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

• 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

WRITING EQUIVALENT EXPRESSIONS

• Try using properties of real numbers to write an equivalent expression for the following:• 5(3n)• (3+5b)+7

ASSIGNMENT

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