1.4- Properties of Real Numbers and Algebraic Expressions Chapter 1 1.4- Properties of Real Numbers and Algebraic Expressions

Writing mathematical sentences Equality-

Write each sentence using mathematical symbols. a) The product of -4 and x is 20. b) Three times the difference of z and 3 equals 9. c) The sum of x and 5 is the same as 3 less than twice x. d)The sum of y and 2 is 4 more than the quotient of z and 8.

Other symbols: Is not equal to Is less than Is less than or equal to Is greater than Is greater than or equal to

Insert <, >, or = -1 -2 12/4 3 3.5 3.05 2/3 1/3 2/5 1/3

Identities Addition Identity- zero when added to any real number results in the same real number the additive identity is 0. a + 0 = 0 + a = a

Identities Addition Identity- zero when added to any real number results in the same real number the additive identity is 0. a + 0 = 0 + a = a Multiplication identity- one when multiplied to any real number results in the same real number the multiplication identity is 1 a ∙ 1 = 1 ∙ a = a

Inverses Opposite or Additive Inverse- For each number a, there is a unique number –a called the additive inverse or opposite of a such that a + (-a) = (-a) + a = 0

Inverses Opposite or Additive Inverse- For each number a, there is a unique number –a called the additive inverse or opposite of a such that a + (-a) = (-a) + a = 0 Reciprocal or Multiplicative Inverse- For each nonzero, there is a unique number 1/a called the multiplication inverse or reciprocal of a such that. a ∙ 1/a = 1/a ∙ a = 1

Write the additive inverse (opposite) and the multiplication inverse (reciprocal) of each. 2 1/3 -2/5 -7

Commutative Property-

Commutative Property- the order in which two real numbers are added or multiplied does not affect their sum or product. For real numbers a and b, Addition : a + b = b + a Multiplication : a ∙ b = b ∙ a

Associative Property-

Associative Property- regrouping numbers that are added or multiplied does not affect their sum or product. For real numbers a, b, and c Addition: (a + b) + c = a + (b + c) Multiplication: (a∙b) ∙ c = a ∙ (b∙c)

Distributive Property-

Distributive Property- multiplication distributes over addition *You only need to do this if there is a variable. If they are all numbers use PEMDAS.* For real numbers a, b, and c a(b + c) = ab + bc a(b – c) = ab - ac

Use the distributive property to multiply. 3(2x + y -(3x – 1) 7a(b – 2)

Write each as an algebraic expression A vending machine contains x quarters. Write an expression for the value of the quarters. Two numbers have a sum of 20. If one number is x, represent the other number as an expression of x. The older sister is 8 years older than her younger sister. If the age of the younger sister is x, represent the age of the older sister as an expression in x.

Simplify- remove grouping symbols and combine like terms. *It does not mean you will get a solution* Simplify each expression 3xy – 2xy + 5 – 7 + x 7x2 + 3 – 5(x2 -4) ½(4a – 6b) – 1/3(9a + 12b – 1) + 1/4

You Do: Student organizer p. 11-12 #1-8

Classwork/Homework textbook p. 38 #1-12 p. 39-40 #2, 4, 6, 8, 14, 16, 18, 20, 22, 26, 28, 34, 36, 42, 47, 54, 66, 68, 76, 78, 86