1. Learn to evaluate algebraic expressions.

2. Vocabulary variable constant algebraic expression evaluate

3. Ron Howard was born in 1954. You can find out what year Ron turned 16 by adding the year he was born to his age. 1954 + 16 In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be 1954 + a.

4. The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change. An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, 1954 + a is an algebraic expression for the year Ron Howard turns a certain age.

5. To evaluate an algebraic expression, substitute a number for the variable. AgeYear born + age = year at age 161954 + 161970 181954 + 181972 211954 + 211975 361954 + 361990 a1954 + a

6. Evaluate k + 9 for each value of k. Ex 1: Evaluating Algebraic Expressions A. k = -5 k + 9 -5 + 9 4 Substitute 5 for k. Add. B. k = -2 k + 9 -2 + 9Substitute 2 for k. 7 Add.

7. Example 2 Evaluate a + 6 for each value of a. A. a = -3 a + 6 -3 + 6 3 Substitute -3 for a. Add. B. a = -5 a + 6 -5 + 6Substitute -5 for a. 1 Add.

8. Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.

9. Evaluate the expression for the given value of the variable. Evaluating Algebraic Expressions Involving Order of Operations 3. 4x – 3 for when x = -2 4(-2) – 3 -8 – 3 -11 Substitute 2 for x. Multiply. Subtract.

10. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations 4. s ÷ 5 + s, for s = -15 -15 ÷ 5 + -15 -3 + (-15) -18 5. 5x 2 + 3x, for x = -2 5(-2) 2 + 3(-2) 5(4) + 3(-2) 20 + (-6) 14 Substitute -15 for s. Divide. Add. Substitute -2 for x. Evaluate the power. Multiply. Add.

11. Example 6 Evaluate the expression for the given value of the variable. A. -3x – 2 for x = 3 -3(3) – 2 -9 – 2 -11 Substitute 3 for x. Multiply. Subtract.

12. 7. r ÷ (-3) + r, for r = 12 12 ÷ -3 + 12 (-4) + 12 8 8. 4 - y 2 + 2y, for y = 3 4 - (3) 2 + 2(3) 4 - (9) + 2(3) (-5) + 6 1 Substitute 12 for r. Divide. Add. Substitute 3 for y. Evaluate the power. Multiply. Add.

13. Evaluate Example 9: Evaluating Algebraic Expressions with Two Variables 6a6a + 4b, for a = 3 and b = 2. 6a6a + 4b 6363 + 4(2) 2 + 8 10 Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add.

14. Example 10 Evaluate 8w8w + 2x, for w = 4 and x = 2. 8w8w + 2x 8484 + 2(2) 2 + 4 6 Substitute 4 for w and 2 for x. Divide and multiply from left to right. Add.

15. Evaluate n + 7 for each value of n. 1. n = -25 2. n = -31 Evaluate each algebraic expression for the given value of the variables 3. -6y – 5 for y = 7 4. -4x 2 + -3x for x = 6 5. + 3y for x = 4 and y = 3 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? -24-18 -47 -162 -56 x -5 84