Chapter 5 Algebra Fundamentals: Algebraic Terms, Roots, and Powers

Numbers, Expressions, and Terms Literal and Real Numbers  Real Numbers Always have the same value.  Never can have other values.  Aka. Constants Examples: 6, 7, 27,1024, etc.  Literal Numbers Take on different values  Can represent constants or variables Examples: E= I * R

Numbers, Expressions, and Terms Algebraic Expressions and Terms  Expressions contain Real, Literal, or both types of numbers  Terms are numbers separated by ‘+’ and ‘-’ 2ab + 4c – 5ac  Three terms: 2ab, 4c, 5ac Expression with one term – monomial Expression w/two + terms - polynomial

Numbers, Expressions, and Terms Coefficients  Of Algebraic term is real number part of term 6 is coefficient of 6xy Coefficient of ax is ‘1’ Exponents  5 3 = 5 * 5 * 5 = 125  X3 = X * X * X = depends on value of X

Finding Values of Algebraic Expressions When expression has real and literal numbers  Need value of literals to find value  6X 2 yields different values for different X’s If X =3 => 6 * 3 2 = 6 * 9 = 54 If X =4 => 6 * 4 2 = 6 * 16 = 96 If X =1 => 6 * 1 2 = 6 * 1 = 6  If x = 3 and y = 4 Find: xy = 3 * 4 = 12 x 2 y = 3 2 * 4 = 9 * 4 = 36

Finding Values of Algebraic Expressions When expression has real and literal numbers  If x = 3 and y = 4 Find: x 2 y 2 = 3 2 * 4 2 = 9 * 16 = 144 4x 3 y 2 = 4 * 3 3 * 4 2 = 1730 (xy) 2 = (3 * 4) 2 = 12 2 = 144 (xy) 2 = x 2 y 2 = 3 2 * 4 2 = 9 * 16 = 144 3x 2 y – xy 2 = 3 * 3 2 *4 – 3 * 4 2 = = 60

Roots

Roots

DC Circuit Examples In Electronics Literal number in equations represent relationships between variables in electrical circuits.  Ohm’s Law E = I * R Voltage across a component = Current through the component time resistance of the component Example problems 5-7 through 5-11 on page 116  Practice exercises – Practice Problems 5-5 on page 117

AC Circuit Examples

AC Circuit Examples Impedance of a circuit  Includes resistance and any reactance Resistance and reactance are orthogonal i.e. an impedance of circuit with 5 ohms resistance and 5 ohms reactance in series has an impedance of the vector sum of the two elements  Z = ( ) 1/2 = 50 1/2 = 7.07 (rounded to 3 places)  Z = 2 1/2 * 5 Example 5-14 on page 119

Work Practice problems For this and all the chapters  Odd number ones have answers in back of book  WORK THEM UNTIL YOU UNDERSTAND THE PROBLEMS