Variables and Expressions & Order of Operations

1. 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

2. Variables and Expressions

3. Vocabulary • 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.

4. Example 1: Write Algebraic Expressions Write an algebraic expression for each verbal expression. • 8 more than a number n • The difference of 7 and 4 times a number x • One-third of the original size of the area a

5. Vocabulary • 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.

7. Example 2: Write Algebraic Expressions with Powers Write each expression algebraically. • The product of 7 and m to the 7th power. • The difference of 4 and x squared.

8. Example 3: Evaluate Powers To evaluatean expression means to find its value. Evaluate each expression: a. b.

9. Example 4: Write Verbal Expressions Write a verbal expression for each algebraic expression.

10. Check for Understanding • Explain the difference between an algebraic expression and a verbal expression. • Write an expression that represents the perimeter of the rectangle. • Give an example of a variable to the fifth power. l w

11. Application 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.

12. Order of Operations

13. Evaluate Rational Expressions • 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.

14. Order of Operations • 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

15. Example 1: Evaluate Expressions Evaluate each expression.

16. Example 1: Evaluate Expressions Evaluate each expression.

17. Example 2: Grouping Symbols Evaluate each expression.

18. Example 2: Grouping Symbols Evaluate each expression.

19. Example 3: Fraction Bar • A fraction bar is another type of grouping symbol. • It indicates that the numerator and denominator should be treated as a single value. Evaluate

20. Evaluate Algebraic Expressions • 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.

21. Example 4: Evaluate an Algebraic Expression Evaluate if a = 7, b = 3, and c = 5.

22. Example 5: Use Algebraic Expressions 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. • Write an expression that represents the volume of a pyramid.

23. Example 5: Use Algebraic Expressions • Find the volume of the pyramid arena.

24. Check for Understanding • Describe how to evaluate • Write an expression involving division where the first step in evaluating the expression is addition.

25. Check for Understanding • Find the Error Laurie and Chase are evaluating Laurie Chase = = = = = = = 255 = 507 Who is correct? Explain your reasoning.