Transcript Document

Unit 12
INTRODUCTION TO
ALGEBRA
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
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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
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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
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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
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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
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FORMULA EXAMPLE

Given that power (P) equals current (I)
squared times resistance (R) and that I = 4
and R = 12, find P
P = I2 R = 42 • 12 = 16 • 12 = 192 Ans

Given the formula: v = vo + gt and that vo =
30, g = 32, and t = 4; find v
V = vo + gt = 30 + 32 • 4 = 30 + 128 = 158 Ans
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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 16
5. Five times x minus 15
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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
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PRACTICE PROBLEMS (Cont)

Express each of the following as an algebraic
expression:
9.
Determine the value of P given the formula: P =
E2/R, where E = 50 and R = 100
10.Determine the value of v given v = vo + gt if vo =15,
g = 9.8, and t = 5
11.Determine the value of the formula: 45.3 – x(xy –
m), where x = 2, y = 3.2, and m = 4.4
12.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
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PROBLEM ANSWER KEY
1.
2.
3.
4.
5.
6.
x – 100
nm
1000/(20x)
m – 16
5x – 15
(x + y) – z
7.
8.
9.
10.
11.
12.
8x + 15 pounds
4L + 1.2 mm
25
64
41.3
1000 mm2
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