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INTRODUCTION TO ALGEBRA

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Unit 12 INTRODUCTION TO ALGEBRA ALGEBRAIC EXPRESSIONS An algebraic expression is a word statement put into mathematical form by using variables, arithmetic numbers or ... – PowerPoint PPT presentation

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Title: INTRODUCTION TO ALGEBRA


1
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
  • Do all the work in parentheses first
  • Do powers and roots next
  • Do multiplication and division from left to right
  • 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
cm2 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 vo gt and that vo 30,
    g 32, and t 4 find v

P I2 R 42 12 16 12 192 Ans
V vo gt 30 32 4 30 128 158 Ans
8
PRACTICE PROBLEMS
  • Express each of the following as an algebraic
    expression
  • 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

9
PRACTICE PROBLEMS (Cont)
  • Express each of the following as an algebraic
    expression
  • The sum of x and y reduced by z
  • Given that the weight of one gallon of paint is x
    pounds, the weight of 8 gallons of paint plus 15
    pounds
  • 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
  • Determine the value of P given the formula P
    E2/R, where E 50 and R 100
  • Determine the value of v given v vo gt if
    vo 15, g 9.8, and t 5
  • Determine the value of the formula 45.3 x(xy
    m), where x 2, y 3.2, and m 4.4
  • The formula for the area of a trapezoid is given
    as A 1/2(b1 b2)h. Find the area of a
    trapezoid given that b1 15 mm, b2 35 mm, and
    h 40 mm

11
PROBLEM ANSWER KEY
  1. x 100
  2. nm
  3. 1000/(20x)
  4. m 16
  5. 5x 15
  6. (x y) z
  • 8x 15 pounds
  • 4L 1.2 mm
  • 25
  • 64
  • 41.3
  • 1000 mm2
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