Statistics Homework

Introduction to Statistics homework: Statistics is defined as a process of analysis and organize the data.

We learn about mean, median, mode in statistics. Mean is same as average in arithmetic. Median is the midvalue of the data. Mode is the value of the data that appears most number of times.

Statistics deals with mean, deviation, variance and standard deviation. The process of finding the mean deviation about median for a continuous frequency distribution is similar as we did for mean deviation about the mean. It is a technology to collect, manage and analyze data. In this article, Basic functions and homework problems on statistics are given.

Statistics Functions and Examples:

In statistics the mean which has the same as average in arithmetic. In statistics mean is a set of data which can be dividing the sum of all the observations by the total number of observations in the data.

Sum of observations

Mean = ------------------------------------

Number of observations

The statistic is called sample mean and used in simple random sampling.

The mean of deviation has discrete frequency distribution and Continuous frequency distribution.

The mean deviation and median for a continuous frequency distribution is similar as for mean deviation about the mean.

Median is found by arranging the data first and using the formula

If n is even,

Median = '1/2[ n/2 "th item value"+(n/2+1) "th item value"]'

If n is odd, Median = '1/2 (n+1)'th item value

Variance: In statistics the variance s2 of a random variable X and of its distribution are the theoretical counter parts of the variance s2 of a frequency distribution. In a given data set of the variance can be determined by the sum of square of each data. Here variance is represented by Var (X). The formula to solve the variance for continuous and discrete random variable distributions can be shown. In statistics variance is the term that explains how average values of the data set vary from the measured data.

s2 = ?(X - M) 2 / N

S2 = ?(X - M) 2 / N

Standard Deviation: It is an arithmetical figure of spread and variability

Ex 1 : Choose the correct for normal frequency distribution.

A. mean is same as the standard deviation

B. mean is same as the mode

C. mode is same as the median

D. mean is the same as the median

Ans: D

Ex 2 : Choose the correct variable for confounding.

A. exercise

B. mean

C. deviation

D. Occupation

Ans : A

Ex 3: The weights of 8 people in kilograms are 60, 58, 55, 72, 68, 32, 71, and 52.

Find the arithmetic mean of the weights.

Sol : sum of total number

Mean = ------------------------------

Total number

60 + 58 + 55 + 72 + 68 + 32 + 71 + 52

= -----------------------------------------------------------

8

468

= -------

8

= 58.5

Ex 4: Find the median of 29, 11, 30, 18, 24, and 14.

Sol : Arrange the data in ascending order as 11, 14, 18, 30, 24, and 29.

N = 6

Since n is even,

Median = '1/2[ n/2 "th item value"+(n/2+1) "th item value"]'

= '1/2' [6/2th item value + (6/2 + 1)th item value]

= '1/2' [3rd item value + 4th item value]

= '1/2' [18 + 30]

= '1/2' * 48

= 24

Ex 5: Find the mode of 30, 75, 80, 75, and 55.

Sol : 75 are repeated twice.

Mode = 75

Ex 6: Find the Variance of (2, 4, 3, 6, and 5).

Sol: First find the mean

Mean = '(2+3+4+6+5)/5 = 20/5=4'

(X-M) = (2-4)= -2, (3-4)= -1, (4-4)=0, (6-4) =2, (5-4) =1

Then we can find the squares of a numbers.

(X-M)2 = (-2)2 = 4, (-1) 2 = 1 , 02 = 0, 22 = 4 , 12 = 1

'sum(X-M)^2= 4+1+0+4+1=10'

Number of elements = 5 , so N= 5-1 = 4

'(sum(X-M)^2)/N = 10/4=2.5'

Here we can add the all numbers and divided by total count of numbers.

= (4 + 16 + 9 + 36 + 25) / 5

= 90 / 5

= 18

Ex 7: Find the Standard deviation of 7, 5, 10, 8, 3, and 9.

Sol:

Step 1:

Calculate the mean and deviation.

X = 7, 5, 10, 8, 3, and 9

M = (7 + 5 + 10 + 8 + 3 + 9) / 6

= 42 / 6

= 7

Step 2:

Find the sum of (X - M) 2

0 + 4 + 9 + 1 + 4 = 18

Step 3:

N = 6, the total number of values.

Find N - 1.

6 - 1 = 5

Step 4:

Locate Standard Deviation by the method.

v18 / v5 = 4.242 / 2.236

= 1.89

Homework practice problems:

1. Choose the correct for statistics is outliers.

A. mode

B. range

C. deviation

D. median

Ans : B

2. Find the arithmetic mean of the weights of 8 people in kilograms is 61, 60, 58, 71, 69, 38, 77, and 51.

Sol : 60.625

3. Find the median of 22, 15, 32, 19, 21, and 13.

Sol : 20

4. Find the mode of 30, 65, 52, 75, and 52.

Sol : 52

5. Find the Variance of (3, 6, 3, 7, and 9).

Sol: 36.8

6. Find the median of 9, 12, 26, 48, 20, and 41.

Sol: 23

Types of Management Plans

Introduction:

The prosperity of an organization depends upon the preparation and execution of the management plans. It is a well known fact that it is impossible for an organization to operate without outlining proper management plans. Over the years through extensive study and management research, many scholars have divided management plans in two types, namely, Strategic Management Plans and Operational Management Plans.

Classification of management plans

Strategic Management Plans - It involves proper planning and far-sightedness for conceptualizing the strengths and weaknesses of the organization, pertaining to the environment in which it exists. Strategic Management Plans deals with the envisioning of at least three to five years in the future and deciding what are the pathways that the organization intends to take and create new vistas of opportunities. It strongly involves the basic elements of market research and financial projections with detailed study of promotional planning and taking all the necessary steps to fulfill the operational requirements. It is the best way to find out the amount of capital to be raised, expansion target and optimum use of the available resources. Strategic managerial plans also deals with relationship managerialas in today's world, management and the correct use of contacts is very important.

Operational Management Plans - It is the interim period which deals with Operational Management Plans. This is also termed as Tactical Planning and it also deals with the aspects that involve the concept of an annual budget. Operational managerialPlans entirely focuses on making sure that a given task is completed. It is irrespective of whether it is driven by the entire organization's budget, any personal budget or any functional area of responsibility. It can also be said that operational managerial plans are indirectly derived from strategic managerial plans. It is an outflow of a detailed strategic managerial plan and can be seen as a part of the initiating and implementation stage of a more comprehensive long term plan.

Standing & Single Use Management Plans -

Standing Plans are further of three types, namely Policies, Procedures and Rules. While Single Use Plans are further of two types, namely, Programs and Budgets. Here is a short note on different types of Standing and Single Use Plans :

Policies - It focuses on accomplishing the organization's objectives by furnishing the broad guidelines for the correct course of action.

Procedures -Procedures outline a more specific set of actions and deals with the implementation of a set of related actions in order to finish a particular task.

Rules - Rules are a set of guidelines that show the way and manner in which a task is to be accomplished. It lays down the do's and don'ts that are to be strictly followed by the members of the organization without any deviation.

Programs - Programs deal with the guidelines that are set for accomplishing a special project within the organization. The project may not be in existence for the entire tenure of the organization, but if the project is accomplished, it might result in short-term success of the organization which might ultimately prove to be extremely helpful.

Budget - A Budget represents a specific period of time which indicates it as a single user financial plan. It is a complete set up indicating the process of procuring the funds and channelizing the funds. It shows in details how funds are to be utilized on labor, raw materials, capital goods, marketing and information systems.

What is an Integer in Math

Introduction to an integral in math:

In mathematics, an integral is one interesting topics in number representation. Integer has a set of numbers in which includes positive numbers, negative numbers and zero. An integer contains complete entity or unit. In integer, there is no fractional parts and also no decimal numbers. Integer performs different types of arithmetic operations which are addition, subtraction, multiplication and division. Let us solve some example problems for an integer in math.

Example for an integral in math:

489, - 546, 0, 84, etc.

Different rules of an integral in math:

Different rules of an integral in math are,

Integer Addition Rules:

In addition, we use the same sign means then we add the same sign integer values and then we get the same sign integral value as result.

Positive integral + Positive integer = Positive integer

Negative integral + Negative integral = Negative integer

Otherwise, we use different signs means then we subtract the different sign integral values and then we get the largest absolute value as result.

Positive integral + Negative integral

Negative integral + Positive integer

Integer Subtraction Rules:

In subtraction, we keep the first integer as same, next we change the subtraction sign to addition and change the second integers sign into its opposite then we follow the same rule for integer addition.

Integer multiplication Rules:

Like addition rule,

Positive integral × Positive integer = Positive integer

Negative integer × Negative integral = Positive integer

Positive integral× Negative integral = Negative integral

Negative integral × Positive integral = Negative integer

Integer Division Rules:

Like multiplication,

Positive ÷ Positive = Positive

Negative ÷ Negative r = Positive

Positive integer ÷ Negative integer = Negative integer

Negative integer ÷ Positive integer = Negative integer

Example problems for an in math:

Some example problems for an integral in math are,

Example 1:

Using addition operation, simplify the given integral

842 + 384

Solution:

Given two numbers are

842 + 384

Both are positive integers and the result is also a positive numbers

Here we add 842 into 384, and we get the result

842 + 384

1226

Solution to the given two is 1226.

Example 2:

Using subtraction operation, simplify the given

958 - 575

Solution:

Given two numbers are

958 - 575

Both are two positive and the result is also a positive numbers

Here we subtract 958 into 575, and we get the result

958 - 575

383

Solution to the given two is 383.

Example 3:

Using multiplication operation, simplify the given

127 × 253

Solution:

Given two numbers are

127 × 253

Both are two positive and the result is also a positive numbers

Here we multiply 127 into 253, and then we get the result

127 × 253

32131

Solution to the given two is 32131.

