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Nouns can be concrete or abstract. Concrete nouns are ―sense‖ nouns. You can see, hear,

smell, taste, and/or touchthem. Abstract nouns are ideas or concepts  – things that you feel or 

think about.

Example: The lonely dog pushed at the fence, longing for freedom.

Dog and fence are concrete nouns. Freedom is an abstract noun.

from the Anthology of Philippine Myths by Damiana L. Eugenio

1According to Maranaw folklore, this world was created by a great Being. It is not known,

however, who exactly is this great Being. Or how many days it took him to create this world.

2This world is divided into seven layers. The earth has also seven layers. Each layer is

inhabited by a different kind of being. The uppermost layer, for example, is the place weare

inhabiting. The second layer is being inhabited by dwarfs. These dwarfs are short, plump, and

long-haired. They are locally known as Karibanga. The Karibanga are said to possess magical

powers. They are usually invisible to the human eye. The third layer of the earth which is found

under the sea or lake is inhabited by nymphs. These nymphs also possess certain magical

powers. It is

stated in the story of Rajah Indarapatra that he met and fell in love with the princessnymph with

whom he had a child.

3The sky also consists of seven layers. Each layer has a door which is guarded day and nightby huge mythical birds called garoda. The seventh layer of the sky is the seat of heaven which

is also divided into seven layers. Every layer in the sky is inhabited by angels. Maranaws

believe that angels do not need food. They all possess wings with which they fly.

4Heaven which is found on the seventh layer of the sky is where good people‗s spirits go after 

death. Saints are assigned to the seventh layer while persons who barely made it‖ are

confined to the lower most layer which is found at the bottom of heaven.

5It is in heaven where we find the tree-of-life. On each leaf of the tree-of-life is written the name

of every person living on earth. As soon as a leaf ripens or dries and falls, the person whose

name it carries also dies.6The soul of every person is found in tightly covered jars kept in one section of heaven. This

particular section of heaven is closely guarded by a monster with a thousand eyes, named

Walo. Walo, in addition to his thousand eyes, has also eight hairy heads. The epic Darangan

speaks of Madale, Bantugan‗s brother and, Mabaning, Husband of Lawanen, entering this

section and retrieving the soul of Bantugan.

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from the Anthology of Philippine Myths by Damiana L. Eugenio

1According to Maranaw folklore, this world was created by a great Being. It

is not known, however, who exactly is this great Being. Or how many days

it took him to create this world.

2This world is divided into seven layers. The earth has also seven layers.

Each layer is inhabited by a different kind of being. The uppermost layer,

for example, is the place weare inhabiting. The second layer is being

inhabited by dwarfs. These dwarfs are short, plump, and long-haired. They

are locally known as Karibanga. The Karibanga are said to possess

magical powers. They are usually invisible to the human eye. The third

layer of the earth which is found under the sea or lake is inhabited by

nymphs. These nymphs also possess certain magical powers. It isstated in the story of Rajah Indarapatra that he met and fell in love with the

princessnymph with whom he had a child.

3The sky also consists of seven layers. Each layer has a door which is

guarded day and night by huge mythical birds called garoda. The seventh

layer of the sky is the seat of heaven which is also divided into seven

layers. Every layer in the sky is inhabited by angels. Maranaws believe that

angels do not need food. They all possess wings with which they fly.

4Heaven which is found on the seventh layer of the sky is where good

people‗s spirits go after death. Saints are assigned to the seventh layer while persons who barely made it‖ are confined to the lower most layer 

which is found at the bottom of heaven.

5It is in heaven where we find the tree-of-life. On each leaf of the tree-of-life

is written the name of every person living on earth. As soon as a leaf ripens

or dries and falls, the person whose name it carries also dies.

6The soul of every person is found in tightly covered jars kept in one

section of heaven. This particular section of heaven is closely guarded by a

monster with a thousand eyes, named Walo. Walo, in addition to his

thousand eyes, has also eight hairy heads. The epic Darangan speaks of 

Madale, Bantugan‗s brother and, Mabaning, Husband of Lawanen,entering this section and retrieving the soul of Bantugan.

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Real Numbers

The type of number we normally use, such as 1, 15.82, -0.1, 3/4, etc… 

Positive or negative, large or small, whole numbers or decimal numbers

are all Real Numbers.They are called "Real Numbers" because they are not Imaginary

Numbers.

Examples of Real Numbers 

  Natural numbers, whole numbers, integers, decimal numbers, rational

numbers, and irrational numbers are the examples of real numbers.

  Natural Numbers = {1, 2, 3,...}

  Whole Numbers = {0, 1, 2, 3,...}

  Integers = {..., -2, -1, 0, 1, 2,...}

  , 10.3, 0.6, , , 3.46466466646666..., , are few more examples.

