1. 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.
( ) 4 X 3 2
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2. 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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3. Getting Started with Algebra
Where did the word
Algebra
originate ?
The word is from
Kitab al-Jabr wa-l-Muqabala
which was a book written in approximately 820 A.D. by a Persian mathematician.
Algebra
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4. a letter used to represent various numbers.
Variables
variable
A is
a letter used to represent various numbers. X
“x” is frequently used as the variable, but many other letters can be used.
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5. leg inseam measurement L
Variables
For example, jean sizes are often given by waist and leg inseam measurements.
waist measurement W
leg inseam measurement L
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6. Here are three examples:
Define each Variable
We must always define what quantity or measurement the letter represents.
Here are three examples: X
= unknown number W
= waist measurement
= leg inseam measurement L
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7. = the speed of light in Einstein’s equation E = mc2 c
Constants
A is
constant
a letter used to represent a number that doesn’t change its value in the problem. For example:
= “pi” = …. p
= the speed of light in Einstein’s equation E = mc2 c
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8. Algebraic ExpressionsAn
algebraic expression
is a mathematical phrase using variables, constants, numerals, & operation signs.
algebraic expression An
will NOT have any of the following symbols: = > < > <
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9. Algebraic Expressions: Examples
x is the variable.
+ is the operation
5 is a numeral and a constant.
is the
algebraic expression
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10. Algebraic Expressions: Examples
p is the variable.
. is the indicated operation
3 is a numeral and a constant.
is the
algebraic expression
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11. Algebraic Expressions: Examples
z is the variable.
- is the operation
9 is a numeral and a constant.
is the
algebraic expression
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12. Algebraic Expressions: Examples
y is the variable.
÷ is the operation
5 is a numeral and a constant.
is the
algebraic expression
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13. Algebraic Expressions: Examples
x and y are variables.
 and + are operations
2 and 5 are numerals and constants.
is the
algebraic expression
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14. Algebraic Expressions: Examples
x and y are variables.
+ ÷  are operations
5 and 2 are numerals and constants.
is the
algebraic expression
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15. 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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16. 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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17. Evaluate an Expression: Example 1a
when
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18. Evaluate an Expression: Example 1b
when
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19. Evaluate an Expression: Example 1c
when
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20. Evaluate an Expression: Example 1d
when
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21. Evaluate an Expression: Example 2
a) when
b) when
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22. Evaluate an Expression: Example 3
when
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23. Evaluate an Expression: Example 4a
when
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24. Evaluate an Expression: Example 4b
when
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25. Evaluate an Expression: Example 5
When and
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26. Evaluate an Expression: Example 6a
When and
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27. Evaluate an Expression: Example 6b
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28. Evaluate an Expression: Example 6c
When and
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29. Application: Area of a Rectangle
The AREA of a Rectangle
Area = length x width
A=l.w
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30. 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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31. English & Algebra ADDITION
The following words translate as ADDITION:
Plus
Sum
Add
Added to
Total
More than
Increased by
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32. The following phrases would translate to :
X + 7
The following phrases would translate to :
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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33. English & Algebra SUBTRACTION
The following words translate as SUBTRACTION:
Minus
Difference
Subtract
Subtracted From
Take away
Less Than
Decreased by
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34. The following phrases would translate to :
X - 7
The following phrases would translate to :
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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35. English & Algebra MULTIPLICATION
The following words translate as MULTIPLICATION:
Multiplied by
Multiply
Product
Times Of
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36. The following phrases would translate to :7x
The following phrases would translate to :
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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37. English & Algebra DIVISION
The following words translate as DIVISION:
Divided by
Divide
Quotient
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38. The following phrases would translate to :
x/7
The following phrases would translate to :
A number divided by seven
Divide a number by seven
The quotient of a number and seven
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39. The following phrases would translate to :
7/x
The following phrases would translate to :
Seven divided by a number
Divide a seven by a number
The quotient of seven and a number
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40. “OF”
“Half of a number” would be or or
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41. “OF”
“Thirty percent of a number” is: or
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42. “Twice” or “Double” “Twice a number” is: “Double a number” is: 1.1 S
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43. Translate a Phrase “Seven more than twice a number” Seven more than
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44. Translate a Phrase (watch for the comma)
“the quotient of seven and a number increased by two”
“the quotient of seven and a number, increased by two”
comma
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45. 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 s is your new salary.
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46. 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 p is the sale price.
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47. Screen bean sampler NO
Remember !
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