Example 4:

Using division operation, simplify the given

9000 ÷ 30

Solution:

Given two numbers are

9000 ÷ 30

Both are two positive and the result is also a positive numbers

Here we divide 9000 by 30, and then we get the result

9000 ÷ 30

300

Solution to the given two integra is 300.

Example 5:

Using multiplication operation, simplify the given integral

Solution:

Given two integra numbers are

Givenintegral number has both positive integral and negative integers so; the result is a negative numbers

Here we multiply - 487 into 213, and then we get the result

Solution to the given two integra is - 103731.

Example 6:

Using addition operation, simplify the given

Solution:

Given two integra numbers are

Both are two negativeintegral so, the result is also a negative numbers

Here we add - 86 into - 252, and then we get the result

Solution to the given two integral is - 338.

Practice problems for an integral in math:

Problem 1:

156 + 845

Answer: 1001

Problem 2:

756 - 345

Answer: 411.

Problem 3:

56 × 245

Answer: 13720

Problem 4:

'9996 / 357'

Answer: 28

Problem 5:

Answer: 607

Problem 6:

Answer: - 601.

Problem 7:

Answer: - 1170

Problem 8:

' 836 / 38'

Answer: 22

Preschool Academics Education in Los Angeles

Even 20 years back from the present time the preschool concept was not that usual however even in that also preschool education in Los Angeles was quite familiar. But in the present scenario this is a very usual thing indeed and this concept has be spread throughout the world and in any country now there are loads of schools for children who are not even eligible for pre primary education. There is a huge availability of preschool Calabasas as well. Actually at present times people are very much busy into work and along with that there is huge competition as well. Therefore just in order to make the children more advanced and interactive parents often choose to send them for preschool education. Even in preschool Agoura Hills people are very much fond of this trend and another reason behind it is the top class infrastructure and guidance they provide to the children.

Such schools are also known as kindergarten that educates children through fun and joy. However there are a number of people according to whom the kindergarten does not pay much to the academics but that is not true. Actually these preschools are is not all about studies but there are a lot more thins to be learnt like how to communicate with others, how to make oneself comfortable in the crowd and much more. Most of the times it is seen that kids do not feel easy when they first step up into their school life but once they are used to other friends and once they learn how to mix up with other people, their communication skill becomes much fluent. A preschool can be called as a warm up session before the nursery school. In the busy places people choose the preschool for their children and preschool Hidden Hills are one of the examples.

If seen in detail it can be figured out that there are some cons of this educational system as well. One of the biggest drawbacks of this the children get less time to spend at home and with the parents as well. Sometimes they lose the homesickness.

But these are not something that cannot be changed. Having a proper family guidance they can have a good start of their educational life. In today's busy days in maximum cases parents fail to pay the proper attention to their children and because of that the kids gradually start feeling depressed. Preschool education is a good way out for them as it does not only make them out of the depressed situation but at the make them happy and busy as well.

All in all such playgroup education has both positive and negative side however the positive effects of such education outweighs the negative points in a large way. Nowadays in fact due to huge competition it is somewhat essential as well to provide the kids this education as it helps them to start a good educational life since the basic of diverse curriculum of academic life gets started here.

Through exciting and varied daily activities that stimulate today's child, our teachers at The Boulevard School provide their classes with an environment that encourages the children to participate in the classroom learning centers. Find out more on preschool Academics in Calabasas .

Why is Geometry Important in Life

Introduction:

Geometry is important in life because it is the learning of space and spatial dealings is an important and necessary area of the mathematics curriculum at every evaluation levels. The geometry theories are important in life ability in much profession. The geometry offers the student with a vehicle for ornamental logical reasoning and deductive thoughts for modeling abstract problems. The study of geometry is important in life because it's increasing the logical analysis and deductive thinking, which assists us expand both mentally and mathematically.

Definition for why is geometry important in life:

This article going to explain about why geometry is important in life. Geometry is a multifaceted science, and a lot of people do not have an everyday need for its most advanced formulas. Understanding fundamental geometry is essential for day to day life, because we never know when the capability to recognize an angle or figure out the region of a room will come in handy.

Importance of geometry in life:

The world is constructing of shape and space, and geometry is its mathematics.

It is relaxed geometry is good preparation. Students have difficulty with thought if they lack adequate experience with more tangible materials and activities.

Geometry has more applications than just inside the field itself. Often students can resolve problems from other fields more easily when they represent the problems geometrically.

Uses of geometry:

Gtry is the establishments of physical mathematics presents approximately surround us. A home, a bike and everything can made by physical constraints is geometrically formed.

Gmetry allows us to precisely compute physical seats and we can relate this to the convenience of mankind.

Anything can be manufacturing use of geometrical constraints like Architecture, design, engineering and building.

Example:

Let us see one example regarding why geometry important in our life. If you want to paint a room in your accommodation, you should know how much square feet of room you are going to cover by paint in order to know how much paint to buy. You should know how much square feet of lawn you contain to buy the correct amount of fertilizer or grass seed. If you required constructing a shed you would have to know how much lumber to buy so you should know the number of the square feet for the walls and the floor.

architecture is a one of the foundation of all technologies and science using the language of pictures, diagrams and design. was fully depends on structure ,size and shape of the object. In every day was very important in architectural through more technologies In a daily life was used in th technology of computer graphics, structural engineering, Robotics technology, Machine imaging, Architectural application and animation application.

In this article why is geometry important in architecture, We see about application of architecture in daily life and technology sides.

Basic concepts of important in architecture:

General application of or important :

Generally was used for identifying size, shape and measurement of an object.

Fining volume, surface area, area ,perimeter of the room a and also properties about shaped objects in building construction.

Also used for more technologies for example : computer graphics and CAD

Computer graphics:

In computer graphics was used to design the building with help of more software technologies. And also how to transferred the object position.

Number Zero Origin

THE ORIGIN OF NUMBER ZERO:-

In this Article the information about the history of zero and its importance, its usage in various cultures is discussed, in addition to that its relevance and importance in fields other than mathematics is discussed

According to Charles Seife, author of "Zero: The Biography of a Dangerous Idea", The Number zero was first used in West circa 1200; it was delivered by an Italian Mathematician, who joined this, with the Arabic numerals. For Zero there are at least two discoveries, or inventions. He says that the one was from the Fertile Crescent. That first came to existence in Babylon, between 400 to 300 B.C. Seife also says that, before 0 getting developed in India, it started in Northern Africa and from the hands of Fibonacci and to Europe Via Italy.

Zero, initially was a mere place holder, Seife says 'That is not a full zero', "A Full zero is a number on its own; It's the average of 1 and -1". "In India zero took as a shape, unlike being a punctuation number between numbers, in the 5th century A.D.", says Dr.Robert Kaplan. He is the author of "The nothing that is: A Natural History of Zero". "It isn't until then and not even full then, that Zero gets citizenship in the republic of numbers," says Kaplan.

In Mayan Culture, In the new world the second look of Zero appears then, in the centuries of A.D. Also Kaplan says, "That I suppose Zero being wholly devised form the scratch"

An Italian book mentioned a point about Zero, saying that The usage of Zero by Ellenistic Mathematicians, would have defined a decimal notation equivalent to the system used by the Indo-Arabic. The Book is titled - "La rivoluzione dimenticata - The Forgotten Revolution" Russo, 2003, Feltrinolli by Lucio Russo.

The ancient Greeks were very doubtful about zero as being a number. They kept posing questions on this topic. "How can nothing be something?", these questions led to philosophical arguments about the usage of zero. Comparing it with vacuum many discussions took place.

number zero origin - More information

More about the number zero origin:-

Zero is written as a circle or an eclipse. Earlier, there was no much difference between the letter o and 0. Type writers earlier had no distinction between o and 0. There was no special key installed on the type writer for zero. A slashed zero was used to distinguish between letter and digit. IBM used the digit zero by putting a dot in the center and this was continued in the Microsoft windows also. Another variation proposed at that time was a vertical bar instead of dot. Few fonts which were designed for the use in computer made the o letter more rounded and digit 0 more angular. Later the Germans had made a further distinction by slitting 0 on the upper right side.

number zero origin - importance

IMPORTANCE:-

The value zero is used extensively in the fields of Physics, Chemistry and also Computer Sciences. In Physics zero is distinguished form all other levels. In Kelvin Scale the coolest temperature chosen is zero. In Celsius scale zero is measured to be the freezing point of water. The intensity of sound is measured in decibels or photons, wherein zero is set as a reference value.

Zero has got very importance as all its binary coding is to be done with 1's and 0's. Before the existence of 0 the binary coding is very difficult. The concept of arrays also uses 0 prominently, for n items it contains 0 to n-1 items. Database management always starts with a base address value of zero.

Star Formation

Introduction on star formation:

The process of star formation involves collapse of dense molecular clouds into a denser ball of plasma to form a star. Star Formation as a subject includes a study of interstellar medium and giant molecular clouds that precede star formation along with a study of young stellar objects including planets of stars.

Precursors to Star Formation

Empty Space, Interstellar Clouds and Cloud Collapse

Typically the space between interstellar objects, both within galaxies like our Milky Way and between galaxies situated far apart, is not an absolute void or vacuum and contains a diffuse interstellar medium (ISM) of gas and dust. ISM has a very low density and about one hundred thousand to one million particles per cubic meter. Its composition by mass is approximately 70% hydrogen and the rest being made up mainly by helium with traces of heavier molecules. Higher density parts of ISM form interstellar clouds whose collapse leads to formation of stars.

Interstellar clouds contain a major part of Hydrogen in the molecular form and are hence referred to as molecular clouds too. Dense giant molecular clouds can often have densities of 100 million particles per cubic meter with very large diameters of 100 light-years (a million trillion km) and a total mass of up to a million times that of our Sun. The process of cloud collapse leads to a rise in temperature.

