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Published byJessie Hart Modified over 4 years ago

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1.4 PROPERTIES OF REAL NUMBERS I CAN IDENTIFY AND USE PROPERTIES OF REAL NUMBERS.

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PROPERTIES OF REAL NUMBERS Relationships that are always true for real numbers are called properties. Rules used to rewrite and compare expressions

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EQUIVALENT EXPRESSIONS Expressions that have the same value for all values of the variables. There are properties which show equivalent expressions which are equivalent for all real numbers.

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COMMUTATIVE PROPERTIES Addition Changing the order of addends does not change the sum a+b = b+a Ex: 12+3 = 3+12 Multiplication Changing order of the factors does not change the product ab = ba Ex: 45 = 54

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ASSOCIATIVE PROPERTIES Addition Changing the grouping of addends does not change the sum (a+b)+c = a+(b+c) Multiplication Changing the grouping of factors does not change the product (ab)c = a(bc)

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IDENTITY PROPERTIES Addition The sum of any real number and 0 is the original number a+0 = a Multiplication The product of any real number and 1 is the original number a1 = a

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ZERO PROPERTY OF MULTIPLICATION What is the product of zero and any real number???? ZERO! That is… a0 = 0

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MULTIPLICATION PROPERTY OF -1 The product of -1 and a is -a -1a = -a

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IDENTIFY THE PROPERTY 310 = 0 Zero property of multiplication 5x+0 = 5x Identity property of addition (x+3)+6 = x+(3+6) Associative property of addition

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PROPERTIES IN USE A movie ticket costs $6.75. A drink costs $1.90. Popcorn costs $2.25. What is the total cost for a ticket, a drink, and popcorn? 6.75 + 1.90 + 2.25 = ? (6.75 + 1.90) + 2.25 = (1.90 + 6.75) + 2.25 = commutative property of addition 1.90 + (6.75 + 2.25) = associative property of addition 1.90 + 9 = simplify inside parentheses $10.90 add

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WRITING EQUIVALENT EXPRESSIONS

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ASSIGNMENT ODDS ONLY P. 26 #7-11, 19, 27-35, 39-47

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