algebra of math survival guide. basic algebra vocabulary a letter that represents a number;...

Algebra

Of Math Survival Guide

Basic Algebra Vocabulary

A letter that represents a number; something that

changes

A collection of variables, numbers and symbols

( +, -, *, ÷)

Translating Verbal Phrases

Words to numbers and numbers to words

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

What is a verbal model?

1st answer this question…What does the word verbal mean?

2nd …What is a model of something?

Translating Verbal Models

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

Your turn!

• 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

Check your work!

• 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

• Substituting a variable with the number it represents (Plug it in, plug it in)

Evaluating Expressions

Evaluate the expression when x=6 and y=3.

1. 4x + 7y = _____________

4 ( ) + 7 ( )

4(6) + 7 (3)

24 + 21

45

Adding and Subtracting Linear Expressions

Simplifying Expressions –

Combining Like Terms

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

• 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)

• 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)

• 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: 4 + 2 + 12 = 12 + 4 +2

One-Step Equations• You only need to complete ONE STEP to

solve the equation!

X + 2 = 5

X = 3

Wait a minute! Yesterday you said x equals 2!

One-Step Equation Check-list

1. Always start on the side with the VARIABLE2. Identify the Inverse Operation

1. Inverse of adding = 2. Inverse of subtraction =3. Inverse of multiplying =4. Inverse of dividing =

3. Balance the equation4. Solve5. Check your answer!

Two-Step Equations1. Always start on the side with the VARIABLE2. Identify the Inverse Operation of the number

without a variable next to it (# farthest away from the variable)

3. Balance the equation (Do the SAME thing to both sides)

4. Solve5. Identify the Inverse Operation of the number near

the variable6. Balance the equation (do the SAME thing to both

sides)7. Solve8. Check your answer!

Examples

1. 2x - 5 = 13

2. (x/2) + 3 = 5

16

5

x3.

You are the variable and you want to be ALONE!

Get RID of your friends and then your family!

• 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

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?

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

Solution to Example 1

Step 1: Write the hours traveled, t.

Step 2: Substitute for t in the expression 8 + 12t

Step 3: Evaluate to find the total distance.

=

=

Now it’s your turn…use the formula 8+12(t)

1. If you travel for 4 hours, what is the total distance?

2. If you travel for 1.5 hours, what is the total distance?

The cost at a store for a package of pens is $3 and for a three-ring binder is $4.

a. Write a variable expression for the cost of buying p packages of pens and b binders.

b. How much would 3 packages of pens and 8 binders cost?

Try this!

Try this!1. A triathlon event consists of 2.4 miles of

swimming, 112 miles of biking, and 26.2 miles of running.

a. Write a variable expression to find the number of miles a person travels in n triathlons

b. How far does a person travel in completing 4 triathlons?

• Plot points on a coordinate plane (x, y)1. If x is positive, move to the right

2. If x is negative, move to the left

3. If y is positive, move up

4. If x is negative, move down

• 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 3 6 9

EQUATION:

_________________

• 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

• Direct and inverse relationships (graphs)– Direct ( y = kx) → Multiplication– Indirect (y = k/x) → Division

m

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