This internal cloud of gas remains in a stable equilibrium with the two forces of gravitational attraction and kinetic energy of particles working against each other. When the cloud gets sufficiently large and massive and the forces of gravity overcome the kinetic energy, then the process of cloud collapse begins. This may happen on its own or sometimes may be triggered by other stellar events such as collision of molecular clouds, a nearby supernova explosion and galactic collisions. Sometimes, an extremely heavy black hole at the core of a galaxy may also play a role in triggering or preventing star formation.

During the process of collapse Interstellar Cloud breaks into smaller pieces until its fragments reach stellar mass with each fragment radiating energy gained by the release of gravitational potential energy. The process of collapse leads to an increase in density restricting energy radiation and causing a rise in the temperature of the cloud. Rising gravitational force also acts to limit further fragmentation leading to formation of rotating spheres of gas called stellar embryos.

History of Protostar:

A wide range of forces caused by turbulence, spin, magnetic fields formed due to spinning and macroscopic flows come into play and are affected by and also affect the cloud geometry. These influences can hinder or accelerate the process of collapse. If the process of collapse continues the dust within the cloud becomes heated leading to a rise in temperature to around 60,000 -100,000 degrees Celsius with its particles emitting radiations of far infrared wavelengths promoting further collapse of the cloud and rise of temperature in the core.

Rising core temperature and declining density of the surrounding gases create conditions congenial to let the energy escape. This allows the core temperature to rise further causing dissociation of hydrogen molecules. Resulting ionization of hydrogen and helium atoms absorbs energy of contraction. The process of collapse continues until a new equilibrium is reached between the internal pressure of hot gases and gravitational forces. The object so formed is called a protostar.

Star Formation

Protostar continues to grow by attracting material and finally when the conditions are just right the process of fusion begins. Resulting radiation further slows the process of collapse. Finally the surrounding gas and dust envelope is eliminated through absorption into protostar or dispersal and further accretion of mass stops though the process of collapse continues.

At this stage the main source of energy continues to be gravitational contraction and the object is called a pre-main sequence (PMS) star. Further collapse stops at a point and fusion process begins in the core replacing gravity as the main source of energy. The object then begins a main sequence star. Further life cycle of the star thus formed depends on its size.

Variables in Statistics Tutor

Introduction :

The variable which is available in the statistics it is called as statistical variable. It is a feature that may acquire choice in adding of one group of data to which a mathematical enumerates can be allocated. Some of the variables are altitude, period, quantity of profit, region or nation of birth, grades acquired at school and category of housing, etc,. Our statistics tutor defines the different types of statistics variables and the example of these types. Our tutor helps to you to know more information about the variables in statistics.

Variables in statistics tutor:

Let us, see the different types used in statistics and the uses of these types. There two kinds of used in statistics. They are,

Statistical 1: Qualitative

Statistical 1: Quantitative

These two kinds are used for various uses based on the statistics. Also, these types are divided into number of categories and which is used to various uses.

Explanation :

Qualitative :

The qualitative variant is the initial category of variable in statistics. Qualitative variables are cannot be measured which are called as attributes.

The qualitative variable is categories into two parts:

Qualitative type 1: Nominal

Qualitative type 2: Ordinal

1. Nominal variable:

Nominal values are the qualitative that does not hold any mathematical proposition like one's sacred quantity or city or surroundings. Using this nominal it does not do any addition, subtraction, even sorted.

2. Ordinal variables:

Ordinal variable is similar to the nominal variable but it uses some logical technique can arrange the variables. For instance in school ( junior and senior).

Quantitative variables:

The next category of statistical is a quantitative. The quantitative can be measured straightly.

The quantitative is categories into two parts:

Quantitative type 1: Continuous

Quantitative type 2: Discrete

1. Continuous :

The variable that can acquire all the values from the specified sequence then it is known as continuous. That is it can take an infinite value from the higher range to lower range of the given series.

Example:

Assume the person's age. Here, age is considered as a numerical value. If the age of the person is in among 36 and 56, the outcome can be any value among 36 and 56; therefore "Age of a person "is continuous variable.

2. Discrete :

The variable that can acquire only a specific value from the given range then it is said to be discrete variable. Hence, it can take the finite number of values only.

Example:

The number of child in the family is among 4 and 6, the outcome will be only 5. That is among 4 and 6, the can take only a specified value 5; therefore, "number of child in a family" is discrete variable.

Activities at Mommy and Me Classes

Mommy and me classes are very helpful for both the mother and her infant or toddler since it brings them much closer to each other. At the present time this social classes are very famous all over the world. The mommy and me Calabasas are found in several diverse places of this country. Not only that in fact mommy and me classes Agoura Hills and Hidden Hills are also very famous and a lot of people are very much fond of it. Many time people ask why such a class is so important to join. Well basically there are endless benefits of such mommy and me class. Let us have a look at its advantages that are lined up below.

It strengthens the bonding between the mother and the child: As already said that the mommy and me classes are a great way to strengthen the bond between the child and the mother. Both get a quality time to spend with each other and this provides them a sense of safety and optimistic self value. Since in this type of a class both the mother and kid interact with each other the most and take part in a single activity together the bond get stronger and flourish.It helps the child to develop the communication and social skill: In these special classes the mommies get chance to develop the social awareness and communication skill of their child. For children who are introvert or timid this type of a class can make a lot of changes. Other than that in such classes the children also get the scope of leveraging their skill of understanding, self control and much more. In fact in some cases it is found that they start learning new things themselves and they start being creative which is a great thing about the children.Great way to make friends: Since in these classes you kid gets the chance to meet a lot more buddies of his age or of different age along with their moms it helps him or her lot make out his best buddy out of the crowd. Friendship is a must need of motherhood, these classes gifts the key of that actually.Lighten the loneliness: If the parents are working the children often feel lonely and they cannot share their loneliness. But if they get chance to spends a single day with their mother through this class it lessens their feeling of loneliness in large extend.Prepares child for school: The mommy and me classes can be termed as a preschool session as well as this contributes a lot in their academics and nursery school.

Other than these classes the children learn to set up with diverse situation, they learn how to figure out and solve problems; they learn to follow directions and much more that point out a good start o their educational and social life. As a whole this is actually a very helpful session for both the mothers and their children.

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Equalative Fraction

Introduction to equalative fraction:

The equivalent fraction, multiplying the numerator and denominator of a fn by the same (non-zero) number, the results of the new fraction is said to be equivalent to the original fraction. The word equivalent means that the two fns have the same value. (Source: Wikipedia)

Before the introduction of the decimal system children need to learn a lot more about fractions, as this was the only way to show a part of a whole number. In the past, using such as 5/2 and 3/5 to describe shares of objects or groups of objects was common. These have been replaced by decimals and the calculations are frequently done and writing is done in a different way to whole numbers.

A fraction consists of numerator and a denominator. This area of mathematics has frequently caused problems for both teachers and students alike, this concern however, is unnecessary if the correct grounding is given and basic concepts are understood.

Equalative fraction - Definition and examples:

Definition for equivalent :

The equivalent frs are fractions that are equal to the each other. We can use cross multiplication to decide to whether two fs are equivalent. The fractions that explain the same amount are called equivalent fs.

The equivalent frs of the same value or equivalent means equal in value. Fraction can look different but be equivalent. These fs are really the same,

Example: 3/4 = 15/20 = 75/100

The rule for equivalent multiplying numerator and denominator of a derived by the same number or a whole fraction, the results of derived is said to be equivalent to the original fraction. The equivalent fraction that two derived values have, the same value and they retain of the same integrity and proportion.

Equalative fraction:

Two frs are equivalent frs if they have the same value. The common denominator is add and subtract fn each derived must have a common denominator they must be same thing. In derived we must find a number that all the denominators will divide evenly into, Example look at the derived 1 / 4 and 1 / 6 .The denominators for these fractions are 4 and 6. A number that 4 and 6 will divide into evenly is 24.

Equalative fn - Example problems:

3 / 4 = 15 / 206 / 7 = 24 / 288 / 10 = 16 / 206 / 8 = 18 / 245 / 7 = 25 / 357 / 8 = 28 / 32

Simplify the equalative and examples:

Simplify the equalative :

A fraction is in simplest method, if the numerator and the denominator are relatively prime numbers. The concept of simplifying derived is obviously connected to the concept of equivalent fractions. One main connection is that when we are simplifying derived, we are basically finding an equivalent fraction in which the numerator and denominator are smaller (and thus simpler) numbers.

The equivalent makes simpler a derived we find a number which will divide into both the numerator and the denominator evenly, leaving no remainder. Example, to simplify the fraction 35 / 20 we divide the numerator and denominator by 5. So, 7 / 4 is the simplified derived for 35 / 20

Equalative fraction - Example problems:

15 / 30 = 3 / 10

25 / 35 = 5 / 7

27 / 36 = 9 / 12

32 / 28 = 8 / 7

45 / 40 = 9 / 8

22 / 14 = 11 / 7

Discrete Mathematics

Introduction to discrete mathematics pdf:

Discrete mathematics is part of 3 main topics

Mathematics Logic

Boolean Algebra

Graph Theory

discrete mathematics pdf-Mathematics Logic

The find of logic which is used in mathematics is called deductive logic. Mathematical arguments must be strictly deductive in nature. In other words, the truth of the statements to be proved must be established assuming the truth of some other statements.

For example, in geometry we deduce the statement the statement that he sum of the three angles of a triangle is 180 degrees from the statement that an external angle of a triangle is equal to the sum of the other (i.e., opposite) two angles of the triangles of the triangle.

The kind of logic which we shall use here is bi-valued i.e. every statement will have only two possibilities, either True' or 'False' but not both.

Definition:- The symbols, which are used to represent statements, are called statement letters or sentence variables.

