Chapter 8 Patterns. Examples: a, b, c,, x, y, z

Transcription

1 Chapter 8 Patterns Alegbra is a way of expressing mathematical ideas that use variables, constants, numerical coefficients, and mathematical operations. Variable is a letter that represents an unknown value or a changing value. Examples: a, b, c,, x, y, z Term is made up of a number and a variable put together by multiplication. However, we do not use the multiplication sign between them. Examples: 5y means 5 times y but we do not write 5 x y. This will confuse us. (REMEMBER Multiplication is repeated addition so this also can mean y + y + y + y + y) Numerical Coefficient is the name given to the number in a term. Examples: the 6 in the term 6a the -3 in the term 3x Constant a value that does not change (or a term with no variable). Examples: -7, 4, 3 Algebraic expression a mathematical statement that contains terms (numbers and variables) and at least one operation ( +, -,, ) Examples: 4 + h 3d 6 F 2 + m

2 Let s try some examples You have already used algebra in many ways without even knowing it. Example 1: When you use formulas like area: Area of a rectangle is length times width OR A = L x W A = Area L = length W = width L and W are variables. The values of L and W change depending on the length and/or width of a given rectangle. Example 2: When you calculating prices per amount: If bars are $2.00, how much for 6 bars? 2.00 x 6 how much for 3 bars? 2.00 x 3 how much for 8 bars? 2.00 x 8 What value changes? We can use an algebraic expression to represent this 2n where n represents the number of bars. Example 3: For the expression 3d + 4. Please indicate the following. a) What is the constant? b) How many terms are there? c) What is the variable(s)? d) What is the number coefficient? ASSIGN: Algebra Worksheet #1

3 Algebra Worksheet #1 1. What is the variable in each algebraic expression? a) 5p b) 2a c) 7t d) 3q e) 9w f) 6b 2. What is the constant in each algebraic expression? a) 10c + 1 b) 18z 3 c) 11m + 5 d) 19d 7 e) 13t 9 f) 17x 3. Identify the variable and the constant in each expression. a) 8z 3 b) 5r + t c) 9c 13 d) 12m + 5 f) 16p - 17 f) 14q 4. Simplify these expressions. Ex: y + y + y = 3y a) p + p + p + p + p b) a + a + a c) q + q + q + q + q + q + q d) z + z e) x x x x x x x x x 5. Write each algebraic expression as repeated addition. a) 2r b) 4t c) 3s d) 5y e) 8n f) 6u 6. Identify each of the following as a variable or a constant. Explain your choice. a) the number of cars in a school parking lot. b) the number of cents in a dollar. 7. It costs $5.00 an hour to rent a bicycle at a resort. Which expression represents the cost to rent for any number of hours? a) 10h b) 7h c) 5h d) 15h

4 8. It costs $6.00 for a dozen roses. Which expression represents the cost of any number of dozen roses? a) 3d b) 6d c) 10d 9. Enzo cuts lawns for $8.00/h a) Copy and complete the chart time (h) earnings ($) b) Identify the variable and the constant. c) Use the variable h to write an algebraic expression that describes Enzo s earnings. 10. Tickets for the school play cost $6.50 each. a) Copy and complete the chart number of tickets cost ($) b) Identify the variable and the constant in this problem. c) Use the variable c to write an algebraic expression that describes the cost of the tickets for the school. 11. The variable x represents the length in centimeters, or a person s handspan. What does 2x represent? 12. Name four examples of constants and variables in your school or community.

5 Translating English to Mathematics When solving algebraic problems we need to develop skills for translating from English to Mathematical symbols i) Words that are commonly used to refer to addition could be: increase, sum, added, plus, gain, greater than, etc. ii) Words that are commonly used to refer to subtraction could be: decrease, difference, diminished, loss, less than, etc. iii) Words that are commonly used to refer to multiplication could be: times, multiply, product, double, triple, etc. iv) Words that are commonly used to refer to division could be: quotient, divided by, etc. Let s try some examples: Example 1: Example 2: Example 3: Example 4: A number plus four. Two times a number. Six divided by a number. Eight times the difference between a number and three. BE CAREFUL WITH greater than and less than we need to switch them around. Example 5: Example 6: Twelve less than a number. Four greater than two times a number.

6 Translating English Expressions to Mathematical Expressions Part A: Write an algebraic expression for each of the following. 1. a number plus six 2. a number minus three 3. a number increased by four 4. a number decreased by seven 5. seven decreased by a number 6. a number times four 7. a number multiplied by five 8. six more than a number 9. ten less than a number 10. one half of a number 11. one third of a number 12. double a number 13. a number divided by eight times a number 15. the product of a number and two 16. the sum of a number and four 17. two times a number less three 18. the product a number and three increased by six 19. the product a number and five decreased by eight 20. four times the difference between a number and nine 21. fives times the sum of a number and seven 22. the product of a number and two, increased by seven 23. the product of a number and two hundred, decreased by seventy-four 24. four times the sum of a number and fifteen 25. two times a number less twelve Part B: Write the following algebraic expression in words. 1. n d/ n 6. 10/ x 3. 2t 7. 3m m (m + 7)