1. Pre-Algebra 1-1 Variables and Expressions 1-1 Variables and Expressions Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Pre-Algebra 1-1 Variables and Expressions Warm Up Evaluate. 1. 21  2(3) 15 31 21 20.4 15.3 5. 7(2.9)  5 4. 6(1.4) + 12 3. 2(9) + (3) 2. 4 + 3  9

3. Pre-Algebra 1-1 Variables and Expressions Problem of the Day Miss Smith obtained the prices below from the landscape company. She plans to buy five birch, two elm, one dogwood, and two oak trees. The landscape company will charge her $15 to plant each tree. How much will it cost? Trees Price Maple Elm Oak Dogwood Crab apple Birch $16.99 $22.99 $19.99 $23.99 $26.99 $17.99 $337.90

4. Pre-Algebra 1-1 Variables and Expressions Learn to evaluate algebraic expressions.

5. Pre-Algebra 1-1 Variables and Expressions Vocabulary variable coefficient algebraic expression constant evaluate substitute

6. Pre-Algebra 1-1 Variables and Expressions A variable is a letter that represents a value that can change or vary. The coefficient is the number multiplied by the variable. CoefficientVariable

7. Pre-Algebra 1-1 Variables and Expressions In the algebraic expression x + 6, 6 is a constant because it does not change. To evaluate an algebraic expression, substitute a given number for the variable, and find the value of the resulting numerical expression. An algebraic expression has one or more variables.

8. Pre-Algebra 1-1 Variables and Expressions Evaluate each expression for the given value of the variable. Additional Examples 1A and 1B: Evaluating Algebraic Expressions with One Variable Substitute 12 for x. Subtract. A. x – 5 for x = 12 12 – 5 7 Substitute 4 for y. Multiply. B. 2y + 1 for y = 4 2(4) + 1 8 + 1 Add. 9

9. Pre-Algebra 1-1 Variables and Expressions Evaluate the expression for the given values of the variable. Additional Example 1C: Evaluating Algebraic Expressions with One Variable C. 6(n + 2) – 4 for n = 5, 6, 7 567567 n Substitute Parentheses Multiply Subtract 6(5 + 2) – 46(7) – 4 42 – 4 38 6(6 + 2) – 46(8) – 4 48 – 4 44 6(7 + 2) – 46(9) – 4 54 – 4 50

10. Pre-Algebra 1-1 Variables and Expressions Evaluate each expression for the given value of the variable. Try This: Examples 1A and 1B Substitute 3 for x. Add. A. x + 5 for x = 3 3 + 5 8 Substitute 11 for c. Multiply. B. 4c + 1 for c = 11 4(11) + 1 44 + 1 Add. 45

11. Pre-Algebra 1-1 Variables and Expressions Evaluate the expression for the given values of the variable. Try This: Example 1C C. 5(n + 3) – 2 for n = 3, 4, 5 345345 n Substitute Parentheses Multiply Subtract 5(3 + 3) – 25(6) – 2 30 – 2 28 5(4 + 3) – 25(7) – 2 35 – 2 33 5(5 + 3) – 25(8) – 2 40 – 2 38

12. Pre-Algebra 1-1 Variables and Expressions Evaluate each expression for the given value of the variables. Additional Example 2: Evaluating Algebraic Expressions with Two Variables Substitute 2 for x and 1 for y. Multiply. A. 4x + 3y for x = 2 and y = 1 4(2) + 3(1) 8 + 3 Substitute 2 for r and 5.5 for p. Multiply. B. 8.5 r – 2p for r = 2 and p = 5.5 8.5(2) – 2(5.5) 17 – 11 Add. 11 Subtract. 6

13. Pre-Algebra 1-1 Variables and Expressions Evaluate each expression for the given value of the variables. Try This: Example 2 Substitute 3 for x and 4 for y. Multiply. A. 3x + 2y for x = 3 and y = 4 3(3) + 2(4) 9 + 8 Substitute 2.5 for q and 2 for r. Multiply. B. 8q – 3.5r for q = 2.5 and r = 2 8(2.5) – 3.5(2) 20 – 7 Add. 17 Subtract. 13

14. Pre-Algebra 1-1 Variables and Expressions Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit. Additional Example 3A: Physical Science Application Substitute 100 for c. Multiply. A. Boiling point of water at sea level: 100°C 1.8(100) + 32 180 + 32 1.8c + 32 Add. 212 100°C = 212°F Water boils at 212°F.

15. Pre-Algebra 1-1 Variables and Expressions Convert the temperature from degrees Celsius to degrees Fahrenheit. Additional Example 3B: Physical Science Application Substitute 15 for c. Multiply. B. Antarctica’s highest recorded temperature (Vanda Station, Scott Coast): 15°C 1.8(15) + 32 27 + 32 1.8c + 32 Add. 59 15°C = 59°F The highest recorded temperature in Antarctica is 59°F.

16. Pre-Algebra 1-1 Variables and Expressions Use the expression 1.8c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit. Try This: Example 3A Substitute 85 for c. Multiply. A. Boiling point of water at an altitude of 4400 meters: 85°C 1.8(85) + 32 153 + 32 1.8c + 32 Add. 185 85°C = 185°F Water boils at 185°F at 4400 m.

17. Pre-Algebra 1-1 Variables and Expressions Convert the temperature from degrees Celsius to degrees Fahrenheit. Try This: Example 3B Substitute 50 for c. Multiply. B. Europe’s highest recorded temperature (Seville, Spain): 50°C 1.8(50) + 32 90 + 32 1.8c + 32 Add. 122 50°C = 122°F The highest recorded temperature in Europe is 122°F.

18. Pre-Algebra 1-1 Variables and Expressions Lesson Quiz Evaluate each expression for the given values of the variables. 1. 6x + 9 for x = 3 2. x + 14 for x = 8 3. 4x + 3y for x = 2, y = 3 4. 1.6x – 2.9y for x = 19, y = 6 5. If n is the amount of money in a savings account, then the expression n + 0.03n can be used to find the amount in the account after it has earned interest for one year. Find the total in the account after one year if $500 is the initial amount. 27 22 17 13 $515