To represent statements usually the letters P, Q, R, ..., p, q, r, ... etc., are used

discrete mathematics pdf-Boolean algebra

Boolean algebra was firstly introduced by British Mathematician George Boole (1813 - 1865).the original purpose of this algebra was to simplify logical statements and solve logic problems. In case of Boolean algebra, there are mainly three operations (i) and (ii) or and (iii) not which are denoted by '^^' ,'vv' and (~) respectively. In this chapter, we will use +, . , ' in place of above operations respectively.

Definition:-Let B be a non-empty set with two binary operations + and ., a unary operation ' and two distinct elements 0 and 1. Then B , +, . ,' is called Boolean algebra, if the following axioms are satisfied.

discrete mathematics pdf-Graph theory

Graphs appear in many areas of mathematics, physical, social, computer sciences and in many other areas. Graph theory can be applied to solve any practical problem in electrical network analysis, in circuit layout, in operations research etc.

By a graph, we always mean a linear graph because there is no such thing as a non-linear graph. Thus in our discussion we shall drop the adjective 'linear', and will say simply a 'graph'

Definition:- A graph G = (V, E) consists of a set of objects V = (v1, v2, ...), whose elements are called vertices (or points or nodes) and an another set E = {e1, e2, ....} whose elements are called edges (or lines or branches) such that each ek is identified with an unordered pair (vi, vj) of vertices. The vertices vi and vj associated with the edge ekare said to be the end vertices of ek.

Online Basic Geometry Definitions

Introduction :

In this article online basic geometry definitions tutor,we will learn some important geometry definitions they are necessary to understand geometry concept.Those basic geometry definitions are used to design a graph with the assistance of those terms. Tutor will teach to individual and guide them to get the solution for problems through some websites via online. Online is a tool for self-learning from websites.

Basic definitions-

Supplementary angles:

We can call any two angles as supplementary angles,if the sum up of them should be 180°

Complementary angles:

We can call any two angles as complementary angles,if the sum up of them should be 90°

Acute triangle:

An acute triangle means a t in which all three angles should be less than 90°.

Obtuse triangle:

Obtuse triangle means one type of tria in this one angle must be greater than 90°.

Right angle triangle:

A right angle tria means one type of tri in which one angle must be a right (90°) angle.

Triangle Inequality:

The triangle inequality means the addition of any two side should be greater than the third side

Scalene Triangle:

A scalene trigle means a triangle with three different unequal length of side.

some more definitions-

Centroid:

The centroid means a point in which three lines will meet each other. This point is a center point of a trigle. If we cut a tria corresponds to that center we will get three equal parts.

Circle:

In circle the distance between the center and to any point present in the outer line of a circle is same.

Radius:

Radius of a circle is the distance between the circle's center and any point present on the circle.

Circumcenter:

In a triae three perpendicular line drawn from the three sides bisect each other . That point is called as circumcenter.From this center point we can draw a circle

Congruent:

Two figures are said to congruent when all the parameters should be same interms of length and angles.

Altitude:

An altitude means a line connecting a vertex to the opposite side.

Vertex:

Vertex means a point.

Transversal:

A transversal means a line which passes through two another lines there is a no issue that should be parallel.

Point:

A point indicates a single location

Plane:

Plane is a flat, two-dimensional object one.

Quadrilateral:

Quadrilateral is defined as a polygon and has exactly 4 sides.

Trapezoid:

A trapezoid means a quadrilateral which contain one pair of opposite side they should be parallel to each other.

Polygon:

A polygon means a two-dimensional geometric object.It is made up of a straight line segment those segments touches at the ends.

Rectangle:

Rectangle means a quadrilateral and should has 4 right angle.

These are the few terms for basic geometry

Rubber Room Ruckus - Los Angeles Unified Policy Run Amok

It was more of thud then a knock and it shook me from the newspaper article I was reading. I should have ignored it; I already knew it was one of the kids who'd been kicking at my door during nutrition and lunch break when they're free to roam school grounds. My room was on the second floor balcony of one of many bungalows located on the southern edge of campus. These same kids had been making quite a commotion just outside my door for weeks on end as I tried vainly to shoo them away with appeals as well as threats. My requests to the main office for assistance always went unanswered.

But this time I decided to act quickly. I raced out and found one of the students standing there laughing at me. I was surprised to see her since they're usually in flight when the door flies open. This young lady was quite brazen; when I asked for her name she smirked and began walking away. That's when I reached out to her half heartedly; I knew I couldn't restrain her in order to get information, but I felt disrespected if I didn't do anything. So I reached out with my arm to show I meant business, but without the intention of grabbing her. My hand slightly touched her upper arm. She continued walking away and disappeared down the stairs. I didn't think anything of it until a few hours later when the Principal walked in to my room in the middle of a lesson and told me to take my things and immediately head over to her office; the police wanted to speak with me.

I spent an hour going back and forth with the two officers about who did what and when. They told me the student claimed I assaulted her and that my actions could be considered child abuse. They're methods were intimidating. I was treated as if I was guilty until proven innocent. They kept repeating the term 'child abuse' and even mentioned incarceration when I asked how serious the charges were. Eventually they left the room and I ended up the day talking to my union rep. She told me they could not have arrested me for what had happened; their intimidation was only a tactic. I wondered if those policemen gave the student the same treatment I got.

The next day I was told to gather my belongings from the classroom and return all room keys to the administrator. They were putting me on administrative leave; I was told to show up at the District office in Van Nuys where I would spend my days in a room filled with other teachers who were in the same boat.

The swiftness of the District's actions and the decidedly abstruse way they dealt with it was quite a shock to me. I never thought that a minor run-in with a student could lead to such punitive action. There are hundreds of other 'rehoused' teachers sitting out the day in so called rubber rooms, many of whom don't even know the allegations against them.

There's a witch hunt going on right now, and the judge and jury has a name and address - John Deasy, Superintendent of schools, LAUSD. This man has been intent on getting rid of classroom teachers for the past two years since becoming Superintendent. He initiated this stalinesque course of action, and he is ruining the lives of good teachers as well as students left dangling in their studies and school work when we're ripped out of the classroom in such a manner.

The District has enough work on their hands improving academics and student performance; they need to stop the charade of hiding behind abstract goals of student safety in order to thin the ranks of teachers for their own purposes.

Get rid of pedophiles, not credentialed school teachers who are just doing their job.

Five Number Summary Online

Introduction to five number summary online help:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we help learn about the different statistics involved in five number summary.

Online:

The specific meaning of the term online is nothing but the connecting two states. Online is mostly used in computer technology and telecommunications. Online can be referred the World Wide Web or it may be Internet.

Five number summary online help:

Different statistics are involved in five number summary are,

Minimum

Maximum

Median

Lower quartile

Upper quartile

Minimum:

Lowest value in the given set of numbers.

Maximum:

Largest value in the given set of numbers.

Median:

Middle value in the given set of numbers.

Lower quartile:

Number between the minimum and median.

Upper quartile:

Number between the maximum and median.

Five number summary online help - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.

The lowest and largest value in the observation can be determined.

The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.

The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.

The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary online help - Example problem:

Example 1:

Help to find the five number summary for the given set of data

{235, 222, 244, 255, 217, 228, and 267}

Solution:

Given set of data

{235, 222, 244, 255, 217, 228, and 267}

{217, 222, 228, 235, 244, 255, 267} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 217 and 267.

Median:

Given observation is odd. So the median is middle of the observation then the median is 235.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {217, 222, and 228}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {244, 255, and 267}.

Answer:

Minimum: 217

Maximum: 267

Median: 235

Lower quartile: {217, 222 and 228}

Upper quartile: {244, 255 and 267}

What is an Integer in Math

Introduction to an integral in math:

In mathematics, an integral is one interesting topics in number representation. Integer has a set of numbers in which includes positive numbers, negative numbers and zero. An integer contains complete entity or unit. In integer, there is no fractional parts and also no decimal numbers. Integer performs different types of arithmetic operations which are addition, subtraction, multiplication and division. Let us solve some example problems for an integer in math.

Example for an integral in math:

489, - 546, 0, 84, etc.

Different rules of an integral in math:

Different rules of an integral in math are,

Integer Addition Rules:

In addition, we use the same sign means then we add the same sign integer values and then we get the same sign integral value as result.

Positive integral + Positive integer = Positive integer

Negative integral + Negative integral = Negative integer

Otherwise, we use different signs means then we subtract the different sign integral values and then we get the largest absolute value as result.

Positive integral + Negative integral

Negative integral + Positive integer

Integer Subtraction Rules:

In subtraction, we keep the first integer as same, next we change the subtraction sign to addition and change the second integers sign into its opposite then we follow the same rule for integer addition.

Integer multiplication Rules:

Like addition rule,

Positive integral × Positive integer = Positive integer

Negative integer × Negative integral = Positive integer

Positive integral× Negative integral = Negative integral

Negative integral × Positive integral = Negative integer

Integer Division Rules:

Like multiplication,

Positive ÷ Positive = Positive

Negative ÷ Negative r = Positive

Positive integer ÷ Negative integer = Negative integer

Negative integer ÷ Positive integer = Negative integer

Example problems for an in math:

Some example problems for an integral in math are,

Example 1:

Using addition operation, simplify the given integral

842 + 384

Solution:

Given two numbers are

842 + 384

Both are positive integers and the result is also a positive numbers

Here we add 842 into 384, and we get the result

842 + 384

1226

Solution to the given two is 1226.

Example 2:

Using subtraction operation, simplify the given

958 - 575

Solution:

Given two numbers are

958 - 575

Both are two positive and the result is also a positive numbers

Here we subtract 958 into 575, and we get the result

958 - 575

383

Solution to the given two is 383.

Example 3:

Using multiplication operation, simplify the given

127 × 253

Solution:

Given two numbers are

127 × 253

Both are two positive and the result is also a positive numbers

Here we multiply 127 into 253, and then we get the result

127 × 253

32131

Solution to the given two is 32131.

