1. Algebra
Notes

2. Order of Operations Parentheses Exponents Multiplication Division
Addition
Subtraction

3. Variable
Using arithmetic you might write something ___ = 45. You need a placeholder for this space.
A placeholder in algebra is called a variable because the value can change

4. Algebraic Expression
An Algebraic Expression is a combination of variables, number and at least one operation

5. Properties
Distributive Property: is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
Associative Properties: The way in which factors and addends are grouped does not change the sum or product.
Identity Properties: The sum or product of an addend or factor and zero is zero
Cumulative Properties: The order in which numbers are multiplies does not change the product.

6. Inverse Operations
Using the opposite operation listed in the problem to undo the operation and find the solution.
In Algebra this is also used to cancel out like terms

7. Use an Equation
Mizzou beat Illinois in Football this weekend buy 10 points, Mizzou scored 23 points. 36 total points were scored by both teams combined. Write an equation for how many points Illinois scored.
23 + Y = 36
Y = 13
Can you think of your own equation?

8. Inequalities
< and > are signs for inequalities. Inequalities are things that are not equal.

9. Integers and Absolute Value
Absolute Value is the distance a number is from zero
A coordinate is a point on the number line
Integers can be written …-2, , 2, …
… means continues without end

10. Adding Integers
To add integers with different signs, subtract their absolute values. Give the results the same sign as the integers with the greater absolute value.

11. Subtracting Integers
Opposites: Positive Integer paired with a negative Integer
Additive Inverse: A number and it’s opposite are called additive inverses of each other
Question: What do you notice about the sum of a number and it’s additive inverse?

12. Additive Inverse Continued…
Additive Inverse can be used to define subtraction for integers
Compare the following addition and subtraction sentences.
Subtraction Addition
8-3= (-3)=5

13. Sample Problems 6-11 is the same as 6+(-11) 6+(-11) =
-4-(-7)=
7-4 is the same as 7+(-4)
7+(-4)=
-8-19 is the same as -8+(-19)
-8+(-19)=
5-(-8) is the same as Double negatives = +
5+8=
116-(-12)=

14. Multiplying Integers
The product of two integers with different signs is negative
X=-3(29)
X=-87
Y=(-6)(-25)
Y=150 If the signs are the same, the product is positive

15. Solve
X=3(-7)
Y=(-9)(18)
X=-9(-5)
5X= if X=-2
(10)(-17)(5)=

16. Multiply you will not be able to solve for the variable
Multiply you will not be able to solve for the variable. Discuss your answers as a class.
-4b
8(-x)
6(-9a)
2ab(6)(-2)
(-5y)(-6)
5x(-4)(-2)
|-3| + |-4| =

17. Dividing Integers
Dividing Integers with Different Signs: The answer (or quotient) of two integers with different signs is negative = -
The quotient of two positive numbers is positive = +
The quotient of two negative integers is positive = +

18. Perimeter
The distance around a figure is called Perimeter. Add the measure of the sides = perimeter
P = perimeter
L= length
W= width
P= L+W+L+W
60in
27in

19. Area The measure of the surface enclosed
by a geometric figure is called the area
Area= Length X Width
60 in
27in

20. Solving Inequalities: Adding or Subtracting
An inequality is a mathematical sentence with < or >.
The sentences 99>82 and 124>107 are inequalities.

21. Solving Inequalities: Adding or Subtracting
Adding the same number to each side of an inequality does not change the truth or message the inequality is saying.
Example: 99 > 82 add 25 to each side
Therefore: >
Answer: > 107

22. Solving Inequalities: Adding or Subtracting
In Words: Adding or subtracting the same number from each side of an inequality does not change the truth of the inequality.
In Symbols: If a > b
In Symbols a + c > b + c
In Symbols a - c > b – c

23. Solving Inequalities: Adding or Subtracting
Solve a + 8 > 3
a - 8 > 3 – 8
a = - 5
Check: Try -4 a number greater than -5
> 3
= 4
4 > 3
The solution is a ≥ -5, all numbers greater than
-5 are possible answers.
Inequalities will have multiple possible answers

24. Solving Inequalities: Adding or Subtracting
Examples
Y-7< 10
Y < 17
Because 10+7 = 17
-42 + k > 18
K > 60
K> 60

25. Solving Inequalities: Multiplying or Dividing
Consider multiplying or dividing each side of the inequality 4<6 by a positive integer
The Inequalities 8<12 and 2<3 are true.
These and other examples suggest the following property.

26. Solving Inequalities: Multiplying or Dividing
In Words: When you multiply or divide each side of a true inequality by a positive integer, the result remains true.
In Symbols: For all integers you can think of for a, b, c: if c > 0
If A > B, then ac > bc or a/c > b/c
Example: 4<6
4x2 < 6x2
8 < 12

27. Solving Inequalities: Multiplying or Dividing
2<4
4/2 < 6/2
2 < 3
Consider Multiplying or dividing each side of 2<4 by a negative integer
2 < 4
2 x -1 < 4 x -1
-2 < -4 FALSE
The inequalities -2 < -4 is false. However, it would be true if you reverse the symbol.
-2 >-4

28. Solving Inequalities: Multiplying and Dividing
In Words: When you multiply or divide each side of an inequality by a negative integer, you must reverse the order symbol
In Symbols: For all integers, a,b,c, where c<0
if a > b then ac < bc
a/c < b/c
Example Problems:
-3y > -39
Y> 13 because -3 x 13 = -39 so the number has to be bigger than 13

29. Using Equations and Inequalities
Believe it or not, you will use math after you graduate high school. However finding the math problems in everyday life can be tricky. We are going to learn word problems together.
Ex: Pedro rides his 10-speed bike for exercise. The last time he rode his bike he had trouble changing gears. Pedro took his bike to Lewis Bike Shop to have it repaired. At the shop, Pedro was told that the total bill for labor and parts would be at least $48. The cost of the parts was $33.
Question: How much could Pedro expect to pay for labor

30. Using Equations and Inequalities
Read the problem and find the main idea.
You need to find out the labor cost.
Let L= labor
Next, look at the information in the problem
The total was at least $48
The parts cost $33
L= labor
$33 + L ≥ $48
L ≥ 15

31. Factors
Factors: The factors of a whole number divide that number with a remainder of 0.
6 is a factor or 78 because 78/6=13 a whole number
You can say that 78 is divisible by six.
78/5=15.6 this is not a factor because it is not a whole number

32. Monomial
Monomial: an integer, a variable, or a product (remember product means multiply) of integers or variables
Example: 2(L+W) this is not a monomial because it has addition
Example: -12abc This expression is a monomial because of integers and variables

33. Factor Facts A number is divisible by:
2 if the ones digit is divisible by 2
3 if the sum of its digits is divisible by 3
5 if the ones digit is 0 or 5
6 if the number is divisible by 2 or 3
10 if the ones digit is 0
Practice a few as a class

34. Monomial Facts Examples: y, 15, ab, 4mk,
2X+3 and m-6 are different from monomials because they have two items

35. Powers and Exponents
An Exponent tells how many times a number (a base) is used as a factor
The smaller written number is the exponent
Numbers that are expressed using exponents are called powers.