Whole Numbers

Definition of Whole Numbers 

  The numbers in the set {0, 1, 2, 3, 4, 5, 6, 7, . . . . } are called whole numbers.  

  In other words, whole numbers is the set of all counting numbers plus zero. 

More about Whole Numbers 

  Whole numbers are not fractions, not decimals.

  Whole numbers are nonnegative integers.

Solved Example on Whole Numbers Annual revenues of three companies are $4,234,223, $6,246,234 and $2,234,233.Which of them is the least?

Choices: A. $2,234,233

B. $4,234,223C. $6,246,234

Correct Answer: ASolution:

Step 1: To compare numbers, begin with the greatest place and compare thedigits.

Step 2: [Write the whole numbers one below the other to compare thedigits in the corresponding places.]

4 2 3 4 2 2 36 2 4 6 2 3 4

2 2 3 4 2 3 3Step 3: 2 million is less than 4 millions and 6 million. [Digits in the millions

place.]

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Step 4: So, 2,234,233 is less than 4,234,223 and 6,246,234.

Step 5: Revenue of $2,234,233 is the least among the given.

Natural Numbers

Definition of Natural Numbers 

  All the counting numbers 1, 2, 3,... are called Natural Numbers.

More about Natural Numbers 

  The set of natural numbers is represented by using the symbol N.

  The main purpose of the natural numbers is counting and ordering.

  All natural numbers are whole numbers but all whole numbers are not natural

numbers.

  A natural number can be written in the form of rational number as . So,all natural numbers are rational numbers.

  The square of any natural number can be expressed as a sum of oddnumbers.

  Natural numbers are a subset of the whole numbers, the integers, the rationalnumbers, and the real numbers.

Examples of Natural Numbers 

Rational Numbers

Definition of Rational Numbers 

  A Rational Number is a real number written as a ratio of integers with a non-

zero denominator.More about Rational Numbers 

  Rational numbers are indicated by the symbol .

  Rational number is written in form, where p and q are integers and q is anon-zero denominator.

  All the repeating or terminating decimal numbers are rational numbers.

  Rational numbers are the subset of real numbers.

Examples of Rational Numbers 

  , 10.3, 0.6, , - All these are examples of rational numbers as they

terminate.

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 Irrational Number

Definition of Irrational Number 

  Irrational numbers are real numbers that cannot be expressed as fractions,terminating decimals, or repeating decimals.

Examples of Irrational Number 

  are few examples of irrational numbers.

Solved Example on Irrational Number Identify the irrational number.

Choices:A. 0.3

B.

C.D.

Correct Answer: C 

Step 1: The value of is 2.4494897427831780981972840747059. . .

Step 2: The value of is 5.

Step 3: The value of is 0.6.

Step 4: Among the choices given, only is an irrational number.

Counting Numbers

Definition of Counting Numbers 

  The numbers which are used for counting from one to infinity are calledCounting Numbers.

More about Counting Numbers 

  Counting numbers are also called as natural numbers.

Examples of Counting Numbers 

  There are 7 apples in the basket shown above.Solved Example on Counting Numbers 

Which of the following is not a counting number?Choices: 

A. 30

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B. 9

C. 0D. 10

Correct Answer: C Solution: 

Step 1: The numbers which are used for counting from one to infinity are calledcounting numbers.

Step 2: 30, 9, and 10 are counting numbers.Step 3: So, 0 is not a counting number.Integers 

Defin i t ions 

  The number line goes on forever in both directions. This is indicated by thearrows.

  Whole numbers greater than zero are called positive integers. Thesenumbers are to the right of zero on the number line.

  Whole numbers less than zero are called negative integers. These numbersare to the left of zero on the number line.  The integer zero is neutral. It is neither positive nor negative.  The sign of an integer is either positive (+) or negative (-), except zero, which

has no sign.  Two integers are opposites if they are each the same distance away from zero,

but on opposite sides of the number line. One will have a positive sign, theother a negative sign. In the number line above, +3 and -3 are labeled asopposites.

Example 1: Write an integer to represent each situation:

10 degrees above zero +10a loss of 16 dollars -16a gain of 5 points +58 steps backward -8

 A non-integer representation uses non-integer  numbers as the radix, or bases, of a positional

numbering system. For a non-integer radix β > 1, the value of  

is

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The numbers d i are non-negative integers less than β. This is also known as a β-

expansion, a notion introduced by Rényi (1957) and first studied in detail by Parry

(1960). Every real number has at least one (possibly infinite) β-expansion.

There are applications of β-expansions in coding theory (Kautz 1965) and modelsof  quasicrystals (Burdik et al. 1998).

