Post on 06-Apr-2018
8/3/2019 Applied Math Chptr1
1/27
8/3/2019 Applied Math Chptr1
2/27
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.
8/3/2019 Applied Math Chptr1
3/27
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.
8/3/2019 Applied Math Chptr1
4/27
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.
8/3/2019 Applied Math Chptr1
5/27
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.
8/3/2019 Applied Math Chptr1
6/27
Place ValuePlace valueof a digit
determines its value and eachplace has a value ten timesas that of the place to the
right.
8/3/2019 Applied Math Chptr1
7/27
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 ..
8/3/2019 Applied Math Chptr1
8/27
Place value chart for mixed decimals
digits Place names
3 hundreds
1 tens4 ones
. decimal point
2 tenths7 hundredths
5 thousandths
6 ten-thousandths
8/3/2019 Applied Math Chptr1
9/27
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.
8/3/2019 Applied Math Chptr1
10/27
Write in words: 1. 346,745
2. 400,352,081
3. 27,357,462.5
4. 269,458.25
5. 80,001.02003
8/3/2019 Applied Math Chptr1
11/27
DRILL EXERCISES
8/3/2019 Applied Math Chptr1
12/27
Write in words. 1. 37,569
2. 29,058
3. 346,745
4. 27,357,462.5
5. 251,000,000.0001
8/3/2019 Applied Math Chptr1
13/27
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.
8/3/2019 Applied Math Chptr1
14/27
FundamentalOperations on WholeNumbers andDecimals
8/3/2019 Applied Math Chptr1
15/27
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.
8/3/2019 Applied Math Chptr1
16/27
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
8/3/2019 Applied Math Chptr1
17/27
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.
8/3/2019 Applied Math Chptr1
18/27
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.
8/3/2019 Applied Math Chptr1
19/27
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
8/3/2019 Applied Math Chptr1
20/27
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
8/3/2019 Applied Math Chptr1
21/27
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.
8/3/2019 Applied Math Chptr1
22/27
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%
8/3/2019 Applied Math Chptr1
23/27
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?
8/3/2019 Applied Math Chptr1
24/27
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
8/3/2019 Applied Math Chptr1
25/27
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:
8/3/2019 Applied Math Chptr1
26/27
Formula: Gross Sales
- Sales Returns and Allowances
___________________________
Net Sales
- Cost of Goods Sold
___________________________
Gross Profit - Operating Expenses
___________________________
NET PROFIT
8/3/2019 Applied Math Chptr1
27/27
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