finanical math

8/13/2019 Finanical Math

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Lifetime Learning, Building Success

1

Mawarid Induction Program

Mathematics & Algebra




2

Topics to be Covered

• Unit 1 Operations with Whole Numbers

• Unit 2 Fractions• Unit 3 Decimals & Percentages

• Unit 4 Exponents or Powers

• Unit 5 Solving Algebraic Equations

• Unit 6 Solving Word Problems




3

Unit 1

Operations with Whole Numbers




4

The Order of Operations

• B - Brackets (innermost first)

• E - Exponents

• D - Division (from left to right)

• M - Multiplication (from left to right)

• A - Addition (from left to right)• S - Subtraction (from left to right)




5

Examples

Ex 1: 3 - 4 + 2 = ?

-1 + 2 = 1

Ex 2: 2 + 6 x 4 2 = ?

2 + 6 x 2 = ?

2 + 12 = 14




6

Examples (cont’d)

Example 3: 2 x (3 + 5) 4 + 2

2 x 8 4 + 2

2 x 2 + 2

4 + 2 = 6

Example 4: 2 + (3 - (2 + 5) x 2) = ?

2 + (3 - 7 x 2) =2 + (3 - 14) =

2 +(- 11) = -9


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7

Examples (cont’d)

Example 5: 42 - (3 - 23 x 4) = ?

42 - (3 - 8 x 4) =

42 - (3 - 32) =

42 - (-29) =

16 + 29 = 45



8

Unit 2

Fractions



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Improper Fractions and

Mixed Numbers• An improper fraction is where the

numerator is larger than the denominator

(Ex: 9/6)• A mixed number is where there is a whole

number and a fraction put together

– (Ex: 2 3/4)



10

Changing Improper Fractions into

Mixed Numbers• Divide the denominator into the numerator

to determine the whole number part of the

mixed number• If there is a remainder, it should be used as

the numerator which goes over the existing

denominator – Example: 9/4 becomes 2 1/4



11

Changing Mixed Numbers to

Improper Fractions• Multiply the whole number part of the

mixed number by the denominator, then add

the numerator• Place that number over the denominator

– Example: 3 4/5 becomes 19/5



12

Adding & Subtracting Fractions

• We must make a common denominator in

order to add & subtract fractions

• Once the common denominator isdetermined, the fractions must be changed

into equivalent fractions

• Then the numerators are added orsubtracted and placed over the common

denominator



13

Adding & Subtracting Fractions

• Example: 2/3 + 3/4 = ?

• Solution:

– The lowest common denominator is 12

– The fractions are converted to 8/12 + 9/12

– The answer is 17/12 or 1 5/12



14

Multiplication of Fractions

• Multiply the numerator of the first fraction by

the numerator of the second fraction

• Multiply the denominator of the first fraction by the denominator of the second fraction

– Example: 3/5 x 1/4

– Solution: Numerator 3 x 1 = 3

– Denominator 5 x 4 = 20

– therefore 3/20 is the solution



15

Division with Fractions

• Turn the second fraction upside down, then

follow the rules for multiplication of fractions

– Example: 3/4 2/5

– Solution:

1. Turn the second fraction upside down (3/4 x 5/2)

2. Multiply numerators and denominators3. The answer is therefore 15/8 or 1 7/8



16

Unit 3

Decimal Numbers & Percentages



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Decimal Numbers

• They are a different way of representing an

amount other than in fraction form

• They are a series of digits separated by a dot

• The digits to the left of the dot represent a

whole number

• The digits to the right of the dot represent

an amount that is less than one

– Example: 25.55




Percentages (%)

• Is a method of expressing an amount in

terms of a part of one hundred

• It is like a fraction that has 100 as thedenominator (25/100 = 25%)

• 100% of an amount means the entire

amount




Converting Fractions to Decimals

• Simply divide the numerator by the

denominator

– Example: 3/5

– Solution: 3 5 = .6




Converting a Fraction

to a Percent• Convert the fraction to an equivalent

fraction that has a denominator of 100

• Place the % sign to the right of thenumerator amount

– Example: 3/5 = 60/100 = 60%




Converting a Decimal

to a Percent• Multiply the decimal number by 100, then

place a % sign after it

• Or, move the decimal point two places tothe right, then place a % sign after it

– Example: 0.57

– Solution: 0.57 x 100 = 57%




Converting a Percent

to a Decimal• Divide the percentage by 100 and take away

the % sign

• Or, move the decimal point two places tothe left, then remove the % sign

– Example: 28.0 %

– Solution: 28.0/100 = .28




Unit 4

Exponents or Powers




What is an Exponent?

