1.1 SKM & PP 1 Getting Started with Algebra What isAlgebra? is a branch of mathematics in which symbols, usually letters, are used to represent quantities.

1.1 S KM & PP 1

Getting Started with Algebra

What isAlgebra ?

is a branch of mathematics in which symbols, usually letters,are used to represent quantities that can be replaced by a number oran expression.

Algebra

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Who invented Algebra ?

is a reasoning skill and language that developed and evolved along with civilization.

No one person invented

Algebra

Algebra

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Where did the word

Algebraoriginate ?

The word is from Kitab al-Jabr wa-l-Muqabalawhich was a book written in approximately 820 A.D. by a Persian mathematician.

Algebra

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Variables

A is

variable

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 inseammeasurement

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Define each Variable

We must always define what quantity or measurement

the letter represents.Here are three examples:

= waist measurement

= leg inseammeasurement

= unknown number

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Constants

A is

constant

a letter used to represent a number that doesn’t change its value

in the problem. For example:

= the speed of light in Einstein’s equation E = mc2

= “pi” = 3.1416….

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AlgebraicExpressions

An algebraic expressionis a mathematical phrase

using variables, constants, numerals, & operation signs. An algebraic

expressionwill NOT have any of the

following symbols:

= > < > <

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Algebraic Expressions: Examples

5x x is the variable.

+ is the operation

5 is a numeral and a constant.

5x algebraic expressionis the

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p3p is the variable.

. is the indicated operation


p3 algebraic expressionis the

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z9 z is the variable.

- is the operation


z9 algebraic expressionis the

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y5

y is the variable.

÷ is the operation


y5

algebraic expressionis the

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y5x2

x and y are variables.

and + are operations

2 and 5 are numerals and constants.y5x2 algebraic expressionis the

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2y5x

x and y are variables.

+ ÷ are operations

5 and 2 are numerals and constants.

2x5x

algebraic expressionis the

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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

evaluatingthe expression.

Evaluating means you will compute a numerical

value.

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Evaluate an Expression:Example 1a

5x Evaluate

4x

5)4(

9

when

5x

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Evaluate an Expression:Example 1b

5x Evaluate

0x

5)0(

5

when

5x

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Evaluate an Expression:Example 1c

5x Evaluate

3x

5)3( 8

when

5x

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Evaluate an Expression:Example 1d

5x Evaluate

5x

5)5(

0

when

5x

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Evaluate an Expression: Example 2

p3Evaluate

5pa) when

p3 )5(3 152p b) when

p3 )2(3 6

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Evaluate an Expression: Example 3

z9 5zwhen

z9

459

Evaluate

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Evaluate an Expression:

Example 4a

y5

5ywhen

y5

55

1

Evaluate

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Evaluate an Expression:

Example 4b

y5

0y when

y5

05

undefined

Evaluate

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Evaluate an Expression:Example 5

y5x2 4x When and 1y

y5x2 )1(5)4(2

)5(813

Evaluate

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Evaluate an Expression: Example 6a

25

yxEvaluat

e

4x When and 1y

25

yx

2)1(5)4(

39

3

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Evaluate an Expression: Example 6b

2y5x

Evaluat

e

8y

2y5x

2)8(5)7(

612

2

andWhenx 7

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Evaluate an Expression: Example 6c

2y5x

Evaluat

e

4x When and 2y

2y5x

2)2(5)4(

09

undefined

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Application: Area of a Rectangle

The AREA of a Rectangle

Area = length x width

A=l.w

cm6w

cm16l

cm6cm16A 2cm96A

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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 :

•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

7x

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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


•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

7x

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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 : x7

•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


7x

•A number divided by seven

• Divide a number by seven

•The quotient of a number and seven

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7/x


x7

•Seven divided by a number

• Divide a seven by a number

•The quotient of seven and a number

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“OF”

x21

•“Half of a number” would be

2x

x5.0or

or

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“OF”

x10030

•“Thirty percent of a number” is:

x3.0or

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“Twice” or “Double”

x2

•“Twice a number” is:

x2

•“Double a number” is:

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Translate a Phrase

x2

“Seven more than twice a number”

7

Seven more than

twice a number

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Translate a Phrase (watch for the

comma)

2x

“the quotient of seven anda number increased by two”

7

2x7

“the quotient of seven and a number,

increased by two”

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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.

1.1 SKM & PP 1 Getting Started with Algebra What isAlgebra? is a branch of mathematics in which symbols, usually letters, are used to represent quantities.

Documents

pp variablesfor example

awhen evaluatekm pp

bwhen evaluatekm pp

algebrakm pp variablesa

algebraic expressionwhen

numerical value

leg inseam measurements

variablea letter