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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. Vocabulary. - PowerPoint PPT Presentation
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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