Algebra Part 4 Of Math Survival Guide

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

Translating Verbal Phrases Translating Expressions 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

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?

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! 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

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

Evaluating Expressions 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. 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

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)

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)

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: 4 + 2 + 12 = 12 + 4 +2

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

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

Two-Step Equations

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!

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.

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

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?

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 8 + 12t

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 8 + 12t Step 3: Evaluate to find the total distance. 8 + 12 (2) 32 = 44 8 + 12 (3) =

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?

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?

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?

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

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: _________________

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

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