1. Chapter 1
The Tools of Algebra

2. 1-2 Expressions & Word Problems
A company rents a house boat for $200 plus and extra $30 per day. Write an expression that can be used to find the total cost to rent a house boat. Words: two hundred dollar rental fee plus thirty dollars per day Variable: let d represent the number of days Expression: d

3. Suppose…
Suppose the Gregoran family wants to rent a house boat for six days. What will be the total cost? Expression: d d = (30) = or 380 The total cost will be $380

4. SALES
At a garage sale, Georgia found some used DVDs and CDs that she wanted to buy. Each DVD was marked at $5 and each CD was marked at $3. Write an expression to find the total cost to buy some DVDs and CDs. Words: Variable: Expression:

5. Suppose…
Suppose she wanted to buy 4 DVDs and 7 CDs. Expression: 5d + 3c The total cost will be $

6. EXIT SLIP!
A studio charges a sitting fee of $25 plus $7 for each portrait sheet ordered. Write an expression that can be used to find the total cost to have photographs taken. Then find the cost of purchasing twelve portrait sheets.

7. 1-3 Properties
When you make a peanut butter and jelly sandwich, do you spread the peanut butter first or the jelly? The order does not matter because in the end you have a tasty sandwich.
Name two other activities where order does not matter.
Name two activities where order does matter.
Name a mathematical operation in which you can switch the numbers and still have the same value.

8. Properties of Addition and Multiplication
Properties- statements that are true for any numbers
Example: and have the same value. This illustrates the Commutative Property of Addition.

9. Commutative Properties
Definition: Commutative Property- the order in which numbers are added or multiplied does not change the sum
Symbols:
For any numbers a and b, a + b = b + a
For any numbers a and b, a x b = b x a
Examples:
6 + 9 = x 7 = 7 x 4

10. Associative Properties
Definition: Associative Property- the order in which numbers are grouped when they are added or multiplied does not change the sum or product.
Symbols:
For any numbers a, b, and c, (a + b) + c = a + (b + c)
For any numbers a, b, and c, (a x b) x c = a x (b x c)
Examples:
(3+6) + 1 = 3 + (6 +1) (5 x 9) x 2 = 5 x (9 x 2)

11. Additive Identity
Definition: Additive Identity- when 0 is added to any number, the sum is the number
Symbols:
For any numbers a, a + 0 = 0 + a = a
Examples:
5 + 0 = 5
0 + 5 = 5

12. Multiplicative Identity
Definition: Multiplicative Identity- when any number is multiplied by 1, the product is the number.
Symbols:
For any numbers a,, a x 1 = 1 x a = a
Examples:
8 x 1 = 8
1 x 8 = 8

13. Multiplicative Property of Zero
Definition: Multiplicative Property of Zero- when any number is multiplied by 0, the product is 0.
Symbols:
For any number a, a x 0 = 0 x a = 0
Examples:
3 x 0 = 0
0 x 3 = 0

14. Identify Properties 4 + (a + 3) = (a + 3) + 4
The order of the numbers and variables changed. This is the Commutative Property of Addition.
1 x (3c) = 3c
The expression was multiplied by 1 and remained the same. This is the Multiplicative Identity Property.

15. Let’s Practice d + 0 = d 8 x 1 = 8 5 x 7 x 2 = 7 x 2 x 5
14 + (9 + 10) = (14 + 9) + 10
8 x 1 = 8 5 x 7 x 2 = 7 x 2 x 5

16. Do these properties apply to subtraction or division?
One way to find out is to look for a counterexample.
Counterexample- an example that shows a conjecture is not true

17. Find a Counterexample
Is division of whole numbers associative? If not, give a counterexample. The Associative Property of Multiplication states (a x b) x c = a x (b x c). Check: (a ÷ b) ÷ c = a ÷ (b ÷ c).

18. Check: (a ÷ b) ÷ c = a ÷ (b ÷ c).
Pick values for a, b, and c.
a= b= c=3
(27 ÷ 9) ÷ 3 = 27 ÷ (9 ÷ 3)
Simplify.
(3) ÷ 3 = 27 ÷ (3)
1 = 9?

19. Your turn!
Is subtraction of decimals associative? If not, give a counterexample. Hint: (a + b) + c = a + (b + c)

20. Simplify Algebraic Expressions
(3 + e) + 7 = (e + 3) +7
= e + (3+ 7)
= e + 10
8 ● (x ● 5)
8 ● (x ● 5) = 8 ● (5 ● x)
= (8 ● 5) ● x
= 40x

21. Your turn!
12 ● (10 ● z) = 10 + (p + 18) =