Variables and Expressions & Order of Operations

Variables and Expressions &

Order of Operations

Objectives: ~ Write verbal expressions for algebraic

expressions and vice versa~Evaluate numerical and algebraic expressions

by using Order of Operations

Variables and Expressions

In algebra, variables are symbols used to

represent unspecified numbers or values. A letter may be used as a variable.

An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations.

In each expression, the quantities being multiplied are called factors, and the result is called the product.

Vocabulary

Write an algebraic expression for each verbal expression.a. 8 more than a number n

b. The difference of 7 and 4 times a number x

c. One-third of the original size of the area a

Example 1: Write Algebraic

Expressions

An expression like is called a power and is

read “x to the nth power”. The variable x is called the base, and n is

called the exponent. The exponent indicates the number of times

the base is used as a factor.

Vocabulary

Symbols Words Meaning

3 to the first power 3

3 to the second power or 3 squared 3 3

3 to the third power or 3 cubed 3 3 3

3 to the fourth power 3 3 3 3

2 times b to the 6th power 2 b b b b b b

x to the nth power x x x … xn factors

Write each expression algebraically.a. The product of 7 and m to the 7th power.

b. The difference of 4 and x squared.

Example 2: Write Algebraic Expressions

with Powers

To evaluate an expression means to find its value.

Evaluate each expression:a. b.

Example 3: Evaluate Powers

Write a verbal expression for each algebraic expression.

Example 4: Write Verbal Expressions

1. Explain the difference between an algebraic

expression and a verbal expression.2. Write an expression that represents the

perimeter of the rectangle.

3. Give an example of a variable to the fifth power.

Check for Understanding

l

w

Lorenzo bought several pounds of chocolate covered peanuts and gave the cashier a $20 bill. Write the expression for the amount of change he will receive if p represents the cost of the peanuts.

Application

Order of Operations

Numerical expressions often contain more

than one operation. A rule is needed to let you know which

operation to perform first. This rule is called the order of operations.

Evaluate Rational Expressions

Evaluate inside grouping symbols

Evaluate all powers

Do all multiplications and/or divisions from left to right

Do all additions and/or subtractions from left to right

Order of Operations

Evaluate each expression.

Example 1: Evaluate Expressions

Evaluate each expression.

Example 1: Evaluate Expressions

Evaluate each expression.

Example 2: Grouping Symbols

Evaluate each expression.

Example 2: Grouping Symbols

A fraction bar is another type of grouping

symbol. It indicates that the numerator and

denominator should be treated as a single value.

Evaluate

Example 3: Fraction Bar

Like numerical expressions, algebraic

expressions often contain more than one operation.

Algebraic expressions can be evaluated when the values of the variables are known.

First, replace the variables with their values. Then, find the value of the numerical

expression using the order of operation.

Evaluate Algebraic Expressions

Evaluate if a = 7, b = 3, and c = 5.

Example 4: Evaluate an Algebraic Expression

The Pyramid Arena in Memphis, Tennessee, is the third largest pyramid in the world. The area of its base is 360,000 square feet and it is 321 feet high. The volume of any pyramid is one third of the product of the area of the base B and its height h.

a. Write an expression that represents the volume of a pyramid.

Example 5: Use Algebraic Expressions

b. Find the volume of the pyramid arena.

Example 5: Use Algebraic Expressions

1. Describe how to evaluate

2. Write an expression involving division where the first step in evaluating the expression is addition.

Check for Understanding

3. Find the Error Laurie and Chase are

evaluating

Laurie Chase = = = = = = = 255 = 507

Who is correct? Explain your reasoning.

Check for Understanding