Example 4:

Using division operation, simplify the given

9000 ÷ 30

Solution:

Given two numbers are

9000 ÷ 30

Both are two positive and the result is also a positive numbers

Here we divide 9000 by 30, and then we get the result

9000 ÷ 30

300

Solution to the given two integra is 300.

Example 5:

Using multiplication operation, simplify the given integral

Solution:

Given two integra numbers are

Givenintegral number has both positive integral and negative integers so; the result is a negative numbers

Here we multiply - 487 into 213, and then we get the result

Solution to the given two integra is - 103731.

Example 6:

Using addition operation, simplify the given

Solution:

Given two integra numbers are

Both are two negativeintegral so, the result is also a negative numbers

Here we add - 86 into - 252, and then we get the result

Solution to the given two integral is - 338.

Practice problems for an integral in math:

Problem 1:

156 + 845

Answer: 1001

Problem 2:

756 - 345

Answer: 411.

Problem 3:

56 × 245

Answer: 13720

Problem 4:

'9996 / 357'

Answer: 28

Problem 5:

Answer: 607

Problem 6:

Answer: - 601.

Problem 7:

Answer: - 1170

Problem 8:

' 836 / 38'

Answer: 22

Tips to Maintain Better Grades In School

One of the more stressful things that you are likely to face in your school career is trying to keep your grades at acceptable levels. Ultimately, this is something that you have control over, although you are going to need to work hard in order to get the highest grades that are possible. If you find that you are struggling in this regard or if you would simply like to do your very best academically, here are some tips that can help you to get those good grades that you desire.

One important thing for you to consider that is often overlooked by students is the position within the classroom where you are sitting. If you tend to gravitate toward the edges or the back of the class, it is likely that you are going to have lower grades as a result. This is not only because of the fact that you will miss out on some of the one-on-one attention that you can get from the teacher, it is also because of the distractions that may take you away from your courses. In addition, seating yourself in the front of the classroom in a position where you are close to the teacher is also going to let them know that you are serious about your school career.

Do you know how to study properly? This is something that many students struggle with but it is one of the more important things that must be mastered. You should work on your study skills and continue to study on a daily basis. Take notes while you're in class and review those notes as a form of studying which will help you to keep everything fresh in mind. If you find that your mind is drifting during the time that you should be studying, try to block your time in small increments so that you can remain focused.

Have you considered the possibility of hiring a tutor? Tutoring is possible for almost any subject, from hiring a math tutor online for kids all the way to getting more specific tutoring for state tests. In either case, the benefits of tutoring are going to be far more than simply getting better grades. When a student uses a tutor successfully, they are going to have higher self-esteem and they will likely have the confidence that is necessary to succeed in life. Make sure that you are taking full advantage of what a tutor has to offer to you during your school career.

Finally, consider the possibility that you are going to need additional help at some point during your schooling. We've already discussed the point of using a tutor but even if a tutor is not desired, you should still seek assistance when any problems display themselves. The sooner you get help for your problems, the more likely it is going to be that you will overcome those difficulties and really succeed. It will also benefit you by showing the teacher and anyone else involved that you are serious about your schooling and want to do your very best.

Ralph Gomez is the author of this article about maintaining better grades in school. Working as a counselor he has shown students many online resources to get tutoring for state tests . Another great resource to use are math tutors online for kids struggling with math. This advice has helped student maintain better grades in school.

Extreme Value Analysis

Extreme value analysis is the branch of mathematics that deals with finding the maximum & minimum of a function. There are different ways to do that; the easiest being that by calculus. One of the other methods are by completing the square but that analysis can only be done in certain specific kinds of functions, quadratic functions to be specific. Many a times mathematics or in that case any branch of science requires finding out the limits(upper or lower) of a function to determine different properties of the function thereof. That's when we need to do the extreme value analysis to suit our needs.

Analytical definition for extreme value analysis

A function f(x) is said to have a local extremum point at the point x*, if there exists some e greater than 0 such that f(x*) greater than or equal to f(x) (for maxima) or if f(x*) less than or equal to f(x) (for minima) when |x - x*| less than e, in a given domain of x. The value of the function at this point is called extremum of the function.

A function f(x) has a global (or absolute) extremum point at x* if f(x*) greater than or equal to f(x) (for maxima) or if f(x*) less than or equal to f(x) (for minima) for all x throughout the function domain.

Tests: for extreme value analysis

There are two tests in calculus to for extreme value analysis, the first derivative test and the second derivative test. First of all, the extreme values occur at the critical points of a function, i.e., wherever the slope of the function is 'zero' or 'not defined'. Then, to check whether these points are actually extremes and also the kind of extremum i.e., whether it is a maximum or a minimum is given by the aforesaid tests. While the first derivative test gives us the kinds of the extreme points by analyzing, manually, the change in the sign of the slope of the function before and after the respective point, the second derivative test directly gives us whether a point is maximum or minimum by simply noticing the sign of the second derivative of the function at the respective point.

Extreme value analysis : A quick glance

Suppose that x* is a critical point at which f'(x*) = 0.

(i) First Derivative Test :

If f'(x) greater than0 on an open interval extending left from x* and f'(x) less than0 on an open interval extending right from x*, then f(x) has a relative maxima at x*.

If f'(x) less than0 on an open interval extending left from x* and f'(x) greater than0 on an open interval extending right from x*, then f(x) has a relative minima at x*.

If f'(x) has the same sign on both an open interval extending left from x* and an open interval extending right from x*, then f(x) does not have a relative extreme at x*.

(ii) The Second Derivative Test :

f(x) has a relative maxima at x*if f''(x*) less than0.

f(x) has a relative minima at x* if f''(x*)greater than0.

f(x) does not have any extreme values at x* if f''(x) = 0.

Q: Show that if the sum of two numbers is constant, their product will be maximum if the two numbers are equal!

A: Let the numbers be x & y, so that, x - y = c (constant)

Now, let M = xy

= M(x) = x(x-c)

= M'(x) = 2x - c

= M''(x) = c less than 0 [ so M'(x)=0 will give a maxima]

so, putting M'(x) = 0 [condition for maxima exam]

= 2x - c = 0

= x = c/2

Therefore, y = x - c = y = c/2 ;

This shows, that the product (M) is maximum when x = y!!!

Learn more on about Perimeter of Trapezoid and its Examples. Between, if you have problem on these topics Rounded Rectangle , keep checking my articles i will try to help you. Please share your comments.

Solving Geometry Angles Problems

Introduction solving geometry angles problems:

Geometry is the most important branch in math. It involves study of shapes. It also includes plane geometry, solid geometry, and spherical geometry. Plane geometry involves line segments, circles and triangles. Solid geometry includes planes, solid figures, and geometric shapes. Spherical geometry includes all spherical shapes. Line segment is the basic in geometry. There are many 2D, 3D shapes.2D shapes are rectangle, square, rhombus etc. 3D sahpes are Cube, Cuboid and pyramid and so on. Basic types of angles are complementary angles and supplementary and corresponding , vertical .

Basic Geometric Properties used in solving problems

Some important theorems used in solving geometry problems :

The sum of the complementary is always 90 degree.

The sum of the supplementary is always 180 degree.

When two parallel lines crossed by the transversal the corresponding angles are formed. Those angles are equal in measure.

When two lines are intersecting then the vertical are always equal.

In a parallelogram the sum of the adjacent are 180 degree. And the opposite are equal in measure.

Solving example of geometry problems

Solving geometry problems using the above properties :

Pro 1. One of the given angles is 50. Solve its complementary angle.

Solution:A sum of complementary angle is 90 degree.

Given angle is 50

So the another angle = 90-50

So the next angle = 40

Pro 2. One of the given angles is 120. Solve its supplementary angle.

Solution: A Sum of supplementary is 180 degrees

Given angle is 120 degrees.

So, the unknown = 180-120.

So,the unknown = 60 degrees.

Pro 3. The angle given is 180.Solve its corresponding .

Solution:Corresponding are equal

So, the answer is 180

Pro 4. A figure has an of 45 degrees. Solve its vertically opposite angle.

Solution:Vertically opposite are equal.

So, the answer is 45 degrees.

Pro 5. One of the two of the triangle is 55 and 120 degree. Solve the measure of third angle

Solution:Sum of = 180 degrees.

So, the third = 180 - (55 + 120)

= 180 - 175

= 5 degrees

So, third angle is 5 degrees.

Pro 6. If one angle of the parallelogram is 60 degree. Solve the other three .

Solution:A sum of the in a parallelogram is 360 degree.

In a parallelogram adjacent angle are supplementary and opposite are equal.

Therefore, opposite angle of 60 degree is also 60 degree.

And the adjacent angle of 60 degree is 180 - 60 =120 degree.

Here, other three angle are 60 degree and 120 degree, 120 degree.

Define Congruence

Introduction to learn define congruence:

In Geometry, we study different figure, their properties the relations between them. Every figure has its shape, size and Position. Given two figures you can easily decide whether they are of the same shape.

Congruent means equal in all respects. If two figures are congruent then it means that the size, shape and measurement of the first figure correspond to the size, shape and measurements of the second figure.Let us learn some concepts on define congruence.

learn define congruence - Concepts

If two persons compare the size shape of their fore-hands, they will do so by comparing thumb with thumb, fore-finger with fore-finger etc. Thus thumb corresponds to thumb. Similarly the two fore-fingers correspond to each other.

When we put a figure on another figure in such a way that the first figure covers the other figure completely i.e. all parts of the first figure completely cover the corresponding parts of the other. Then these figures will be said to be congruent to each other.

The relation property of two figures being congruent is called congruence. When two figures are congruent we denote them symbolically as. One figure ? second figure. The property of congruence, as you know is symbolically represented as ?.

learn define congruence - problems

Problem 1:

Two triangles are congruent, if all the sides and all the angles of one are equal to the corresponding sides and angles of other. For the example, in triangles of PQR and XYZ in Figure.

