Preview Warm Up California Standards Lesson Presentation

Warm Up Simplify. 1. 21 – 2(3) 15 2. 4 + 3  9 31 3. 2(9) + (3) 21 4. 6(1.4) + 12 20.4 5. 7(2.9) – 5 15.3

AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2. AF1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. California Standards

Vocabulary expression variable numerical expression algebraic expression evaluate

An expression is a mathematical phrase that contains operations, numbers, and/or variables. A variable is a letter that represents a value that can change or vary. There are two types of expressions: numerical and algebraic. A numerical expression does not contain variables. An algebraic expression contains one or more variables. Numerical Expressions Algebraic Expressions 3 + 2 4(5) 27 – 18 x + 2 4n p – r

To evaluate an algebraic expression, substitute a given number for the variable. Then use the order of operations to find the value of the resulting numerical expression.

Additional Example 1A: Evaluating Algebraic Expressions with One Variable Evaluate the expression for the given value of the variable. x – 5 for x = 12 12 – 5 Substitute 12 for x. 7 Subtract.

Order of Operations PEMDAS: 1. Parentheses 2. Exponents 3. Multiply and Divide from left to right. 4. Add and Subtract from left to right. Remember!

Additional Example 1B: Evaluating Algebraic Expressions with One Variable Evaluate the expression for the given value of the variable. 2y + 1 for y = 4 2(4) + 1 Substitute 4 for y. 8 + 1 Multiply. 9 Add.

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

Check It Out! Example 1 Evaluate each expression for the given values of the variable. A. x + 5 for x = 3 3 + 5 Substitute 3 for x. 8 Add. B. 4c + 1 for c = 11 4(11) + 1 Substitute 11 for c. 44 + 1 Multiply. 45 Add.

Check It Out! Example 1C Evaluate the expression for the given values of the variable. 5(n + 3) – 2 for n = 3, 4, 5 n Substitute Parentheses Multiply Subtract 3 4 5 5(3 + 3) – 2 5(6) – 2 30 – 2 28 5(4 + 3) – 2 5(7) – 2 35 – 2 33 5(5 + 3) – 2 5(8) – 2 40 – 2 38

Additional Example 2: Evaluating Algebraic Expressions with Two Variables Evaluate each expression for the given values of the variables. A. 4x + 3y for x = 2 and y = 1 4(2) + 3(1) Substitute 2 for x and 1 for y. 8 + 3 Multiply. 11 Add. B. 9r – 2p for r = 3 and p = 5 9(3) – 2(5) Substitute 3 for r and 5 for p. 27 – 10 Multiply. 17 Subtract.

Check It Out! Example 2 Evaluate each expression for the given values of the variables. A. 3x + 2y for x = 3 and y = 4 3(3) + 2(4) Substitute 3 for x and 4 for y. 9 + 8 Multiply. 17 Add. B. 8q – 3r for q = 2 and r = 2 8(2) – 3(2) Substitute 2 for q and 2 for r. 16 – 6 Multiply. 10 Subtract.

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

Additional Example 3B: Physical Science Application Use the expression 1.8c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. Boiling point of water at an altitude of 4400 t meters: 85°C 1.8c + 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.

Check It Out! Example 3A Convert the temperature from degrees Celsius to degrees Fahrenheit. Europe’s highest recorded temperature (Seville, Spain): 50°C 1.8c + 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.

Check It Out! Example 3B Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit. 10°C 1.8c + 32 1.8(10) + 32 Substitute 10 for c. 18 + 32 Multiply. 50 Add. 10°C = 50°F

Lesson Quiz 1. 6x + 9 for x = 3 2. x + 14 for x = 8 27 Evaluate each expression for the given value(s) of the variables. 1. 6x + 9 for x = 3 2. x + 14 for x = 8 3. 4x + 3y for x = 2, y = 3 4. y(27 – x) 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 48 $515