1. Course 2 1-7 Variables and Algebraic Expressions 1-7 Variables and Algebraic Expressions Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 2 1-7 Variables and Algebraic Expressions 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. Course 2 1-7 Variables and Algebraic Expressions 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. Course 2 1-7 Variables and Algebraic Expressions Learn to evaluate algebraic expressions.

5. Course 2 1-7 Variables and Algebraic Expressions Vocabulary variable constant algebraic expression evaluate

6. Course 2 1-7 Variables and Algebraic Expressions 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. Course 2 1-7 Variables and Algebraic Expressions 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. Course 2 1-7 Variables and Algebraic Expressions To evaluate an algebraic expression, substitute a number for the variable. AgeYear born + age = year at age 161954 + 161970 181954 + 181972 211954 + 211975 361954 + 361990 a1954 + a

9. Course 2 1-7 Variables and Algebraic Expressions 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 + 9Substitute 2 for k. 11 Add.

10. Course 2 1-7 Variables and Algebraic Expressions 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 + 6Substitute 5 for a. 11 Add.

11. Course 2 1-7 Variables and Algebraic Expressions 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. Course 2 1-7 Variables and Algebraic Expressions Evaluate the expression for the given value of the variable. Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations A. 4x – 3 for x = 2 4(2) – 3 8 – 3 5 Substitute 2 for x. Multiply. Subtract.

13. Course 2 1-7 Variables and Algebraic Expressions Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 3 + 15 18 C. 5x 2 + 3x, 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. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 2A Evaluate the expression for the given value of the variable. A. 3x – 2 for x = 3 3(3) – 2 9 – 2 7 Substitute 3 for x. Multiply. Subtract.

15. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 4 + 12 16 C. 4y 2 + 2y, 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. Course 2 1-7 Variables and Algebraic Expressions Evaluate Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6a6a + 4b, for a = 3 and b = 2. 6a6a + 4b 6363 + 4(2) 2 + 8 10 Substitute 3 for a and 2 for b. Divide and multiply from left to right. Add.

17. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 3 Evaluate 8w8w + 2x, for w = 4 and x = 2. 8w8w + 2x 8484 + 2(2) 2 + 4 6 Substitute 4 for w and 2 for x. Divide and multiply from left to right. Add.

18. Course 2 1-7 Variables and Algebraic Expressions 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. 6y – 5 for y = 7 4. 4x 2 + 3x for x = 6 5. + 3y for x = 4 and y = 3 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? 3832 37 162 56 x 23 84

19. Course 2 1-7 Variables and Algebraic Expressions 1-8 Translate Words into Math Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

20. Course 2 1-7 Variables and Algebraic Expressions Warm Up Evaluate each algebraic expression for the given value of the variables. 1. 7x + 4 for x = 6 2. 8y – 22 for y = 9 3. 12x + for x = 7 and y = 4 4. y + 3z for y = 5 and z = 6 46 50 86 8y8y 23

21. Course 2 1-7 Variables and Algebraic Expressions Problem of the Day A farmer sent his two children out to count the number of ducks and cows in the field. Jean counted 50 heads. Charles counted 154 legs. How many of each kind were counted? 23 ducks and 27 cows

22. Course 2 1-7 Variables and Algebraic Expressions Learn to translate words into numbers, variables, and operations.

23. Course 2 1-7 Variables and Algebraic Expressions Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

24. Course 2 1-7 Variables and Algebraic Expressions OperationVerbal Expressions Algebraic Expressions add 3 to a number a number plus 3 the sum of a number and 3 3 more than a number a number increased by 3 subtract 12 from a number a number minus 12 the difference of a number and 12 12 less than a number a number decreased by 12 take away 12 from a number a number less than 12 n + 3 x – 12

25. Course 2 1-7 Variables and Algebraic Expressions OperationVerbal Expressions Algebraic Expressions 2 times a number 2 multiplied by a number the product of 2 and a number 6 divided into a number a number divided by 6 the quotient of a number and 6 2m or 2 m ÷ a6a6 ÷ 6 or a

26. Course 2 1-7 Variables and Algebraic Expressions Additional Example 1: Translating Verbal Expressions into Algebraic Expressions Write each phrase as an algebraic expression. A. the quotient of a number and 4 quotient means “divide” B. w increased by 5 increased by means “add” w + 5 n4n4

27. Course 2 1-7 Variables and Algebraic Expressions Write each phrase as an algebraic expression. Additional Example 1: Translating Verbal Expressions into Algebraic Expressions C. the difference of 3 times a number and 7 the difference of 3 times a number and 7 D. the quotient of 4 and a number, increased by 10 3 x – 7 the quotient of 4 and a number, increased by 10 4n4n + 10

28. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 1 A. a number decreased by 10 decreased means “subtract” B. r plus 20 plus means “add” r + 20 n – 10 Write each phrase as an algebraic expression.

29. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 1 Write each phrase as an algebraic expression. C. the product of a number and 5 D. 4 times the difference of y and 8 y – 8 n 5 the product of a number and 5 5n5n 4 times the difference of y and 8 4(y – 8) 4

30. Course 2 1-7 Variables and Algebraic Expressions When solving real-world problems, you may need to determine the action to know which operation to use. ActionOperation Put parts together Put equal parts together Find how much more Separate into equal parts Add Multiply Subtract Divide

31. Course 2 1-7 Variables and Algebraic Expressions Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how far he can drive in h hours. Additional Example 2A: Translating Real-World Problems into Algebraic Expressions You need to put equal parts together. This involves multiplication. 55mi/h · h hours = 55h miles

32. Course 2 1-7 Variables and Algebraic Expressions On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly. Additional Example 2B: Translating Real-World Problems into Algebraic Expressions The total points include 2 points for each short- answer question. Multiply to put equal parts together. In addition to the points for short-answer questions, the total points included 50 points on the essay. Add to put the parts together: 50 + 2q 2q2q

33. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 2A Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours. You need to put equal parts together. This involves multiplication. 8 units/h · h hours = 8h

34. Course 2 1-7 Variables and Algebraic Expressions Check It Out: Example 2B At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour. Her total wage includes $2 for each unit produced. Multiply to put equal parts together. In addition the pay per unit, her total income includes $8 per hour. Add to put the parts together: 2u + 8. 2u2u

35. Course 2 1-7 Variables and Algebraic Expressions Lesson Quiz Write each phrase as an algebraic expression. 1. 18 less than an number 2. the quotient of a number and 21 3. 8 times the sum of x and 15 4. 7 less than the product of a number and 5 x 21 x – 18 8(x + 15) 5n – 7 5. The county fair charges an admission of $6 and then charges $2 for each ride. Write an algebraic expression to represent the total cost after r rides at the fair. 6 + 2r