Solution:

PQ = XY, PR = XZ, QR = YZ

?P = ?X, ?Q = ?Y and ?R = ?Z

Thus we can say

APQR is congruent to AXYZ and we write

'Delta' PQR ? 'Delta' XYZ

Relation of congruence between two triangles is always written with corresponding or matching

Parts in proper order

Here 'Delta' PQR ? 'Delta' XYZ also means P corresponds to X, Q corresponds to Y and R corresponds to Z.

This congruence may also be written as AQRP ? 'Delta' YZX which means, Q corresponds to Y,

R corresponds to Z and P corresponds to X. It also means corresponding parts; (elements) are equal, namely

QR = YZ, RP = ZX, QP = YX, ?Q = ?Y, ?R = ?Z and ?P = ?X.

This congruence may also be written as

'Delta' RPQ ? 'Delta' ZXY

But NOT as 'Delta' PQR ? 'Delta' YZX

Or NOT as 'Delta' PQR ? 'Delta' ZXY

Problem 2:

Solve ABC and DEF are two triangles such that AB = DE,

Solution:

Given Data:

AB=BC and AD=CE

To prove:

Proof:

Comparing triangles ABC and DEF,

AB=DE (data)

BC = EF (data)

Solve the congruent triangle problem was possible due to SAS postulate.

Congruence learning defined Problem 3:

Solution:

Given data:

QR = SR

Proof:

Compare D TQR and D TSR,

QR = SR (data)

TR = TR (common side)

QT = TS (CPCT)

Now compare D PTQ and D PTS,

TQ = TS (prove above)

PT = PT (common side)

Make Science Experiments

Introduction to make science experiments:

Science experiments are fun. They interest the kids very much. An experiment is demonstrative. The observation the primary graders do stay for ever in their mind. They can recall the experiments and answer the questions. Science experiments are much better than theoretical learning. Hence schools are advised to conduct science experiments. The children should be made to take part in it. Science experiments are one way of learning science.

An eggy experiment of science:

An eggy experiment is one way of teaching the children about science.

The experiments requires

(1) a small drinking glass

(2) lemon juice

(3)eggshells

(4) lime stone.

These are inexpensive materials that can be brought by the students to the classroom. Each child can do the experiment by himself and record the observation.

The experiment:

Step 1: Let us ask the children to put the eggshells in the drinking glass.

Step 2: Let us ask them to pour the lemon juice into the drinking glass enough to cover the egg shell.

Step 3: Let us ask the shildren to observe what happens.

Step 4: Observation shows us that the bubbles come out.

Step 5: What made the bubbles come out?

Step 6: Reasoning : the eggshells contain calcium carbonate. It reacts with the lemon juice and produces carbon dioxide gas. The gas comes out bubbling through the lemon juice.

Step 7: Repeat the experiment with limestone instead of eggshell and note what happens

Step 8: Lime stone contains calcium carbonate and carbon dioxide is released and it comes out bubbling . The little children will remember this experiment and will remember that carbon dioxide is released when calcium carbonate reacts with lemon juice .

Plants need light , air and water to live - an experiment.

We can conduct experiment on plants to see how it survives.

Experiment 1:

The children are asked to keep two pots with plants, one outside the class an the other inside the class. Let the children water both the plants. The plant that is outside the class room grows well. It has fresh yellow flowers. The plant that is inside the classroom sheds its leaves,

The teacher asks the kids "Why is this plant shedding its leaves?

Usually the children come up with varying answers. The teacher then explains that the leaves need the sunlight with which it cooks the food for the plant. Without the sunlight , the plant dies .

Experiment 2 : Now the teacher asks the children to keep the other plant also outside the classroom. She asks the children to water one plant and not to water the other plant. Now she asks the children to observe the two plants the next day. What do they see?

The plant that is watered is alive while the plant that is not watered droops down. This experiment shows that the plant needs water for survival.

Experiment 3 : The teacher locks one pot of plant inside the cupboard and the other flower pot is left outside the class room. After a few hours, the plant inside the cupboard is observed. The plant is not fresh. The leaves droops proving that air is essential for survival. The flower is withered.

These three experiments prove that air, water and sunshine are essential for the survival of plants.

Ancient Greek Mathematics

Introduction to ancient greek mathematics :

Ancient greeks are regarded as one of the major discoverer of "Geometry". The greeks were not intrested in numbers much. So they showed their interest in geometry which led to major discoveries. The notable achievements of the greek mathematicians were observed mainly in the period of 6th century BC to 4th century AD.

The word "Mathematics" was termed by pythagoreans (the followers of pythagoras) from the greek word "mathema" meaning " subject of instructions".

Major discoveries in ancient greek mathematics

Some of the major discoveries made by the ancient greek mathematicians are as follows :

The concept of theorems and postulates was introduced by the ancient greek mathematicians.

Euclid's elements were introduced.

One of the most important discovery was theory of conic sections during Hellinistic period.

Archimede's principle was introduced during this period.

Some major contributions were also made in the field of astronomy.

Other achievements were also made in number theory, applied mathematics, mathematical analysis and were close to integral calculus.

Major ancient greek mathematicians

The most famous greek mathematicians are:

Pythagoras

Pythagoras had major contributions in the field of Mathematics. He introduced pythagoras theorem and its proof. He also proved the existence of irrational numbers. He had interests in other fields such as astronomy and philosophy. His studies had a great influence on Plato. He also established an academy with an aim to spread Mathematics in the universe.

Anaxagoras

He was a pre - Socratic greek philospher. He made a significant contribution in the field of cosmology. He studied the celestial bodies closely.

Aristarchus

He was a Greek mathematician and an astronomer. He was the first astronomer to place sun at the center of the solar system instead of Earth. He proposed heliocentric model of solar system. He calculated distance of sun, moon from earth and their sizes.

Thales

He introduced Thales theorem and many corollaries which he used to calculate the height of pyramid and distance of ship from the shore.

Euclid

He introduced a book named Elements. He defined the terms theorems, proofs, postulates etc. His major contribution was conic section.

Archimedes

Archimedes gave an approximate value of Pi. He also calculated area covered by the arc of parabola and had major contribution in area of calculus. He produced the solution for infinite summation series.

Eudoxus

His contributions are observed in modern integration.

and many other greek mathematicians existed during the hellinistic period.

The origins of Greek mathematics are not easily documented. The earliest advanced civilizations in the country of Greece and in Europe were the Minoan and later Mycenean civilization, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, they left behind no mathematical documents.

Help With Third Grade Math

Introduction to help with third grade math:

Study of basic arithmetic operations and arithmetic functions is called mathematics. Help with third grade math used to learn some basic math operation. In mathematics, basic concept is arithmetic operations.

The basic arithmetic operations are addition, subtraction, division, multiplication and placing values. The help with third grade math is deals with basic algebra and involves a basic math operation only. In this article we are discussing about help with third grade math.

Examples problems for help with third grade math:

Basic addition problems for help with third grade math:

1. Find the add value of the given nos, using addition operation, 322 + 415 + 208

Solution:

Given nos using addition operation for, 322 + 415 + 208

First step, we are going to add the first two nos,

322 + 415 = 737

Then add third number with first two nos of sum values,

737+ 208 = 945

Finally we get the answer for given nos are 945.

2. Find the add value of the given nos, using addition operation, 907 + 549 + 284

Solution:

Given nos using addition operation for, 907 + 549 + 284

First step, we are going to add the first two numbers,

907 + 549 = 1456

Then add third number with first two numbers of sum values,

1456 + 284 = 1740

Finally we get the answer for given numbers are 1740.

Basic subtraction problems for help with third grade math:

1. Find the subtract value of the given numbers, using subtraction operation, 840 - 453 - 385

Solution:

Given numbers using subtraction operation for, 840 - 453 - 385

First step, we are going to add the first two numbers,

840 - 453 = 387

Then subtract third number with first two nos of subtracted values,

387 - 385 = 2

Finally we get the answer for given numbers are 2.

2. Find the subtract value of the given numbers, using subtraction operation, -278 + 452 - 603

Solution:

Given numbers using subtraction operation for, -278 + 452 - 603

First step, we are going to add the first two numbers,

-278 + 452 = 174

Then subtract third number with first two numbers of subtracted values,

174 - 603 = -429

Finally we get the answer for given nos are -429.

Basic multiplication problems for help with third grade math:

1. Find the multiply value of the given nos, using multiplication operation, 45 * 31 * 2.

Solution:

Given nos using multiplication operation for, 45 * 31 * 2

First step, we are going to multiply the first two nos,

45 * 31 = 1395

Then multiply the third number with first two nos of multiplied values,

1395 * 2 = 2790

Finally we get the answer for given numbers are 2790.

2. Find the multiply value of the given numbers, using multiplication operation, 11 * 5 * 10

Solution:

Given numbers using multiplication operation for, 1 * 5 * 1

First step, we are going to multiply the first two numbers,

11 * 5 = 55

Then multiply the third number with first two numbers of multiplied values,

55 * 10 = 550

Finally we get the answer for given numbers are 550.

10 Ways to Effectively Communicate During Online Tutoring Lessons

Communication is said to be the key to personal and career success. Thus, it wouldn't be wrong to consider communication as an effective arsenal in the online learning arena. As internet-based learning progresses in leaps and bounds, online tutors are exceedingly engaging in different techniques to make online classrooms a success. However, it is essential to lay sole emphasis on communication to ensure that students can reap maximum benefits out of online sessions. Here are some constructive tips that will enable tutors to communicate better while conducting learning sessions. Take a look.

