1. 1.1 Evaluate Expressions Objective: To be able to evaluate algebraic expressions and use exponents 8-18-15

2. equivalent ANSWER 2, 3 ANSWER Prerequisite Skills VOCABULARY CHECK Copy and complete the statement. 2 3 1. In the fraction, is the numerator and is the denominator. ?? 2. Two fractions that represent the same number are called fractions. ? 100 ANSWER 3. The word percent (%) means “divided by.” ?

3. Prerequisite Skills SKILLS CHECK Perform the indicated operation. 4. + 2 3 3 5 5. – 5 6 3 4 6.6. 3 5 2 5 7.7. 1 2 5 8 ANSWER 1 15 4 ANSWER 1 12 ANSWER 4 5 6 25

4. 9. 23% 8. 4% Prerequisite Skills SKILL CHECK Write the percent as a decimal. ANSWER 0.23 ANSWER 0.015 0.04 ANSWER 10. 1.5% 11. 2.5% ANSWER 0.025

5. Prerequisite Skills SKILL CHECK 12. Find the perimeter and area of the rectangle. 11 in. 4 1 2 ANSWER 31 in., 49 in. 2 1 2

6. A variable is a letter used to represent one or more numbers. Expressions consist of numbers, variables and operations. An algebraic expression, or variable expression, is an expression that includes at least one variable. To evaluate an algebraic expression, substitute a number for each variable, perform the operation(s), and simplify the result, if necessary.

7. Algebraic Expressions Algebraic expression MeaningOperations 5(n) 5n 5●n 5 times nmultiplication 14 divided by y division 6 + c6 plus cAddition

8. Substitute 3 for n. Multiply. = 39 Subtract. = 2 Substitute 3 for n. = 3 Divide. EXAMPLE 1 Evaluate algebraic expressions Evaluate the expression when n = 3. a. 13 n = 13 3 9 3 b. 9 n = c. n – 1 = Substitute 3 for n. Add. = 11 d. n + 8 = 3 – 13 – 1 3 + 8

9. GUIDED PRACTICE for Example 1 = 12 = 6 = 4 Evaluate the expression when y = 2. 1. 6y 2. 8 y 3. y + 4 = 9 4. 11 – y

10. EXAMPLE 2 Evaluate an expression Movies The total cost of seeing a movie at a theater can be represented by the expression a + r where a is the cost (in dollars) of admission and r is the cost (in dollars) of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments. Find the total cost.

11. Add. The total cost is $14.75 ANSWER Substitute 7.50 for a and 7.25 for r. = 14.75 = 7.50 + 7.25 Write expression.Total cost = EXAMPLE 2 Evaluate an expression SOLUTION a + r

12. Expression Using Exponents A power is an expression that represents repeated multiplications of the same factor. For example, 81 is a power of 3 because 81 = (3)(3)(3)(3). A power can be written in a form using two numbers base and an exponent. The exponent represents the number of times the base is used as a factor.

13. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. 27 and 3 3 are equivalent. 7 Exponent Base 2

14. ProductWords Power EXAMPLE 3 Read and write powers Write the power in words and as a product. seven to the first power a. 7 1 7 five to the second power, or five squared b. 5 2 5 c.c. 1 3 2 one half to the third power, or one half cubed 1 2 1 2 1 2 z to the fifth power d. z 5 z z z z z

15. GUIDED PRACTICE for Examples 2 and 3 5. WHAT IF? In Example 2, suppose you go back to the theater with a friend to see an afternoon movie. You pay for both admissions.Your total cost (in dollars) can be represented by the expression 2a. If each admission costs $4.75, what is your total cost? The total cost is $9.50. ANSWER

16. GUIDED PRACTICE for Examples 2 and 3 ProductWords Power Write the power in words and as a product. Nine to the fifth power 6. 9 5 Two to the eighth power 7. 2 8 n to the fourth power 9 9 9 9 9 2 2 2 2 8.8. n4n4 n n

17. EXAMPLE 4 Evaluate powers Evaluate the expression. a. x 4 = 2 4 = 16 = (1.5)(1.5)(1.5) = 3.375 = 2 2 2 2 b. n 3 = 1.5 3 b. n 3 when n = 1.5 SOLUTION a. x 4 when x = 2

18. GUIDED PRACTICE for Example 4 Evaluate the expression. 9. x 3 when x = 8 9. 51210. 6.25 10. k 3 when k = 2.5 ANSWER

19. GUIDED PRACTICE for Example 4 Evaluate the expression. 11. d 4 when d = 1 3 11. 1 81 ANSWER

20. SOLUTION EXAMPLE 5 Evaluate a power Storage cubes Write formula for volume. = 14 3 Substitute 14 for s. = 2744 Evaluate power. Each edge of the medium-sized pop-up storage cube shown is 14 inches long. The storage cube is made so that it can be folded flat when not in use. Find the volume of the storage cube. V = s3s3 The volume of the storage cube is 2744 cubic inches.

21. GUIDED PRACTICE for Example 5 WHAT IF? In Example 5, suppose the storage cube is folded flat to form a square. Find the area of the square. The area of the square is 196 in 2. ANSWER

22. Homework 1.1 Exercises 1-49 all pages 5 and 6