1 4 PROPERTIES OF REAL NUMBERS I CAN

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 • a • b = b • a • Ex: 4 • 5 = 5 • 4

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 • (a • b) • c = a • (b • c)

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 • a • 1 = a

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

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

IDENTIFY THE PROPERTY • 31 • 0 = 0 • Zero property of multiplication • 5 x+0 = 5 x • 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

WRITING EQUIVALENT EXPRESSIONS •

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