Download algebraic expression

Getting Started with
Algebra
What is Algebra ?
Algebra is a branch of
mathematics in which
symbols, usually letters,
are used to represent
quantities that can be
replaced by a number or
an expression.
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Getting Started with
Algebra
Who invented Algebra ?
Algebra is a reasoning
skill and language that
developed and evolved
along with civilization.
No one person
invented Algebra
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Getting Started with
Algebra
Where did the word
Algebra originate ?
The word Algebra is from
Kitab al-Jabr wa-l-Muqabala
which was a book written in
approximately 820 A.D. by a
Persian mathematician.
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Variables
A variable is
a letter used to represent
various numbers.
“x” is frequently used as
the variable, but many
other letters can be used.
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Variables
For example, jean sizes are
often given by waist and leg
inseam measurements.
waist
measurement
leg inseam
measurement
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Define each Variable
We must always define what
quantity or measurement the
letter represents.
Here are three examples:
= unknown number
= waist measurement
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= leg inseam
measurement
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Constants
A constant is
a letter used to represent
a number that doesn’t
change its value in the
problem. For example:
= “pi” = 3.1416….
= the speed of light
in Einstein’s equation
E = mc2
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Algebraic
Expressions
An algebraic expression
is a mathematical phrase
using variables, constants,
numerals, & operation signs.
An algebraic expression
will NOT have any of the
following symbols:
=
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<
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Algebraic Expressions:
Examples
x5
x is the variable.
+ is the operation
5 is a numeral and a constant.
x  5 is the
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algebraic expression
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Algebraic Expressions:
Examples
3p
p is the variable.
.
is the indicated operation
3 is a numeral and a constant.
3p is the algebraic expression
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Algebraic Expressions:
Examples
9z
z is the variable.
- is the operation
9 is a numeral and a constant.
9z
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is the algebraic expression
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Algebraic Expressions:
Examples
5
y
y is the variable.
÷ is the operation
5 is a numeral and a constant.
5
y
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is the algebraic expression
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Algebraic Expressions:
Examples
2x  5y
x and y are variables.
 and + are operations
2 and 5 are numerals
and constants.
2x  5y is the algebraic expression
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Algebraic Expressions:
Examples
x5
y2
x and y are variables.
+ ÷  are operations
5 and 2 are numerals
and constants.
x  5 is the algebraic expression
x 2
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Substitution
When a variable is
replaced with a numerical
value, that is called
substitution.
Sometimes, in higher
mathematics, a variable is
replaced with an expression.
That is also called
substitution.
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Evaluate an
Algebraic Expression
When a numerical value is
substituted into an
algebraic expression and
then simplified, that is
called
evaluating
the expression.
Evaluating means you will
compute a numerical value.
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Evaluate an Expression:
Example 1a
Evaluate
when
x5
x4
x5
 (4)  5
9
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Evaluate an Expression:
Example 1b
Evaluate
when
x5
x0
x5
 (0)  5
5
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Evaluate an Expression:
Example 1c
Evaluate
when
x5
x3
x5
 (3)  5
8
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Evaluate an Expression:
Example 1d
Evaluate
when
x5
x  5
x5
 (5)  5
0
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Evaluate an Expression:
Example 2
Evaluate
a) when
3p
p5
3p  3(5)  15
b) when
p2
3p  3(2)  6
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Evaluate an Expression:
Example 3
Evaluate
when
9z
z5
9z
 95
4
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Evaluate an Expression:
Example 4a
Evaluate
when
5
y
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5
y
y5
5
1

5
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Evaluate an Expression:
Example 4b
Evaluate
when
y0
5 5

y 0
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5
y
undefined
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Evaluate an Expression:
Example 5
Evaluate
When
2x  5y
x4
and
y 1
2x  5y
 2(4)  5(1)
 8  (5)
 13
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Evaluate an Expression:
Example 6a
Evaluate
x5
y2
x  4 and y  1
x5
( 4)  5

(1)  2
y2
When
9

3
3
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Evaluate an Expression:
Example 6b
Evaluate
x5
y2
x  7 and y  8
x5
(7)  5

(8)  2
y2
When
12

6
2
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Evaluate an Expression:
Example 6c
Evaluate
When
x7
y3
x7
and
y8
x  7 (7)  7 0
 0

y  3 (8)  3 5
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Evaluate an Expression:
Example 6d
Evaluate
When
x5
y2
x4
and
y2
x5
( 4)  5

y2
(2)  2
9

0
undefined
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Application:
Area of a Rectangle
The AREA of a Rectangle
Area = length x width
A=l.w
w  6cm
l  16cm
A  16cm6cm
A  96 cm
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Translating:
English into Algebra
In order to solve
problems, English phrases
must be translated into
the language of algebra.
The following slides list
keywords which can help
us translate.
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English & Algebra
ADDITION
The following words translate as
ADDITION:
•Plus
•Sum
•Add
•Added to
•Total
•More than
•Increased by
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X+7
The following phrases would
translate to : x  7
•A number plus seven
•The sum of a number and seven
•Add a number and seven
•Seven added to a number
•The total of seven and a number
•Seven more than a number
• A number increased by seven
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English & Algebra
SUBTRACTION
The following words translate as
SUBTRACTION:
•Minus
•Difference
•Subtract
•Subtracted From
•Take away
•Less Than
•Decreased by
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X-7
The following phrases would
translate to : x  7
•A number minus seven
•The difference of a number and
seven
•Subtract a number and seven
•Seven subtracted from a number
•Seven take away a number
•Seven less than a number
• A number decreased by seven
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English & Algebra
MULTIPLICATION
The following words translate as
MULTIPLICATION:
•Multiplied by
•Multiply
•Product
•Times
•Of
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7x
The following phrases would
translate to : 7x
•A number multiplied by seven
•Multiply seven and a number
•The product of a number and seven
•The product of seven and a number
•Seven times a number
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English & Algebra
DIVISION
The following words translate as
DIVISION:
•Divided by
•Divide
•Quotient
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x/7
The following phrases would
translate to :
x
7
•A number divided by seven
• Divide a number by seven
•The quotient of a number and seven
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7/x
The following phrases would
7
translate to :
x
•Seven divided by a number
• Divide a seven by a number
•The quotient of seven and a number
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“OF”
“Half of a number” would be
1
x
2
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or
0.5x
or
x
2
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“OF”
“Thirty percent of a number” is:
30
x
100
or
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0.3x
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“Twice” or “Double”
•“Twice a number” is:
2x
•“Double a number” is:
2x
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Translate a Phrase
“Seven more than twice a number”
Seven more than twice a number
2x  7
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Translate a Phrase
“Seven less than twice a number”
Seven less than twice a number
2x  7
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Translate a Phrase
(watch for the comma)
“the quotient of seven and
a number increased by two”
7
x2
“the quotient of seven and a number,
increased by two”
7
2
x
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Salary Increase?
Suppose you will get
a salary increase of 3%.
Let
s represent your old salary.
The increase is 3% of your current
salary, so 0.03s is the increase.
Your new salary will be the sum of
the old salary and the increase.
So, s + 0.03s is your new salary.
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Discount?
Suppose the bookstore has all
merchandise on sale for 15% off.
Let p represent the regular price.
The discount is 15% of the regular
price, so 0.15p is the discount.
The sale price will be the
difference of the regular price
and the discount
So, p - 0.15p is the sale price.
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That’s All for Now!
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