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Getting Started with Algebra

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Presentation on theme: "Getting Started with Algebra"— Presentation transcript:

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 1.1 S KM & PP

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 1.1 S KM & PP

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 1.1 S KM & PP

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. 1.1 S KM & PP

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 1.1 S KM & PP

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 1.1 S KM & PP

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 1.1 S KM & PP

8 Algebraic Expressions
An algebraic expression is a mathematical phrase using variables, constants, numerals, & operation signs. algebraic expression An will NOT have any of the following symbols: = > < > < 1.1 S KM & PP

9 Algebraic Expressions: Examples
x is the variable. + is the operation 5 is a numeral and a constant. is the algebraic expression 1.1 S KM & PP

10 Algebraic Expressions: Examples
p is the variable. . is the indicated operation 3 is a numeral and a constant. is the algebraic expression 1.1 S KM & PP

11 Algebraic Expressions: Examples
z is the variable. - is the operation 9 is a numeral and a constant. is the algebraic expression 1.1 S KM & PP

12 Algebraic Expressions: Examples
y is the variable. ÷ is the operation 5 is a numeral and a constant. is the algebraic expression 1.1 S KM & PP

13 Algebraic Expressions: Examples
x and y are variables.  and + are operations 2 and 5 are numerals and constants. is the algebraic expression 1.1 S KM & PP

14 Algebraic Expressions: Examples
x and y are variables. + ÷  are operations 5 and 2 are numerals and constants. is the algebraic expression 1.1 S KM & PP

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. 1.1 S KM & PP

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. 1.1 S KM & PP

17 Evaluate an Expression: Example 1a
when 1.1 S KM & PP

18 Evaluate an Expression: Example 1b
when 1.1 S KM & PP

19 Evaluate an Expression: Example 1c
when 1.1 S KM & PP

20 Evaluate an Expression: Example 1d
when 1.1 S KM & PP

21 Evaluate an Expression: Example 2
a) when b) when 1.1 S KM & PP

22 Evaluate an Expression: Example 3
when 1.1 S KM & PP

23 Evaluate an Expression: Example 4a
when 1.1 S KM & PP

24 Evaluate an Expression: Example 4b
when 1.1 S KM & PP

25 Evaluate an Expression: Example 5
When and 1.1 S KM & PP

26 Evaluate an Expression: Example 6a
When and 1.1 S KM & PP

27 Evaluate an Expression: Example 6b
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28 Evaluate an Expression: Example 6c
When and 1.1 S KM & PP

29 Application: Area of a Rectangle
The AREA of a Rectangle Area = length x width A=l.w 1.1 S KM & PP

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. 1.1 S KM & PP

31 English & Algebra ADDITION
The following words translate as ADDITION: Plus Sum Add Added to Total More than Increased by 1.1 S KM & PP

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 1.1 S KM & PP

33 English & Algebra SUBTRACTION
The following words translate as SUBTRACTION: Minus Difference Subtract Subtracted From Take away Less Than Decreased by 1.1 S KM & PP

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 1.1 S KM & PP

35 English & Algebra MULTIPLICATION
The following words translate as MULTIPLICATION: Multiplied by Multiply Product Times Of 1.1 S KM & PP

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 1.1 S KM & PP

37 English & Algebra DIVISION
The following words translate as DIVISION: Divided by Divide Quotient 1.1 S KM & PP

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 1.1 S KM & PP

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 1.1 S KM & PP

40 “OF” “Half of a number” would be or or 1.1 S KM & PP

41 “OF” “Thirty percent of a number” is: or 1.1 S KM & PP

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 1.1 S KM & PP

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. 1.1 S KM & PP

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. 1.1 S KM & PP

47 Screen bean sampler NO Remember ! 1.1 S KM & PP


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