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# Variable and Algebraic Expressions

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• 1. Warm Up Problem of the Day Lesson Presentation 1-7 Variables and Algebraic Expressions Course 2
• 2. Warm Up Evaluate. 1. 5(7) – 1 2. 7(18 – 11) 3. 22 + 17  8 + 3 4. 36 + 15(40 – 35) 5. 3 3 + 7(12 – 4) 34 49 161 111 83
• 3. Problem of the Day If charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs \$12? \$28
• 4. Learn to evaluate algebraic expressions.
• 5. Vocabulary variable constant algebraic expression evaluate
• 6. 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.
• 7. 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.
• 8. To evaluate an algebraic expression, substitute a number for the variable. 1954 + a a 1990 1954 + 36 36 1975 1954 + 21 21 1972 1954 + 18 18 1970 1954 + 16 16 Year born + age = year at age Age
• 9. Evaluate k + 9 for each value of k . Additional Example 1: Evaluating Algebraic Expressions A. k = 5 k + 9 5 + 9 14 Substitute 5 for k. Add. B. k = 2 k + 9 2 + 9 Substitute 2 for k. 11 Add.
• 10. Check It Out: Example 1 Evaluate a + 6 for each value of a . A. a = 3 a + 6 3 + 6 9 Substitute 3 for a. Add. B. a = 5 a + 6 5 + 6 Substitute 5 for a. 11 Add.
• 11. Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.
• 12. Evaluate the expression for the given value of the variable. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations A. 4 x – 3 for x = 2 4( 2 ) – 3 8 – 3 5 Substitute 2 for x. Multiply. Subtract.
• 13. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 3 + 15 18 C. 5 x 2 + 3 x , for x = 2 5( 2 ) 2 + 3( 2 ) 5(4) + 3(2) 20 + 6 26 Substitute 15 for s. Divide. Add. Substitute 2 for x. Evaluate the power. Multiply. Add.
• 14. Check It Out: Example 2A Evaluate the expression for the given value of the variable. A. 3 x – 2 for x = 3 3( 3 ) – 2 9 – 2 7 Substitute 3 for x. Multiply. Subtract.
• 15. Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 4 + 12 16 C. 4 y 2 + 2 y , for y = 3 4( 3 ) 2 + 2( 3 ) 4(9) + 2(3) 36 + 6 42 Substitute 12 for r. Divide. Add. Substitute 3 for y. Evaluate the power. Multiply. Add.
• 16. Evaluate Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6 a + 4 b , for a = 3 and b = 2 . 6 a + 4 b 6 3 + 4( 2 ) 2 + 8 10 Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add.
• 17. Check It Out: Example 3 Evaluate 8 w + 2 x , for w = 4 and x = 2 . 8 w + 2 x 8 4 + 2( 2 ) 2 + 4 6 Substitute 4 for w and 2 for x. Divide and multiply from left to right. Add.
• 18. Lesson Quiz 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. 6 y – 5 for y = 7 4. 4 x 2 + 3 x for x = 6 5. + 3 y for x = 4 and y = 3 6. The expression 7 d gives the number of days in d weeks. Evaluate 7 d for d = 12. How many days are in 12 weeks? 38 32 37 162 56 x 23 84