1 1 Variables and Expressions Learn to evaluate

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

1 -1 Variables and Expressions An algebraic expression has one or more variables. 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. Pre-Algebra

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

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

1 -1 Variables and Expressions Example 2: Evaluating Algebraic Expressions with Two Variables Evaluate each expression for the given value of the variables. A. 4 x + 3 y for x = 2 and y = 1 4(2) + 3(1) 8+3 11 Substitute 2 for x and 1 for y. Multiply. Add. B. 8. 5 r – 2 p for r = 2 and p = 5. 5 8. 5(2) – 2(5. 5) 17 – 11 6 Pre-Algebra Substitute 2 for r and 5. 5 for p. Multiply. Subtract.

1 -1 Variables and Expressions Example 3 A: Physical Science Application Use the expression 1. 8 c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit. A. Boiling point of water at sea level: 100°C 1. 8 c + 32 1. 8(100) + 32 Substitute 100 for c. 180 + 32 Multiply. 212 Add. 100°C = 212°F Water boils at 212°F. Pre-Algebra

1 -1 Variables and Expressions Example 3 B: Physical Science Application Convert the temperature from degrees Celsius to degrees Fahrenheit. B. Antarctica’s highest recorded temperature (Vanda Station, Scott Coast): 15°C 1. 8 c + 32 1. 8(15) + 32 Substitute 15 for c. 27 + 32 Multiply. 59 Add. 15°C = 59°F The highest recorded temperature in Antarctica is 59°F. 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. Coefficient Pre-Algebra Variable

1 -1 Variables and Expressions An algebraic expression has one or more variables. 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. Pre-Algebra

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

1 -1 Variables and Expressions Try This: Example 2 Evaluate each expression for the given value of the variables. A. 3 x + 2 y for x = 3 and y = 4 3(3) + 2(4) 9+8 17 Substitute 3 for x and 4 for y. Multiply. Add. B. 8 q – 3. 5 r for q = 2. 5 and r = 2 8(2. 5) – 3. 5(2) 20 – 7 13 Pre-Algebra Substitute 2. 5 for q and 2 for r. Multiply. Subtract.

1 -1 Variables and Expressions Try This: Example 3 A Use the expression 1. 8 c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit. A. Boiling point of water at an altitude of 4400 meters: 85°C 1. 8 c + 32 1. 8(85) + 32 Substitute 85 for c. 153 + 32 Multiply. 185 Add. 85°C = 185°F Water boils at 185°F at 4400 m. Pre-Algebra

1 -1 Variables and Expressions Try This: Example 3 B Convert the temperature from degrees Celsius to degrees Fahrenheit. B. Europe’s highest recorded temperature (Seville, Spain): 50°C 1. 8 c + 32 1. 8(50) + 32 Substitute 50 for c. 90 + 32 Multiply. 122 Add. 50°C = 122°F The highest recorded temperature in Europe is 122°F. Pre-Algebra