Basics of Positive and Negative Numbers

Positive and negative numbers are all integers. Integers are whole numbers that are either 

greater than zero (positive) or less than zero (negative). For every positive integer, there's a

negative integer, called an additive inverse, that is an equal distance from zero.

You indicate a positive or negative number by using positive (+) and negative ( –) signs. 

 Although you don't have to include a positive sign when you write positive numbers, you must

always include the negative sign when you write negative numbers.

  Positive numbers are bigger, greater, or higher than zero. They are on the opposite side of 

zero from the negative numbers. Positive numbers get bigger and bigger the farther theyare from zero: 81 is bigger than 25 because it‘s farther away from zero; 212° F, the boiling 

temperature of water, is farther away from zero than 32° F, the temperature at which water 

freezes. They‘re both positive numbers, but one is bigger than the other.  

  Negative numbers are smaller than zero. Negative numbers get smaller and smaller thefarther they are from zero. This can get confusing because you may think that –400 is

bigger than –12. But just think of  –400° F and –12° F. Neither temperature is pleasant to

think about, but –400° is definitely less pleasant — colder, lower, smaller. When dealing

with negative numbers, the number closer to zero is the bigger number.

  Zero (0) has the unique distinction of being neither positive nor negative. Zero separates

the positive numbers from the negative ones. In a line with zero in the middle, negative

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numbers line up on the left, and positive numbers line up on the right: –4, –3, –2, –1, 0 1, 2,

3, 4.

When you visualize negative and positive numbers in a line like this, it's easy to figure out

which numbers are greater than others: For any two numbers in the line, the number to the

right is always greater.

Fraction (mathematics)

From Wikipedia, the free encyclopedia

 A cake with one fourth (a quarter) removed. The remaining three fourths are shown. Dotted

lines indicate where the cake may be cut in order to divide it into equal parts. Each fourth of the

cake is denoted by the fraction ¼.

 A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any

number of equal parts. When spoken in everyday English, a fraction describes how many parts

of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar ,

or simple fraction (examples: and 17/3) consists of an integer  numerator , displayed above a

line (or before a slash), and a non-zero integer denominator , displayed below (or after) that

line. Numerators and denominators are also used in fractions that are not common, including

compound fractions, complex fractions, and mixed numerals.

The numerator represents a number of equal parts, and the denominator, which cannot be zero,

indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4,

the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells

us that 4 parts make up a whole. The picture to the right illustrates or 3/4 of a cake.

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Fractional numbers can also be written without using explicit numerators or denominators, by

using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10−2 respectively, all

of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having

an implied denominator of one: 7 equals 7/1.

Other uses for fractions are to represent ratios and to represent division.[1] Thus the fraction 3/4

is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4

(three divided by four).

In mathematics the set of all numbers which can be expressed in the form a/b, where a and b

are integers and b is not zero, is called the set of  rational numbers and is represented by the

symbol Q, which stands for  quotient. The test for a number being a rational number is that it can

be written in that form (i.e., as a common fraction). However, the word fraction is also used to

describe mathematical expressions that are not rational numbers, for example algebraic

fractions(quotients of algebraic expressions), and expressions that contain irrational numbers, 

such as √2/2 (see square root of 2) and π/4 (see proof that π is irrational).

The decimal numeral system (also called base ten or occasionally denary) has ten as its base. 

It is the numerical base most widely used by modern civilizations.[1][2] 

DECIMAL

Decimal notation often refers to a base-10 positional notation such as the Hindu-Arabic

numeral system; however, it can also be used more generally to refer to non-positional systems

such as Roman or  Chinese numerals which are also based on powers of ten.Decimals also refer to decimal fractions, either separately or in contrast to  vulgar fractions. In

this context, a decimal is a tenth part, and decimals become a series of nested tenths. There

was a notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently

an  Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions

and other divisions of measures, like the inch. It is possible to follow a decimal expansion with a

vulgar fraction; this is done with the recent divisions of the troy ounce, which has three places of 

decimals, followed by a trinary place.

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 beaker = a liquid measuring container 

burette = measures volume of solution

clay triangle = a wire frame with porcelain used to

support a crucible 

. wire gauze = used to spread heat of a burner flame

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  test tube = used as holder of small amount of 

solution

forceps = holds or pick up small objects

graduated cylinder = measures approximatevolume

graduated pipette = measures solution volumes 

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 condenser = used in distillation

crucible = used to heat a small amount of a solid

substance at a very high temperature

Precaution

1. Wear safety glasses/goggles

2. Tie back long hair 

3. Store chemicals on shelves with labels

4. Keep bags away from burners

5. Turn of gas when not in use

6. Light bunsen burners on orange 'safety' flame

7. Wash hands after handling chemicals

8. Keep a fire extinguisher handy

9. Wipe up spills immediately

10. Keep reactive metals in jars filled with oil.