Transcript PowerPoint Presentation 11: Algebra

PRESENTATION 11
What Is Algebra
ALGEBRAIC EXPRESSIONS
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An algebraic expression is a word statement put
into mathematical form by using variables,
arithmetic numbers or constants, and signs of
operation.
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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
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
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
EVALUATION OF FORMULAS
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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
EVALUATION OF FORMULAS
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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.
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Substitute the numerical values for x, y, and m
53.8 – 8.7[(8.7(3.2) – 22.6)]
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Perform the operations within parentheses or
brackets, multiplication first
53.8 – 8.7(27.84 – 22.6)
EVALUATION OF FORMULAS
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Perform the operations within
parentheses or brackets, subtraction next
53.8 – 8.7(5.24)
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Perform the multiplication
53.8 – 45.588
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Perform the subtraction
8.212 = 8.2 (rounded)
USING FORMULAS
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Example: The total resistance (RT) of the
circuit shown is computed from the
formula:
RR
RT  R1 
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2
3
R2  R3
Determine the total resistance (RT) using
the values in the figure to the nearest
tenth ohm
USING FORMULAS
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Substitute the values: R1 = 52 Ω, R2 = 75 Ω, R3
= 108 Ω
75  108  
RT  52  
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75   108 
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
8,100 2
RT  52  
183 
USING FORMULAS
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Perform the division
8,100 Ω2 ÷ 183 Ω ≈ 44.3 Ω
RT  52   44.3 
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Perform the addition
52 Ω + 44.3 Ω = 96.3 Ω
RT = 96 Ω
PRACTICAL PROBLEMS
• Express each of the following as an
algebraic expression:
1. Add 12 to six times x
2. One-quarter m times R
3. Divide d by the product of 14 and f
4. Twice M decreased by one-third R
5. Square F, add G, and divide the sum by H
PRACTICAL PROBLEMS
• Algebraic expressions
1. 6x + 12
2. 1/4(mR)
3. d ÷14f
4. 2M – 1/3R
5. (F2 + G) ÷ H
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
PRACTICAL PROBLEMS
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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
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The value of the expression is about 521.29