b + c) = (a + b) + c
\n" ); document.write( "3 + (4 + 5) = (3 + 4) + 5
\n" ); document.write( "\"regroup - elements do not physically move, they simply group with a new friend.\"
\n" ); document.write( "5.
\n" ); document.write( "Associative Property of Multiplication
\n" ); document.write( "a • (b • c) = (a • b) • c
\n" ); document.write( "3 • (4 • 5) = (3 • 4) • 5
\n" ); document.write( "\"regroup - elements do not physically move, they simply group with a new friend.\"
\n" ); document.write( "6.
\n" ); document.write( "Additive Identity Property
\n" ); document.write( "a + 0 = a
\n" ); document.write( "4 + 0 = 4
\n" ); document.write( "\"the value that returns the input unchanged\"
\n" ); document.write( "7.
\n" ); document.write( "Multiplicative Identity Property
\n" ); document.write( "a • 1 = a
\n" ); document.write( "4 • 1 = 4
\n" ); document.write( "\"the value that returns the input unchanged\"
\n" ); document.write( "8.
\n" ); document.write( "Additive Inverse Property
\n" ); document.write( "a + (-a) = 0
\n" ); document.write( "4 + (-4) = 0
\n" ); document.write( "\"the value that brings you back to the identity element under addition\"
\n" ); document.write( "9.
\n" ); document.write( "Multiplicative Inverse Property
\n" ); document.write( "chart math m1
\n" ); document.write( "chartm2
\n" ); document.write( "\"the value that brings you back to the identity element under multiplication\"
\n" ); document.write( "10.
\n" ); document.write( "Zero Property of Multiplication
\n" ); document.write( "a • 0 = 0
\n" ); document.write( "4 • 0 = 0
\n" ); document.write( "\"zero times any value is 0\"
\n" ); document.write( "11.
\n" ); document.write( "Closure Property of Addition
\n" ); document.write( "a + b is a real number
\n" ); document.write( "10 + 5 = 15 (a real number)
\n" ); document.write( "\"the sum of any two real numbers
\n" ); document.write( "is another real number\"
\n" ); document.write( "12.
\n" ); document.write( "Closure Property of Multiplication
\n" ); document.write( "a • b is a real number
\n" ); document.write( "10 • 5 = 50 (a real number)
\n" ); document.write( "\"the product of any two real numbers is another real number\"
\n" ); document.write( "13.
\n" ); document.write( "Addition Property of Equality
\n" ); document.write( "If a = b, then a + c = b + c.
\n" ); document.write( "If x = 10,
\n" ); document.write( "then x + 3 = 10 + 3
\n" ); document.write( "\"adding the same value to both sides of an equation will not change the truth value of the equation.\"
\n" ); document.write( "14.
\n" ); document.write( "Subtraction Property of Equality
\n" ); document.write( "If a = b, then a - c = b - c.
\n" ); document.write( "If x = 10,
\n" ); document.write( "then x - 3 = 10 - 3
\n" ); document.write( "\"subtracting the same value from both sides of an equation will not change the truth value of the equation.\"
\n" ); document.write( "15.
\n" ); document.write( "Multiplication Property of Equality
\n" ); document.write( "If a = b, then a • c = b • c.
\n" ); document.write( "If x = 10,
\n" ); document.write( "then x • 3 = 10 • 3
\n" ); document.write( "\"multiplying both sides of an equation by the same value will not change the truth value of the equation.\"
\n" ); document.write( "16.
\n" ); document.write( "Division Property of Equality
\n" ); document.write( "If a = b, then a / c = b / c, assuming c ≠ 0.
\n" ); document.write( "If x = 10,
\n" ); document.write( "then x / 3 = 10 / 3
\n" ); document.write( "\"dividing both sides of an equation by the same non-zero value will not change truth value of the equation.\"
\n" ); document.write( "17.
\n" ); document.write( "Substitution Property
\n" ); document.write( "If a = b, then a may be substituted for b, or conversely.
\n" ); document.write( "If x = 5, and x + y = z,
\n" ); document.write( "then 5 + y = z.
\n" ); document.write( "\"a value may be substituted for its equal.\"
\n" ); document.write( "18.
\n" ); document.write( "Reflexive (or Identity) Property of Equality
\n" ); document.write( "a = a
\n" ); document.write( "12 = 12
\n" ); document.write( "\"a real number is always
\n" ); document.write( "equal to itself\"
\n" ); document.write( "19.
\n" ); document.write( "Symmetric Property of Equality
\n" ); document.write( "If a = b, then b = a.
\n" ); document.write( "symmetry
\n" ); document.write( "\"quantities that are equal can be read forward or backward\"
\n" ); document.write( "20.
\n" ); document.write( "Transitive Property of Equality
\n" ); document.write( "If a = b and b = c,
\n" ); document.write( "then a = c.
\n" ); document.write( "If 2a = 10 and 10 = 4b,
\n" ); document.write( "then 2a = 4b.
\n" ); document.write( "\"if two numbers are equal to the same number, then the two numbers are equal to each other\"
\n" ); document.write( "21.
\n" ); document.write( "Law of Trichotomy
\n" ); document.write( "Exactly ONE of the following holds: a < b, a = b, a > b
\n" ); document.write( "If 8 > 6, then 8 not equal sign 6 and
\n" ); document.write( "8 is not < 6.
\n" ); document.write( "\"for two real numbers a and b, a is either equal to b, greater than b, or less than b.\" (common sense) \n" ); document.write( "