Keep students engaged and active during the sessions. Let them read, write and draw as you teach.Most online tutoring sessions are taught on whiteboards. While writing on whiteboard it is best to make use of colored pens. Use different colored pens while writing. This will make the lessons visually organized and easily readable.Encourage students to ask questions and seek solutions to their doubts. They shouldn't be shy about asking queries from online tutor. Share with them all the subject knowledge you have. Provide them with useful online resources. This will help in effective communication of a lesson.Let students access all possible learning resources during the tutoring hours. Help your students leverage the power of internet and utilize different educational resources under your guidance.Mark your presence to the student through online chatting. In non-voice tutoring sessions, the student cannot hear your voice or see your body language or facial expression to ensure your availability. Be attentive about the response you get on the chat box. It will make the classroom more lively.Make use of pointer as earnestly as possible. At times, students might not be able to keep track of the movement of your mouse as you work across the whiteboard. Using a pointer tool enables you to guide the students with clear visibility and helps them to locate your activity. Moreover, using a pointer will put less strain on your eyes too.If you are using VoIP technique to conduct the teaching sessions, take turns while speaking. During heavy traffic influx, VoIP technology may not work meticulously. If the student is asking a question, stop the lesson and listen to the query attentively.Provide regular feedback. Feedback is an important element of communication. Without feedback, the communication process remains incomplete. Affirm your presence with verbal communication and gestures. Using smileys to convey your agreement or disagreement is the best way.Avoid giving negative feedback. Avoid the use of negative phrases even if you find some fallacy at the student's end. Refrain the use of negative terms and use polite statements instead.Be genuine in your ways of communication. If you find something lacking from the student's end ensure to rectify it by sharing all your knowledge and concern.

Effective communication will ensure that students grasp every bit of knowledge that you share during tutoring sessions. So follow these communication tips and enhance the productivity of your online sessions.

Tutor Pace Inc. is an established online tutoring provider that is favored by both students and online tutors for its technology-empowered and cost-effective tutoring online services and packages. Rate this Article

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Variables in Statistics Tutor

Introduction :

The variable which is available in the statistics it is called as statistical variable. It is a feature that may acquire choice in adding of one group of data to which a mathematical enumerates can be allocated. Some of the variables are altitude, period, quantity of profit, region or nation of birth, grades acquired at school and category of housing, etc,. Our statistics tutor defines the different types of statistics variables and the example of these types. Our tutor helps to you to know more information about the variables in statistics.

Variables in statistics tutor:

Let us, see the different types used in statistics and the uses of these types. There two kinds of used in statistics. They are,

Statistical 1: Qualitative

Statistical 1: Quantitative

These two kinds are used for various uses based on the statistics. Also, these types are divided into number of categories and which is used to various uses.

Explanation :

Qualitative :

The qualitative variant is the initial category of variable in statistics. Qualitative variables are cannot be measured which are called as attributes.

The qualitative variable is categories into two parts:

Qualitative type 1: Nominal

Qualitative type 2: Ordinal

1. Nominal variable:

Nominal values are the qualitative that does not hold any mathematical proposition like one's sacred quantity or city or surroundings. Using this nominal it does not do any addition, subtraction, even sorted.

2. Ordinal variables:

Ordinal variable is similar to the nominal variable but it uses some logical technique can arrange the variables. For instance in school ( junior and senior).

Quantitative variables:

The next category of statistical is a quantitative. The quantitative can be measured straightly.

The quantitative is categories into two parts:

Quantitative type 1: Continuous

Quantitative type 2: Discrete

1. Continuous :

The variable that can acquire all the values from the specified sequence then it is known as continuous. That is it can take an infinite value from the higher range to lower range of the given series.

Example:

Assume the person's age. Here, age is considered as a numerical value. If the age of the person is in among 36 and 56, the outcome can be any value among 36 and 56; therefore "Age of a person "is continuous variable.

2. Discrete :

The variable that can acquire only a specific value from the given range then it is said to be discrete variable. Hence, it can take the finite number of values only.

Example:

The number of child in the family is among 4 and 6, the outcome will be only 5. That is among 4 and 6, the can take only a specified value 5; therefore, "number of child in a family" is discrete variable.

Elementary Algebra Test

Introduction to elementary algebra test:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. Elementary algebra is the one of the basic foundation of algebra. In this article we shall discuss about the examples involved in algebra.

Algebra is a set of mathematics which includes any numbers like real numbers , complex numbers and other matrices. We can also perform any operation like addition, subtraction, multiplication and division .

In algebra we can perform the operations of variables , equations, inequalities, algebraic word problems, geometry problems and other number theories.

The Following topics are covered under elementary algebra test:

Rational numbers

Operations with negative and positive numbers

Monomials and polynomials

Formulas of abridged multiplication

Division of polynomials

Division of polynomial by linear binomial

Divisibility of binomials

Factoring of polynomials

Algebraic fractions

Proportions

Examples for elementary algebra test:

Example 1: Solve the following problem 'sqrt(36)' *'sqrt(25)' =?

solution: 36= 6*6, 25 =5*5

= 'sqrt(6*6)' * 'sqrt(5*5)'

= 6*5

= 30

Example 2: What is the value of the expression 3x2 + 3xy - 3y2 when x = 2 and y = - 4?

Solution: here x=2 and y =-4

apply the values in the above equation, we get

= 3*(2)2+3(2)(-4)-3(-4)2

= 3(2*2) -24-3(-4*-4)

= 3(4) - 24 -3(16)

= 12-24- 48

= 12-72

= -60.

Example 3:: Solve the equation: 5(-3x - 3) - (x - 1) = -4(4x + 2) + 11

Solution: Given the equation

5(-3x - 3) - (x -1) = -4(4x + 2) - 8

Multiply factors.

-15x - 15 - x - 1 = -16x - 8 -8

Group like terms.

-16x - 16 = -16x - 16

Add 16x + 16 to both sides and write the equation as follows

0 = 0

For x value will be true for all statements x and therefore all real numbers are solutions to the given equation.

Example 4: Simplify the expression 5(a -4) + 5b - 5(a -b -4) + 6

Solution: Given the algebraic expression

5(a -4) + 5b - 5(a -b -4) + 6

Multiply factors.

= 5a - 20 + 5b -5a + 5b + 20 + 6

Group like terms.

= 10b + 6.

Example 5: Simplify: 4c + 2d - 3d + 5c + d = 0

Solution:

Step 1: Group together the like terms:

4c + 2d - 3d + 5c + d = 0

(4c + 5c) + (2d - 3d +d) = 0

Step 2: Then simplify:

9c = 0,

c = 0

Answer: c = 0.

Example 6: Solve: 6(c - 5) + 4 = 9

Solution:

Step 1: Remove the brackets

6c - 30 + 4 = 9

Step 2: Isolate variable a

6c = 30 - 4 +9

6c = 35

c='(35)/(6)' = 5.83

Answer: c = 5.83

practice problems for elementary algebra test:

Problem 1: Michael and his four school friends are planned to share the cost of a 2 bedroom apartment. The rent amount is 'x' dollars. Write the expression for Michael's share.

Problem 2: Write the expression for following: "Add 7 times a number y from twice the cubic of the number".

Problem 3: The price of an i-pod is 'r' dollars. The i-pod is on sale for 25% offer. Write the expression for savings that is being offered on the i-pod.

Problem 4: Simplify and solve: 2x + 2 =40.

Problem 5: Solve the equation for z: z + 58 = 10

Problem 6: Solve the following expression: 6yz + z2, if y = -1 and z= -2.

Problem7: In a class of 50 students wrote a mathematics test. 15 students got an average score of 85. The other students got an average score of 70. Find the average score of the 50 students.

Problem 8: Add the following expressions: (a - 3) + (2a + 17)

Answer 1: Michael's share is x/5.

Answer 2: 3y2 + 7.

Answer 3: The offered price of an i-pod is 0.25r

Answer 4: x = 19.

Answer 5: z = -48

Answer 6: 13.

Answer 7: The average of the 5o students = 74.5

Answer 8: a = -20.

Test Question:

1) If a integer is divided by 4 and then 3 is subtracted, the result is 0. What is the number?

12

4

3

2

2) If A represents the number of apples purchased at $15 each and B represents the amount of bananas purchased at $10 each, which of the next represents the total value of the purchases?

A+B

25(A+B)

10A+ 15B

15A+ 10B

3) Martin has scored of 87, 81, and 88 on the first 3 of 4 tests. If he needs an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test?

85

86

87

92

93

Statistics Homework

Introduction to Statistics homework: Statistics is defined as a process of analysis and organize the data.

We learn about mean, median, mode in statistics. Mean is same as average in arithmetic. Median is the midvalue of the data. Mode is the value of the data that appears most number of times.

Statistics deals with mean, deviation, variance and standard deviation. The process of finding the mean deviation about median for a continuous frequency distribution is similar as we did for mean deviation about the mean. It is a technology to collect, manage and analyze data. In this article, Basic functions and homework problems on statistics are given.

Statistics Functions and Examples:

In statistics the mean which has the same as average in arithmetic. In statistics mean is a set of data which can be dividing the sum of all the observations by the total number of observations in the data.

Sum of observations

Mean = ------------------------------------

Number of observations

The statistic is called sample mean and used in simple random sampling.

The mean of deviation has discrete frequency distribution and Continuous frequency distribution.

The mean deviation and median for a continuous frequency distribution is similar as for mean deviation about the mean.

Median is found by arranging the data first and using the formula

If n is even,

Median = '1/2[ n/2 "th item value"+(n/2+1) "th item value"]'

If n is odd, Median = '1/2 (n+1)'th item value

Variance: In statistics the variance s2 of a random variable X and of its distribution are the theoretical counter parts of the variance s2 of a frequency distribution. In a given data set of the variance can be determined by the sum of square of each data. Here variance is represented by Var (X). The formula to solve the variance for continuous and discrete random variable distributions can be shown. In statistics variance is the term that explains how average values of the data set vary from the measured data.

s2 = ?(X - M) 2 / N

S2 = ?(X - M) 2 / N

Standard Deviation: It is an arithmetical figure of spread and variability

Ex 1 : Choose the correct for normal frequency distribution.

