Unit 12 INTRODUCTION TO ALGEBRA

2 ALGEBRAIC EXPRESSIONS 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

3 ALGEBRAIC EXPRESSIONS 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 5x + 10

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

5 EVALUATION OF FORMULAS 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  Also recall PEMDAS discussed earlier

6 EVALUATION OF FORMULAS 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

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

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

9 PRACTICE PROBLEMS (Cont) 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

10 PRACTICE PROBLEMS (Cont) 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 = Determine the value of v given v = v o + gt if v o =15, g = 9.8, and t = Determine the value of the formula: 45.3 – x(xy – m), where x = 2, y = 3.2, and m = 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

11 PROBLEM ANSWER KEY 1. x – nm /(20x) 4. m – x – (x + y) – z 7. 8x + 15 pounds 8. 4L mm mm 2