Chapter 1 Overall Review of Chapter 1

1.1 Expressions and Formulas

Students Will Be Able To:• Use Order of Operations to Evaluate Expressions• Use Formulas

Review: Order of Operations

The Order of Operations is a rule used to clarify which procedures should be performed first in a given mathematical expression.

Remember there are 4 Steps of Order of Operations.

Order of Operations

• Grouping Symbols can be used to clarify the order of operations.

• When calculating the value of an expression start with the innermost set of grouping symbols.

Ex 1a: Simplify an Expression

Ex 1b: Simplify an Expression

Try this! Order of Op!

Find the value of:

3

Use Your Calculator!

1. Simplify :

2. Describe the Procedure the calculator used to get the answer.

3. Where should parenthesis be placed so that the expression has each of the following values?

a) -10

b) 29

c) -5

Use Your Calculator Again!

1. Evaluate:

2. Describe the Procedure the calculator used to get the answer.

3. If you removed the parenthesis, would the solution remain the same? Why or Why not?

Ex 2: Fraction Bar!

• A fraction bar can act as a grouping symbol.

Try this! Fraction Bar!

• Simplify:

Remember: Terminology

• Variable: A letter that represents a number or a set of numbers.

• Algebraic expression: one or more algebraic terms in a phrase that may include variables, constants, and operating symbols (+, -, x, and ÷). It does NOT have an equal sign.

• Algebraic Equation: Includes variables, operations, and an equal sign.

Don’t Forget!

Expressions are simplified (or evaluated)

Equations are solved. You cannot solve something that doesn’t have an equal sign.

Ex 3: Evaluate an Expression

• Evaluate the expression if s = 2 and t = -3

You Try!.

Evaluate the expression for x=5, y=-2, and z=-1

-9

1-2 Properties of Real Numbers

Objectives: students will be able 1) to classify real numbers and 2) use the properties of real numbers to

evaluate expressions

What are Real Numbers?

• Real Numbers are all the numbers we use in everyday life.

• Every Real Number will correspond to exactly one point somewhere on a Number Line.

• Real Numbers can be Rational or Irrational

Rational Numbers

• Includes all integers, as well as all terminating or repeating decimals• Examples of rational numbers:

Special Rational Numbers

Rational numbers can be broken down to other sub-sets.

• Integers: {…-2, -1, 0, 1, 2, …}

• Whole numbers: {0, 1, 2, …}

• Natural numbers: {1, 2, 3, …}

Irrational Numbers

• Irrational numbers: nonterminating, nonrepeating decimals• Examples of irrational numbers:

The Real Number Diagram

Example 1: Name The Sets!

Name the sets of numbers to which each number belongs.

Properties of Real Numbers

Example 2: Simplify each expression.

1-3 Solving Equations

Objectives: students will be able to 1) translate verbal expressions into algebraic expressions and equations,

and vice versa and 2) solve equations using the properties of equality

Write an Algebraic Expression

Write an algebraic expression to represent each verbal expression.

a) 7 less than a number

b) Three times the square of a number

c) The cube of a number increased by 4 times the same number

d) Twice the sum of a number and 5

Writing Verbal Sentence

Example 2: Write a verbal sentence to represent each equation.

The difference of a number and 8 is -9.

A number divided by 6 is equal to the number squared.

Ex 3: Solve each equation.

Solve each equation.

Ex 4: Solving Formulas

1-5 Solving Inequalities

Objective: students will be able to solve inequalities

Solving Inequalities v. Solving Equations

What is the difference between solving an equation and solving an inequality?

• When multiplying or dividing BOTH sides of an inequality by a negative number, the inequality sign must be reversed.

Remember Graphing Inequalities?

• When graphing inequalities on a number line:

• When an inequality is solved, if the variable is on the left the inequality symbol will tell you which way to shade.• For example, x < 5 will result in an open circle on 5 and then

will be shaded to the left (since the arrow is pointing left). This only works when the variable is on the left hand side.

Different Notations

• There are two different types of notation you may be asked to use when writing your solution: set-builder notation or interval notation.

• Set-builder notation

This is read as “the set of all numbers x such that x is less than 5”

Set Builder Notations

The Set Builder Notation for x < 5 is

This is read as “the set of all numbers x such that x is less than 5”

Interval Notation

The left number indicates the left bound of the graph, while the right number indicates the right bound.

Parenthesis In Interval Notation

• Parenthesis are used to indicate • 1) a graph is unbounded in a certain direction• 2) a graph cannot equal a number, meaning that the graph contains an open circle

Brackets In Interval Notation

• Brackets are used to indicate closed circles.

Let’s practice interval notation.• Write each solution using interval notation.

Ex 1: Solve and Graph

Example 1: Solve and graph each inequality. Write solutions in Interval Notation.

Try These…

• Solve and Write your Solution in Interval Notation