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# Chapter1.1

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### Chapter1.1

1. 1. Warm Up California Standards Lesson Presentation Preview
2. 2. Warm Up Simplify. 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. 3. AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2 x + 5) 2 . AF1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality , expression, constant ) correctly. California Standards
4. 4. Vocabulary expression variable numerical expression algebraic expression evaluate
5. 5. 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. x + 2 4 n p – r 3 + 2 4(5) 27 – 18 Algebraic Expressions Numerical Expressions
6. 6. 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.
7. 7. Evaluate the expression for the given value of the variable. Additional Example 1A: Evaluating Algebraic Expressions with One Variable Substitute 12 for x. Subtract. x – 5 for x = 12 12 – 5 7
8. 8. Order of Operations PEMDAS: 1. P arentheses 2. E xponents 3. M ultiply and D ivide from left to right. 4. A dd and S ubtract from left to right. Remember!
9. 9. Evaluate the expression for the given value of the variable. Additional Example 1B: Evaluating Algebraic Expressions with One Variable Substitute 4 for y. Multiply. 2 y + 1 for y = 4 2( 4 ) + 1 8 + 1 Add. 9
10. 10. Evaluate the expression for the given values of the variable. Additional Example 1C: Evaluating Algebraic Expressions with One Variable 6( n + 2) – 4 for n = 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 7 6 5 Subtract Multiply Parentheses Substitute n
11. 11. Evaluate each expression for the given values of the variable. Check It Out! Example 1 Substitute 3 for x. Add. A. x + 5 for x = 3 3 + 5 8 Substitute 11 for c. Multiply. B. 4 c + 1 for c = 11 4( 11 ) + 1 44 + 1 Add. 45
12. 12. Evaluate the expression for the given values of the variable. Check It Out! Example 1C 5( n + 3) – 2 for n = 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 5 4 3 Subtract Multiply Parentheses Substitute n
13. 13. Evaluate each expression for the given values of the variables. Additional Example 2: Evaluating Algebraic Expressions with Two Variables Substitute 2 for x and 1 for y. Multiply. A. 4 x + 3 y for x = 2 and y = 1 4( 2 ) + 3( 1 ) 8 + 3 Substitute 3 for r and 5 for p. Multiply. B. 9 r – 2 p for r = 3 and p = 5 9( 3 ) – 2( 5 ) 27 – 10 Add. 11 Subtract. 17
14. 14. Evaluate each expression for the given values of the variables. Check It Out! Example 2 Substitute 3 for x and 4 for y. Multiply. A. 3 x + 2 y for x = 3 and y = 4 3( 3 ) + 2( 4 ) 9 + 8 Substitute 2 for q and 2 for r. Multiply. B. 8 q – 3 r for q = 2 and r = 2 8( 2 ) – 3( 2 ) 16 – 6 Add. 17 Subtract. 10
15. 15. Use the expression 1.8 c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit. Additional Example 3A: Physical Science Application Substitute 100 for c. Multiply. 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 at sea level.
16. 16. Additional Example 3B: Physical Science Application Substitute 85 for c. Multiply. Boiling point of water at an altitude of 4400 t 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. Use the expression 1.8 c + 32 to convert the temperature from degrees Celsius to degrees Fahrenheit.
17. 17. Convert the temperature from degrees Celsius to degrees Fahrenheit. Check It Out! Example 3A Substitute 50 for c. Multiply. 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. 18. Use the expression 1.8 c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit. Check It Out! Example 3B Substitute 10 for c. Multiply. 10°C 1.8( 10 ) + 32 18 + 32 1.8c + 32 Add. 50 10 ° C = 50 ° F
19. 19. Lesson Quiz Evaluate each expression for the given value(s) of the variables. 1. 6 x + 9 for x = 3 2. x + 14 for x = 8 3. 4 x + 3 y 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 + 0.03 n 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