1. Algebra
Part 4
Of Math Survival Guide

2. Basic Algebra Vocabulary
Variable
A letter that represents a number; something that changes
Expression
A collection of variables, numbers and symbols
( +, -, *, ÷)

3. Translating Verbal Phrases
Translating Expressions
Words to numbers and numbers to words

4. Writing Expressions
The following common words and phrases indicate, addition, subtraction, multiplication, and division.
Addition
Subtraction
Multiplication
Division
Plus
The sum of
Increased by
Total
More than
Added to
Minus
The difference of
Decreased by
Fewer than
Less than
Subtracted From
Times
The product of
Multiplied by Of
Each
Divided by
The quotient of
Per

5. Translating Verbal Models
What is a verbal model?
1st answer this question…
What does the word verbal mean?
2nd …
What is a model of something?

6. Let’s look at a verbal models in math…
The sum of 5 and 4
The difference of 10 and 8
The product of -3 and 9
The quotient of -25 and -5

7. Your turn! Verbal models The sum of 8 and a number
The difference of 24 and a number
The product of 5 and a number
The quotient of 5 and a number
2/3 of a number
Verbal models

8. Check your work! Variable Expressions The sum of 8 and a number 8 + n
The difference of 24 and a number 24 - n
The product of 5 and a number 5n
The quotient of 5 and a number 5/n
2/3 of a number 2/3n
Variable Expressions

9. Evaluating Expressions
Substituting a variable with the number it represents (Plug it in, plug it in)

10. Evaluating Expressions
Evaluate the expression when x=6 and y=3.
4x + 7y = _____________
4 ( ) + 7 ( )
4(6) + 7 (3) 45

11. Adding and Subtracting Linear Expressions
Simplifying Expressions – Combining Like Terms

12. Like Terms Like terms are terms that are exactly alike
You can add or subtract terms with the exact same variables
You can add and subtract constants
EX: 3x + 2xy + 4x – 5xy

13. Properties Associative – you “associate” with your group of friends
Think of parentheses as groups of numbers
This property relates to how numbers are grouped
EX: (3+2) + 4 = 3 + (2 + 4)

14. Properties Distributive – a teacher distributes a test to the class
He/she hands out the test to each student
You must pass the number outside the parentheses to the numbers on the inside
You MULITIPLY the numbers when they are distributed
EX: -5(3x + 2)

15. Properties Commutative – we commute back and forth to school
This property is related to the order in which numbers are placed
Think of the word COP – Commutative (Order) Property
EX: =

16. One-Step Equations
You only need to complete ONE STEP to solve the equation!
Wait a minute! Yesterday you said x equals 2!
X + 2 = 5
X = 3

17. One-Step Equation Check-list
Always start on the side with the VARIABLE
Identify the Inverse Operation
Inverse of adding =
Inverse of subtraction =
Inverse of multiplying =
Inverse of dividing =
Balance the equation
Solve
Check your answer!
I-B-S
Remember

18. Two-Step
Equations

19. Two-Step Equations Always start on the side with the VARIABLE
Identify the Inverse Operation of the number without a variable next to it (# farthest away from the variable)
Balance the equation (Do the SAME thing to both sides)
Solve
Identify the Inverse Operation of the number near the variable
Balance the equation (do the SAME thing to both sides)
Check your answer!

20. You are the variable and you want to be ALONE!
Examples
Get RID of your friends and then your family!
1. 2x - 5 = 13
2. (x/2) + 3 = 5 3.

21. Problem Solving with Equations
Determine what is being asked
Define your variables
Develop the equation you are going to use to solve the problem
Solve and interpret your answer
Make sure you are able to explain how you came to your answer

22. Example 1 – Using a Variable Expression
You are taking a bike trip. After riding 8 miles, you change your speed to 12 miles per hour. What is the total distance you travel if you stay at this speed for 2 hours? For 3 hours?

23. original distance + speed X time
Solution to Example 1
Let the variable t represent the time that your ride the bike at 12 miles per hour. So, the total distance your travel is
original distance + speed X time t

24. Solution to Example 1 = = 8 + 12 (2) 32 44 8 + 12 (3)
Step 1: Write the hours traveled, t.
Step 2: Substitute for t in the expression t
Step 3: Evaluate to find the total distance.
(2) 32 = 44
8 + 12
(3) =

25. Now it’s your turn… use the formula 8+12(t)
If you travel for 4 hours, what is the total distance?
If you travel for 1.5 hours, what is the total distance?

26. Try this!
The cost at a store for a package of pens is $3 and for a three-ring binder is $4.
Write a variable expression for the cost of buying p packages of pens and b binders.
How much would 3 packages of pens and 8 binders cost?

27. Try this!
A triathlon event consists of 2.4 miles of swimming, 112 miles of biking, and 26.2 miles of running.
Write a variable expression to find the number of miles a person travels in n triathlons
How far does a person travel in completing 4 triathlons?

28. Relationships between two variables
Plot points on a coordinate plane (x, y)
If x is positive, move to the right
If x is negative, move to the left
If y is positive, move up
If x is negative, move down

29. Relationships between two variables
Understand graphs, tables, and formulas
How to use a table of values and then graph the x and y’s x 1 2 3 y 6 9
EQUATION:
_________________

30. Relationships between two variables
How does a change in one variable affect the other
EXAMPLE:
In the Bike Tour, the more customers we had, the more $$ we made
The more hours you study, the better grades you will make

31. Relationships between two variables
Direct and inverse relationships (graphs)
Direct ( y = kx) → Multiplication
Indirect (y = k/x) → Division n m