This pdf includes the following topics:- Expressions What is a variable? Algebraic Expressions What are coefficients? What is a term? What are constants? Writing Algebraic Expressions
1. Algebraic Expressions and Terms Unit 1
2. Expressions You are familiar with the following type of numerical expressions: 12 + 6 3 (12) 6 (3 + 2) 15 - 4 (6)
3. What is a variable? In the expression 12 + B, the letter “B” is a variable. A variable is a letter or symbol that represents an unknown value.
4. Algebraic Expressions When variables are used with other numbers, parentheses, or operations, they create an algebraic expression. a + 2 (a) (b) 3m + 6n - 6
5. What are coefficients? A coefficient is the number multiplied by the variable in an algebraic expression. Algebraic Expression Coefficient 6m + 5 6 8r + 7m + 4 8, 7 14b - 8 14
6. What is a term? A term is the name given to a number, a variable, or a number and a variable combined by multiplication or division. Algebraic Expressions Terms a + 2 a, 2 3m + 6n - 6 3m, 6n, - 6
7. What are constants? A constant is a number that cannot change its value. In the expression: 5x + 7y - 2 the constant is - 2.
8. Figure it out! Identify the terms, coefficients, and constants. 1. 12a - 6b + 4 2. 4x - 2y 3. c - 32 4. 3x + 2
9. Writing Algebraic Expressions You can translate word phrases into variable expressions. Examples: 1. Three more than a number = 2. The quotient of a number and 8 = 3. Six times a number = 4. 15 less than a number = 5. The quotient of 30 and a number plus 10 =
10. Key words to look for: Addition: Subtraction: Add Minus Plus Difference Sum Subtract Total Less than Increased by Decreased by More than less
12. Write algebraic expressions for these word phrases 1. Four more than s 2. The product of 7 and c 3. Nine less than x 4. A number divided by the sum of 4 and 7. 5. Twice the sum of a number plus 4. 6. The sum of ¾ of a number and 7. 7. Ten times a number increased by 150.
13. Write an algebraic phrase for these situations 1. A car was traveling 35 miles per hour for a number of hours. 2. Bob ran 7 times a week for a number of weeks. 3. The plumber added an extra $35 to her bill. 4. Thirty-five fewer people came than the number expected.
14. How do you describe a variable expression? Variable Meaning Operation 5x, 5·x, (5)(x) 5 times x Multiplication (same as x·5) 5÷ x 5 divided by Division 5/x x 5 + x (same as x + 5 plus x Addition 5–x 5 minus x subtraction
15. Evaluate a Variable Expression Example 1: Evaluate each expression when n = 4. Simplify Simplify(means (meansto tosolve solvethe theproblem problemor orperform perform as many of the indicated operations as possible.) as many of the indicated operations as possible.) a. n + 3 Solution: n + 3 = 4 + 3Substitute 4 for n. Simplify =7 b. n – 3 Solution: n – 3 = 4 – 3 Substitute 4 for n. Simplify =1
16. Evaluate an Algebraic Expression Example 2: Evaluate each expression if x = 8. a. 5x Substitute 8 for x. Simplify 5x = 5(8) Solution: Using Usingparenthesis parenthesisisisthe thepreferred preferredmethod methodtotoshow show Solution: = 40 multiplication. multiplication.Additional Additionalways waystotoshow showmultiplication multiplicationare are 55· ·88and 5 x 8. and 5 x 8. b. x÷4 Substitute 8 for x. x÷4=8÷4 Simplify Solution: =2 x 8 Recall Recallthat thatdivision divisionproblems problemsare arealso also 4 4 fractions – this problem could be fractions – this problem could be 2; written writtenas: as: because x x 4 4
17. Evaluating More Expressions Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. a. 5xy Substitute 4 for x; 6 for y. simplify Solution: 5xy = 5(4)(6) = 120 b. z Substitute 24 for z; 6 for y. Simplify. y Solution: z 24 y 6 =4
18. Now You Try… Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 4ac A 2. a÷c A 3. a+b+c A 4. ba A 5. b–c A 6. c÷b A
19. You Try #1 Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 4ac Substitute Substitutethe thevalue valuefor foraa==66and andcc==33 into intothe theproblem problemand andmultiply multiply 4ac = 4(6)(3) = (24)(3) = 72 Click Clickto toreturn returntoto “You try it” slide “You try it” slide
20. You Try #2 Evaluate each expression given that a = 6, b = 12, and c = 3. 2.a ÷ c Substitute Substitutethe thevalue valuefor foraa==66and andcc==33 into intothe theproblem problemand anddivide divide a÷c=6÷3 =2 Click Clickto toreturn returntoto “You try it” slide “You try it” slide
21. You Try #3 Evaluate each expression given that a = 6, b = 12, and c = 3. 3. a + b + c Substitute Substitutethe thevalue valuefor foraa==6,6,b=12, b=12, and and c = 3 into the problem, thenadd. c = 3 into the problem, then add. a + b + c = 6 + 12 + 3 = 18 + 3 = 21 Click Clickto toreturn returntoto “You try it” slide “You try it” slide
22. You Try #4 Evaluate each expression given that a = 6, b = 12, and c = 3. 4.ba Substitute Substitutethe thevalue valuefor forb=12 b=12and andaa==66 into intothe theproblem, problem, then thenmultiply. multiply. ba = (12)(6) = 72 Click Clickto toreturn returntoto “You try it” slide “You try it” slide
23. You Try #5 Evaluate each expression given that a = 6, b = 12, and c = 3. 5.b - c Substitute Substitutethe thevalue valuefor forb=12 b=12and andaa==33 into intothe theproblem, problem, then thensubtract. subtract. b – c = 12 – 3 =9 Click Clickto toreturn returntoto “You try it” slide “You try it” slide
24. You Try #6 Evaluate each expression given that a = 6, b = 12, and c = 3. 6.c ÷ b Substitute Substitutethe thevalue valuefor forc=3 c=3and andbb==12 12into into the theproblem, problem, then thenDivide Divide c 3 Note: Note:ItItisisbetter betterto torewrite rewritethis thisdivision Divideboth both numeratorand c b problem as a fraction. problem as a fraction. division and denominatorby by b 12 This Thisfraction fractioncan cannow nowbebereduced reducedto toits its the GCF = (3) to simplest form. the GCF = (3) to reducethis this 3 3 1 simplest form. fraction. ItItisisOK OKtotohave haveaafraction 12 3 4 asasanananswer. answer. fraction Click Clickto toreturn returntoto “You try it” slide “You try it” slide
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