Applied Math Chptr1

8/3/2019 Applied Math Chptr1

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ARITHMETICThe study of numbers and the ways

they are used in making calculations is

called arithmetic.In arithmetic, there are four

fundamental operations or basic

processes. These are addition,subtraction, multiplication, and division.


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Number and Numeral A numberis one or more units or things.

A number that denotes one or more

whole units is a whole numberor aninteger. A number that denotes a part orportion of a unit is called a fraction. A

mixed numberis a combination of awhole number and a fraction. A numberpreceded by a decimal point and whosevalue is less than one unit is called adecimal.


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Combination of a whole number and adecimal is a mixed decimal. A decimal

fraction or decimal is another way ofrepresenting a fraction whose denominatoris in the power of 10.

For example, the fraction 7/10 represents0.7 in decimal. A complex decimalis anumber consisting of a decimal or mixed

decimal and a fraction. Examples are 0.331/3 and 0.66 2/3.


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Numeration System A system of reading and writing numbers

is a numeration system. This consists of

symbols and rules or principles on how touse theses symbols. Our system ofreading and writing numbers is thedecimal system or the Hindu-Arabic

system. Ten digits are used ---0,1,2,3,4,5,6,7,8, and 9. This system isbased on groups of ten. It uses the placevalue concept.


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Place ValuePlace valueof a digit

determines its value and eachplace has a value ten timesas that of the place to the

right.


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Place value chart for whole numbers:

PERIODS PLACE NAMES

units ones, tens, hundreds

thousands thousands, ten thousands,

hundred thousands

millions millions, ten millions, hundredmillions

billions Billions, ten billions, hundredbillions

trillions trillions,

uadrillions uadrillions ..


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Place value chart for mixed decimals

digits Place names

3 hundreds

1 tens4 ones

. decimal point

2 tenths7 hundredths

5 thousandths

6 ten-thousandths


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Examples: Write in figures. 1. six hundred nineteen billion, eight hundred

four million, eleven thousand and seventhousandths.

2. ten million, three hundred forty-fourthousand, five hundred twenty-one.

3. three thousand four hundred fifty-two tenthousandths.

4. ninety trillion, eighty million, twentythousand.


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Write in words: 1. 346,745

2. 400,352,081

3. 27,357,462.5

4. 269,458.25

5. 80,001.02003


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DRILL EXERCISES


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Write in words. 1. 37,569

2. 29,058

3. 346,745

4. 27,357,462.5

5. 251,000,000.0001


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Write in figures. 1. Twelve million, three hundred forty-

three thousand, five hundred twenty-one.

2. Three hundred four million, sevenhundred nine thousand, four hundred six.

3. Three thousand four hundred fifty-twoten thousandths.

4. Two million, five thousand pesos.

5. Three thousand, one hundred twelvedollars and thirteen cents.


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FundamentalOperations on WholeNumbers andDecimals


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A. Addition Additionis the process of combining two

or more similar numbers or quantities.

Thus, seven pesos can be added to threepesos, the sum is ten pesos. But sevenpesos cannot be added to three dollars.

Addendsare numbers to be added. Theanswer in addition is called sum or total.


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Laws of Addition 1. Commutative Law: We can change the

order of the addends without changing thesums. Ex: 3+4 = 4+3

2. Associative Law: We can change thegrouping of the addends without changingthe sums. Ex: (3+4)+6 = 3+(4+6)

3. Identity Law: Zero is the identitynumber in addition. If we add zero to acertain number, the answer is the certainnumber. Ex: 8 + 0 = 8 ; 0 + 2 = 2


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B. Subtraction Subtractionis the process of taking one

number from another showing how much

is left. It is the inverse of addition. Thelarger number from which something is tobe subtracted is called the minuend.

Subtrahendis the smaller number to besubtracted. The answer is calleddifferenceor remainder. Like in addition,only similar numbers can be subtracted.


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C. Multiplication

Multiplicationis the process of combining equaladdends as many times as there are units inanother number. Hence, it is repeatedaddition. The answer in multiplication is the

product. The number to be multiplied a certainnumber of times is called the multiplicand. Thenumber of times it is to be added or multipliedis called the multiplier. Two or more numbers

that are multiplied together are called thefactors. The multiplier and the multiplicand arefactors of the product.


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Properties or Laws ofMultiplication 1. Commutative Property: We can change the

order of the factors without changing theproducts. Ex: 3x4 = 4x3

2. Associative Property: We can change thegrouping of the factors without changing theproducts. Ex:(3x4)x5 = 3x(4x5)

3. Zero Property: The product of zero timesany number is zero.

Ex: 0x5 = 0 ; 15x0 = 0


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4. Identity Property: The multiplicativeidentity element is one. A certain number

multiplied by one is that certain number. Ex: 1 x 5 = 5 ; 17 X 1 = 17

5. Distributive Property: Renaming afactor as an addition expression will givethe same product as simply multiplying the

factors. Ex: 5 x (10+3) = 5 x 13 ; 65 = 65


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D. Division Divisionis the process of finding how many

times one number is contained in another. It isthe process of separating a number into agiven number of equal parts. It is the inverseof multiplication and a short method ofsubtraction.

The dividendis the number to be divided or tobe separated into equal parts. The divisoristhe number by which the dividend is divided.The quotientis the answer in division.


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E. Averages Simple Average

To get the simple average, we get the sum

of all the given values and divide the sum bythe number of values.

Example:

Find the average of the following grades:85%, 78%, 87%, 80%,83%,90%

Sum is 503% ; the average is 503/6 = 83 5/6%


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Weighted Average To get the weighted average, we multiply

the quantities by the measures involved.

Then, we divide the sum of the productsby the sum of the quantities.

EX: a sewer made 10 bags. On 3 bags,

she spent 2 hours each, on 4 bags, 3hours each; and on 3 bags, I hour each.What was the average time spent oneach bag?


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Solution: 3 bags x 2 hours = 6 hours

4 bags x 3 hours = 12 hours

3 bags x 1 hour = 3 hours

________________________

10 bags 21 hours

21hours / 10 bags = 2.1 hours or

2 hours and 6 minutes


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F. Four FundamentalOperations in Business PROFIT AND LOSS

Profitis the amount by which the sales are

greater than the cost of goods sold and theoperating expenses.

Margin also means gain or profit.

The formula in computing profits is:


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Formula: Gross Sales

- Sales Returns and Allowances

___________________________

Net Sales

- Cost of Goods Sold

___________________________

Gross Profit - Operating Expenses

___________________________

NET PROFIT


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Define the following terms(discussbriefly):

1. Gross sales 2. Refunds

3. Net sales

4. Cost of goods sold or buying price

5. Inventory

6. Gross profit

7. Operating expenses

8. Net profit

9. Gross loss

10. Net loss

Applied Math Chptr1

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