A. mean is same as the standard deviation

B. mean is same as the mode

C. mode is same as the median

D. mean is the same as the median

Ans: D

Ex 2 : Choose the correct variable for confounding.

A. exercise

B. mean

C. deviation

D. Occupation

Ans : A

Ex 3: The weights of 8 people in kilograms are 60, 58, 55, 72, 68, 32, 71, and 52.

Find the arithmetic mean of the weights.

Sol : sum of total number

Mean = ------------------------------

Total number

60 + 58 + 55 + 72 + 68 + 32 + 71 + 52

= -----------------------------------------------------------

8

468

= -------

8

= 58.5

Ex 4: Find the median of 29, 11, 30, 18, 24, and 14.

Sol : Arrange the data in ascending order as 11, 14, 18, 30, 24, and 29.

N = 6

Since n is even,

Median = '1/2[ n/2 "th item value"+(n/2+1) "th item value"]'

= '1/2' [6/2th item value + (6/2 + 1)th item value]

= '1/2' [3rd item value + 4th item value]

= '1/2' [18 + 30]

= '1/2' * 48

= 24

Ex 5: Find the mode of 30, 75, 80, 75, and 55.

Sol : 75 are repeated twice.

Mode = 75

Ex 6: Find the Variance of (2, 4, 3, 6, and 5).

Sol: First find the mean

Mean = '(2+3+4+6+5)/5 = 20/5=4'

(X-M) = (2-4)= -2, (3-4)= -1, (4-4)=0, (6-4) =2, (5-4) =1

Then we can find the squares of a numbers.

(X-M)2 = (-2)2 = 4, (-1) 2 = 1 , 02 = 0, 22 = 4 , 12 = 1

'sum(X-M)^2= 4+1+0+4+1=10'

Number of elements = 5 , so N= 5-1 = 4

'(sum(X-M)^2)/N = 10/4=2.5'

Here we can add the all numbers and divided by total count of numbers.

= (4 + 16 + 9 + 36 + 25) / 5

= 90 / 5

= 18

Ex 7: Find the Standard deviation of 7, 5, 10, 8, 3, and 9.

Sol:

Step 1:

Calculate the mean and deviation.

X = 7, 5, 10, 8, 3, and 9

M = (7 + 5 + 10 + 8 + 3 + 9) / 6

= 42 / 6

= 7

Step 2:

Find the sum of (X - M) 2

0 + 4 + 9 + 1 + 4 = 18

Step 3:

N = 6, the total number of values.

Find N - 1.

6 - 1 = 5

Step 4:

Locate Standard Deviation by the method.

v18 / v5 = 4.242 / 2.236

= 1.89

Homework practice problems:

1. Choose the correct for statistics is outliers.

A. mode

B. range

C. deviation

D. median

Ans : B

2. Find the arithmetic mean of the weights of 8 people in kilograms is 61, 60, 58, 71, 69, 38, 77, and 51.

Sol : 60.625

3. Find the median of 22, 15, 32, 19, 21, and 13.

Sol : 20

4. Find the mode of 30, 65, 52, 75, and 52.

Sol : 52

5. Find the Variance of (3, 6, 3, 7, and 9).

Sol: 36.8

6. Find the median of 9, 12, 26, 48, 20, and 41.

Sol: 23

Learning About Addition

Introduction of learning about addition :

Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+).

For example, in the above picture on the right, there are 1 + 4 apples-meaning one apple and four other apples-which is the same as five apples. Therefore, 1 + 4 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more. This is how we have to learn addition learning.

Learning of addition properties:

I) Positive number addition:

Positive integers are whole numbers greater than zero. Example: 2 + 3, 2 + 9, 20 + 45 + 23...etc. Example: 2 + 3 = 5, 3 + 7 = 10

II) Negative number addition:

The addition is done for negative numbers. Example: -19, -38, -458, -594, and 6558...etc. Negative numbers indicated by the minus sign (-). Example: (-2) + 3= 1, 3 + (-5) = -2.

Adding Integers Rules:

Rule 1: The sum of two positive integers is always positive integer.

Rule 2: To add a positive and a negative integer

Find the absolute value of each integer.Subtract the small number from the larger number you get in Step 1.The answer from Step 2 takes the sign of the integer with the greater absolute value.

Properties for adding numbers:

The properties are,

Identity property: 0+c=c+0=c

Example: 41+0=0+41=41.

Community property: a+b=b+a

Example: 200+16=16+200.

Associative property: (a+b)+c=a+(b+c)

Example: (5+24)+7=5+(24+7)=36.

Inverse property: c+(-c)=0

Example: 7+(-7)=0

Examples for learning about addition:

Example 1: 705 + 922 = 1627

Example 2: 4694 + 5887 + 6559 = 17140

Example 3: 4633+ 565 + 879 + 1336 = 7413

Example 4: Find two consecutive integers whose sum is equal 127.

Solution:

Let x and x+1 be the two numbers. Use the fact that their sum is equal to 127 to write the equation

x + (x + 1) = 127

2x +1 = 127

Solve for x to obtain

x = 63

The two numbers are

x = 63 and x + 1 = 64

Problem 5: Find three consecutive integers whose sum is equal to 888

Solution:

Let the three numbers be x, x+1 and x+2. Their sum is equal to 888, hence

x + (x + 1) + (x + 2) = 888

Solve for x and find the three numbers

x = 295, x + 1 = 296 and x + 2 = 297

Adding decimals

3.25

(+) 2.34

5.59

Online Tutoring And The Future of Learning

Teachers today are faced with more students than ever before. Even school districts that make an effort to keep their classes small are forced to add more students than any one teacher can effectively teach. Students who happen to fall behind in their classes for any reason can find themselves falling further and further behind over time. Even students with great potential may find themselves frustrated by teachers who simply do not have the time to give them the individual attention that they deserve.

The future of education is the internet. No other form of communication and training comes even close to providing the benefits of online learning. Although great transformations take time, one way to benefit from internet education now is through web tutoring services.

Subjects like chemistry and physics are not just about memorizing a few facts and repeating them back when asked to do so. In order to learn advanced concepts students must be fully engaged. This is why the quality of tutoring matters.

This dilemma is being faced in homes and classroom everywhere. A tried and true method that many parents have used is that of hiring a tutor. Unfortunately, great tutors are as rare as great teachers are.

The best way to master a subject is to learn it directly from someone who knows it well and who knows how to teach. While anyone can be a tutor, not everyone can be effective at it. This distinction might not matter with simple subjects, but as study material becomes more complex, it matters a lot.

Finding the right tutor usually involves travel, trial and error. Students must go to the location of the tutor and return home afterwards. Between getting there and back, they have spent more time travelling than learning. With an online tutor, no travel is necessary. Students simply log on and start learning. Over time, this gives students who use an online tutor a serious advantage over those who do not.

One of the major reasons that parents do not hire tutors for their kids is the cost. Frankly, many parents cannot afford to pay for tutoring services. Good tutoring is expensive, the time and money involved can quickly spiral out of control. Online tutoring reduces these expenses to a bare minimum; without reducing the quality of tutoring.

The great pity of modern education is that young and curious students do not always get the chance to challenge themselves. Many brilliant kids languish in classrooms, uninspired and disappointed. Taking learning to the web with online tutoring means that students everywhere are finally getting the educations that they deserve.

Number of Divisors

Introduction to Whole Number Divisors:

A division method can be done by using the division symbol ÷. The division can be otherwise said to be inverse of multiplication. The one of the major operation in mathematics is division operation. In division, a ÷ b = c, in that representation "a" is said to be dividend and "b" is said to be divisor and "c" is said to be quotient. The letter "c" represents the division of a by b. Here the resultant answer "c' is said to be quotient. Let us see about whole number divisors in this article.

Whole Number Divisors for the Number eighty

The numbers that can divide by eighty is said to be the divisors of eighty.

Let us assume that eighty can be divided by 2, 4, 5, 8, and 10.

Example 1:

Divide the whole number 80 ÷ 2

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

2)80(

The number 2 should go into 8 for 4 times. So, put 4 in the right side of the bracket.

2)80(40

8

---------------

00

00

-------------------

The zero can be placed just near the 4 in the quotient place.

The solution for dividing eighty by 2 is 40.

Example 2:

Divide the whole number 80 ÷ 4

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

4)80(

The number 4 should go into 8 for 2 times. So, put 2 in the right side of the bracket.

4)80(20

8

---------------

00

00

-------------------

The zero can be placed just near the 2 in the quotient place.

The solution for dividing eighty by 4 is 20.

More Problems to Practice for Finding the Divisors for eighty

Example 3:

Divide the whole number eighty ÷ 5

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

5)80(

The number 5 should go into 8 for 1 time. So, put 1 on the right side of the division bracket.

5)80(1

5

---------------

30

-------------------

Then the number 5 should go into 30 for 6 times. So put 6 just near the 1 on the quotient place.

5)80(16

5

---------------

30

30

----------------

0

----------------

The solution for dividing 80 by 5 is 16.

Example 4:

Divide the whole number 80 ÷ 8

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 8 should go into 8 for 1 time. So put 1 on the right side of the division bracket.

8)80(10

8

---------------

00

----------------

The zero can be placed just near the 1 in the quotient place.

The solution for dividing eighty by 8 is 10.

Example 5:

Divide 80 ÷ 10

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 10 should go into 8 for 0 times. So, take the digit as two digits in a given number of the division bracket.

Then the number 10 should go into eighty for 8 times. So put 8 on the right side of the division bracket.

10)80(8

80

---------------

0

-------------------

The solution for dividing eighty by 10 is 8.

Therefore, the divisors for the whole number eighty are 2, 4, 5, 8 and 10.