Presentation on theme: "1.4 PROPERTIES OF REAL NUMBERS I CAN IDENTIFY AND USE PROPERTIES OF REAL NUMBERS."— Presentation transcript:
1.4 PROPERTIES OF REAL NUMBERS I CAN IDENTIFY AND USE PROPERTIES OF REAL NUMBERS.
PROPERTIES OF REAL NUMBERS Relationships that are always true for real numbers are called properties. Rules used to rewrite and compare expressions
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.
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
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)
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
ZERO PROPERTY OF MULTIPLICATION What is the product of zero and any real number???? ZERO! That is… a0 = 0
MULTIPLICATION PROPERTY OF -1 The product of -1 and a is -a -1a = -a
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
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