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PRESENTATION 11 What Is Algebra

This presentation provides an overview of algebraic expressions and their importance in mathematical equations. It also covers the evaluation of formulas using numerical values. Practical problems with solutions are included to enhance understanding.

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PRESENTATION 11 What Is Algebra

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  1. PRESENTATION 11 What Is 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 ∙ or *] replaces multiply, times, product of • Division (÷ or / or —) replaces divide by, quotient of

  3. ALGEBRAIC EXPRESSIONS • The statement “add 5 to x” is expressed algebraically as x + 5 • The statement “12 is decreased by b” is expressed algebraically as 12 – b • The cost in dollars of 1 pound of grass seed is d. The cost of 6 pounds of seed is expressed as 6d

  4. ALGEBRAIC EXPRESSIONS • Perimeter (P) is the distance around an object. The perimeter of a rectangle equals twice its length (l) plus twice its width (w). The perimeter of a rectangle expressed as a formula is P = 2l + 2w

  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

  6. EVALUATION OF FORMULAS • Example: What is the value of the expression 53.8 – x(xy – m), where x = 8.7, y = 3.2, and m = 22.6? Round the answer to 1 decimal place. • Substitute the numerical values for x, y, and m 53.8 – 8.7[(8.7(3.2) – 22.6)] • Perform the operations within parentheses or brackets, multiplication first 53.8 – 8.7(27.84 – 22.6)

  7. EVALUATION OF FORMULAS • Perform the operations within parentheses or brackets, subtraction next 53.8 – 8.7(5.24) • Perform the multiplication 53.8 – 45.588 • Perform the subtraction 8.212 = 8.2 (rounded)

  8. USING FORMULAS • Example: The total resistance (RT) of the circuit shown is computed from the formula: • Determine the total resistance (RT) using the values in the figure to the nearest tenth ohm

  9. USING FORMULAS • Substitute the values: R1 = 52 Ω, R2 = 75 Ω, R3 = 108 Ω • Consider the numerator and the denominator as being enclosed within parentheses and perform the operation within parentheses 75 Ω(108 Ω) = 8,100 Ω2 75 Ω + 108 Ω = 183 Ω

  10. USING FORMULAS • Perform the division 8,100 Ω2 ÷ 183 Ω ≈ 44.3 Ω • Perform the addition 52 Ω + 44.3 Ω = 96.3 Ω RT = 96 Ω

  11. PRACTICAL PROBLEMS • Express each of the following as an algebraic expression: • Add 12 to six times x • One-quarter m times R • Divide d by the product of 14 and f • Twice M decreased by one-third R • Square F, add G, and divide the sum by H

  12. PRACTICAL PROBLEMS • Algebraic expressions • 6x + 12 • 1/4(mR) • d ÷14f • 2M – 1/3R • (F2 + G) ÷ H

  13. PRACTICAL PROBLEMS • Determine the value of the expression using the values for each variable and round to 2 decimal places: hm(2s + 1 + 0.5h), where h = 6.7, m = 3.9, and s = 7.8

  14. PRACTICAL PROBLEMS • Substitute the values and solve using the order of operations 6.7(3.9)[2(7.8) + 1 + 0.5(6.7)] = 6.7(3.9)(15.6 + 1 + 3.35) = 6.7(3.9)(19.95) = 521.2935 ≈ 521.29 • The value of the expression is about 521.29

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