Unit 12 INTRODUCTION TO ALGEBRA 1 ALGEBRAIC EXPRESSIONS

Unit 12 INTRODUCTION TO ALGEBRA 1

ALGEBRAIC EXPRESSIONS l An algebraic expression is a word statement put into mathematical form by using variables, arithmetic numbers or constants, and signs of operation • • Addition (+) replaces add, sum, plus, increase, greater than Subtraction (–) replaces minus, decreased by, less than Multiplication [( ) or ∙] replaces multiply, times, product of Division (÷ or / or —) replaces divide by, quotient of 2

ALGEBRAIC EXPRESSIONS l l The statement “add 17 to x” is expressed algebraically as x + 17 The statement “ 10 is added to the product of x and 5” is expressed algebraically as 5 x + 10 3

ALGEBRAIC EXPRESSIONS l l The cost, in dollars, of 1 pound of hamburger is d. The cost of 9 pounds of hamburger is 9 d The statement “the product of 15 and x decreased by the product of 7 and y” is expressed algebraically as 15 x – 7 y 4

EVALUATION OF FORMULAS l l The order of operations must be followed when evaluating formulas. This order is as follows: 1. Do all the work in parentheses first 2. Do powers and roots next 3. Do multiplication and division from left to right 4. Do addition and subtraction from left to right Ø Also recall PEMDAS discussed earlier 5

EVALUATION OF FORMULAS l Given that the area of a rectangle is length (L) times width (w) find the area of a rectangle with a length of 5 cm and a width of 6 cm. Area = length × width LW = 5 cm • 6 cm = 30 cm 2 Ans 6

FORMULA EXAMPLE l Given that power (P) equals current (I) squared times resistance (R) and that I = 4 and R = 12, find P P = I 2 R = 42 • 12 = 16 • 12 = 192 Ans l Given the formula: v = vo + gt and that vo = 30, g = 32, and t = 4; find v V = vo + gt = 30 + 32 • 4 = 30 + 128 = 158 Ans 7

PRACTICE PROBLEMS l Express each of the following as an algebraic expression: 1. 2. 3. 4. 5. Subtract 100 from x The product of n and m Divide 1000 by the product of 20 and x Reduce m by 16 Five times x minus 15 8

PRACTICE PROBLEMS (Cont) l Express each of the following as an algebraic expression: 6. The sum of x and y reduced by z 7. Given that the weight of one gallon of paint is x pounds, the weight of 8 gallons of paint plus 15 pounds 8. Given that the length of a spring is L millimeters, and that the spring is stretched to 4 times its original length plus 1. 2 millimeters 9

PRACTICE PROBLEMS (Cont) l Express each of the following as an algebraic expression: 9. Determine the value of P given the formula: P = E 2/R, where E = 50 and R = 100 10. Determine the value of v given v = vo + gt if vo =15, g = 9. 8, and t = 5 11. Determine the value of the formula: 45. 3 – x(xy – m), where x = 2, y = 3. 2, and m = 4. 4 12. The formula for the area of a trapezoid is given as: A = 1/2(b 1 + b 2)h. Find the area of a trapezoid given that b 1 = 15 mm, b 2 = 35 mm, and h = 40 mm 10

PROBLEM ANSWER KEY 1. 2. 3. 4. 5. 6. x – 100 nm 1000/(20 x) m – 16 5 x – 15 (x + y) – z 7. 8. 9. 10. 11. 12. 8 x + 15 pounds 4 L + 1. 2 mm 25 64 41. 3 1000 mm 2 11