1. WARM UP Simplify 1. –5 – 7 2. 7 + (– 4) −12 3. –6  7 3 (−5)(−4)
1. –5 – 7
(– 4)
3. –6  7
(−5)(−4)
−3/7  ⅘
−⅘ ÷ 11/3
−12 3
−42 20
−12/35
−12/55

2. ALGEBRAIC EXPRESSIONS & PROPERTIES OF NUMBERS

3. OBJECTIVES Evaluate algebraic expressions Write equivalent expressions
Solve problems algebraically

4. KEY TERMS & CONCEPTS Additive identity Evaluating
Algebraic expressions
Associative Properties
Commutative Properties
Constant
Equivalent expressions
Evaluating
Multiplicative identity
Substitute a number
Value
variables

5. ALGEBRAIC EXPRESSIONS
In algebra we use letters to represent numbers.
For example, in the formula for the area of a circle:
A stands for the area and r stands for the radius.
A and r can represent various numbers, so they are called variables
The symbol can represent only one number ( ), so it is called constant.

6. ALGEBRAIC EXPRESSIONS
Algebraic expressions consist of numerals, variables and other mathematical symbols such as + or √.
Some examples of algebraic expressions:
x + 5
|y – 8|
When we substitute numbers for the variables in an expression and then calculate the number, we get the value of the expression for those replacements
We say that we are evaluating the expression.

7. EXPRESSING ALGEBRAIC EXPRESSIONS
Meaning
Operation
5(n)  n n
5 times n
Multiplication
14 ÷ y
14 divided by y
Division
6 + c
6 plus c
Addition
8 – x
8 minus x
Subtraction

8. EXAMPLES a. 12  n = 13  3 substitute 3 for n
Evaluate the expression when n = 3
a. 12  n = 13  substitute 3 for n
= multiply
b = = substitute 3 for n
divide
c . n – 1 = 3 – 1 = substitute 3 for n
subtract
d. n + 8 = = substitute 3 for n
add

9. EXAMPLES 1. Evaluate 2y + x for x = 3 and y = 5 2y + x = 2  5 + 3
Substituting 3 for x and 5 for y =
Calculating
= 13
The value of the expression is 13.
2. Evaluate –(-x) for x = -7
-(-x) = -(-(-7))
Substituting -7 for x
= -(7)
Calculating within the parenthesis PEMDAS
= -7
The value of the expression is -7.

10. MORE EXAMPLES
1. Evaluate |x| + 2|y| for x = 15 and y = -10 |x| + 2|y| = |15|+ 2|-10|
Substituting 15 for x and -10 for y
=  10
Finding absolute value =
= 35
The value of the expression is 35.

11. TRY THIS… Evaluate each expression 5x – y for x = 10 and y = 5
-(-y) for y = -8
|x| - 2|y| for x = -16 and y = -4

12. APPLY ORDER OF OPERATIONS
Mathematicians have created an order of operations to evaluate an expression involving more than one operation
PEMDAS
Parenthesis
Exponents
Multiply/divide
Add/subtract

13. ORDER OF OPERATIONS STEPS
Step 1 – Evaluate expressions inside grouping symbols: Parenthesis
Step 2 – Evaluate powers: Exponents
Step 3 – Multiply and Divide from left to right
Step 4 – Add and Subtract from left to right
PEMDAS
Parenthesis – exponents – multiplication/division – addition/subtraction
“Please excuse my dear aunt sally”

14. EXAMPLES Evaluate the expression 27 ÷ 3 2 - 3
Step 1 There are no grouping symbols (parenthesis), so go to step 2
Step 2 Evaluate powers – 27 ÷  2 – 3 = 27 ÷ 9 
(Exponents)
Step 3 Multiply and divide from left to right ÷ 9  2 – 3 = 3  2 - 3
Step 4 Add and subtract from left to right  = 6 – 3 = 3
The value of this expression is 3

15. TRY THIS…
Evaluate using PEMDAS when x = 9 and y = -4 4

16. EQUIVALENT EXPRESSIONS
The subtraction theorem tells us that the expressions m – n and m + (-m) will always have the same value whenever we make the same substitutions in both expressions.
Equivalent expressions always have the same value for all acceptable replacements (substitutions).

17. EXAMPLES
1. Use the subtraction theorem to write equivalent expressions. 4y – x = 4y + (-x)
Adding an inverse
3p + 5q = 3p – (-5q)
Using the subtraction theorem in reverse.

18. TRY THIS… Use the subtraction theorem to write equivalent expressions
-5x – 3y
17m – 45
-6p + 5t
-5x + (-3y)
17m + (-45)
– 6p – (-5t)

19. NUMBER PROPERTIES
Number properties help us identify equivalent expressions.
Commutative Properties tells us that we can change order when adding or multiplying and obtain an expression equivalent to the original one.
Example: a + b = b + a = 3 + 1
a x b = b x a x 1 = 1 x 3
Associative Property tells us that we can change grouping when adding or multiplying and obtain an equivalent expression.
Example: a + (b + c) = (a + b) + c (3 + 2) = (5 + 3) + 2
a × (b × c) = (a × b) × c × (3 × 2) = (5 × 3) × 2

20. EXAMPLES
1. Use the commutative property of addition to write an expression equivalent to 3x + 4y.
3x + 4y = 4y + 3x
Changing order
2. Use the associative property of multiplication to write an expression equivalent to 3x(7y  9z)
3x(7y  9z) = (3x  7y)  9z
Changing grouping

21. MORE EXAMPLES
We use both the commutative & associative properties to write equivalent expressions.
3. Use the commutative and associative properties of addition to write an expression equivalent to
(5/x + 2y) + 3z
5/x + 2y + 3z = 5/x +(2y + 3z)
Using the associative property
= 5/x +(3z + 2y)
Using the commutative property

22. TRY THIS……
Use the associative property of addition to write an expression equivalent to (8m + 5n) + 6p.
Use the commutative property of multiplication to write an expression equivalent to (17x)(-9t).
Use the commutative and associate properties of multiplication to write an expression equivalent to p(4q  16r)

23. NUMBER PROPERTIES a –a = 0
Identity Property: The number “0” is the additive identity and the number “1” is the multiplicative identity.
a –a = 0
Example: Write an expression equivalent to 4x – 2 by adding o. Use 7y – 7y for 0:
4x – 2 = 4x y – 7y adding 0
= 4x + 7y – 2 – 7 y rearranging
The expression 4x – 2 and 4x + 7y – 2 – 7y are equivalent

24. EXAMPLES 1. Write an expression equivalent to x/3y. Use 8/8 for 1
Multiplying by 1
Multiplying numerators and denominators.
The expression x/3y and y are equivalent. They will represent the same number for any acceptable replacements for x and y.

25. TRY THIS……
Write an expression equivalent to 8a – b by adding 0. Use x – x for 0.
Write an expression equivalent to 19t/3x. Use 9/9 for 1.
8a + x – b – x

26. CH. 1.3 HOMEWORK
Textbook pg. 18 #4, 12, 16, 24, 30, 34, 36 & 43