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

2. Writing mathematical sentences
Equality-

3. 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.

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

5. Insert <, >, or =
12/
2/ /3
2/ /3

6. 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

7. 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

8. 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

9. 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

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

11. Commutative Property-

12. 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

13. Associative Property-

14. 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)

15. Distributive Property-

16. 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

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

18. 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.

19. 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

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

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