• It is when a number is multiplied by itself

“n” times, if “n” is the exponent

• Given the expression 23:

– The 2 is called the “base”

– The 3 is called the “exponent”

– The expression 23 is called a “Power”

– The 2 is multiplied by itself 3 times 2 x 2 x 2

– The answer is 8




Negative Exponents

• Exponents (n) can be negative numbers

• It means that the number raised to the

negative power (-n) is a denominator raisedto the positive power (n) where one (1) is

the numerator

– Example: 2-4 = 1/24 = 1/(2x2x2x2) = 1/16




Powers of Ten (10)

• Given the expression 103 , we simply need

to write a 1 with 3 - 0’s beside it in order to

get the solution 1000101 = 10

102 = 100

104 = 10000100 = 1 (any number with a 0 exponent = 1)

10-6 = 1/1000000




Operations with Exponents

Having the Same Base• Addition/Subtraction

– if we have the expression 23 + 24 , we must

calculate each expression before adding themtogether (solution 8 + 16 = 24)

– if we have the expression 23

- 22

, we mustcalculate each expression before subtracting

them (solution 8 - 4 = 4)





Having the Same Base (Cont’d) • Multiplication

– If we have the expression 32 x 34 , we can

simplify the expression by adding theexponents (n) together and using the sum as the

exponent for the base of 3 as follows:

32 x 34 = 32 +4 = 36 = 729

It is simply (3 x 3) x (3 x 3 x 3 x 3) = 36





Having the Same Base (Cont’d) • Division

– If we have the expression, 34 32 , we can

simplify the expression by subtracting thesecond exponent from the first one and using

the result as the exponent (n) for the base of 3

as follows:

34 32 = 34-2 = 32 = 9




Unit 5

Solving Algebraic Equations




Equations with one

Unknown Variable• An equation is an equality between two

mathematical terms

• These terms can be numbers, variables(expressed with letters), or a combination of

both

• For Example: 3n + 5 = 14 is an algebraicequation with “n” being the unknown

variable




Solving Equations with one

Unknown Variable• First we need to collect alike terms on each

side of the equation

• Second, we need to perform operations toisolate numbers on one side of the equation

and variables on the other side

• In order for the equation to remainunaffected, whatever we do to one side of the

equation, we must also do to the other side




Examples

#1. 2n + 3n + 4n = 3 + 5 + 10

Solution:

Step 1. Collect alike terms 9n = 18

Step 2. Divide both sides by 9 n = 2




Examples

#2. 3n + 5 = 20

Solution:

Step 1. Subtract 5 from both sides 3n = 15





Examples

#3. 2n + 4 = 3n - 2

Solution:

Step 1. Subtract 2n from both sides

4 = n - 2

Step 2. Add 2 to each side

6 = n or n = 6




Examples

# 4. 3(2n + 5) = n + 20

Solution:

Step 1. Multiply the terms in the brackets by 36n + 15 = n + 20

Step 2. Subtract n from both sides

5n + 15 = 20Step 3. Subtract 15 from both sides 5n = 5





Unit 6

Solving Word Problems




Percentage Increases &

Decreases• When prices or interest rates go up or down

we must be able to compute the new price

or the rate of change etc.• The formula for solving problems like these

is as follows:

New Amount - Original Amount = Rate of ChangeOriginal Amount




Example #1

If the original price of a clock was $80 and then

it went up by 20%, what was the new price of

the clock?Solution: Let X = New Amount

Original Amount = $80

Rate of Change = 20% or .20

X - 80 = .20 > X - 80 = 16 > X = 96

80




Example #2

A stock price went up by 25% to $100.

What was the price before it went up?

Solution: Let X = Original Amount

New Amount = 100 Rate of Change = 25%

100 - X = .25 > 100 - X = .25X

X

100 = 1.25X > X = 80



Example #3

• The price of a shirt went from $50 to $40.

What was the % change in price?

Solution: Let X = rate of change in price

New Amount = 40 Original Amount = 50

40 - 50 = X > - 10 = X

50 50

X = - .20 or - 20%

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