Variable and Expression

In the previous post we have discussed about Completing the Square and In today's session we are going to discuss about Variable and Expression. When we study about the algebra and finding the solution of the algebraic equations, we say that the child must have the knowledge of the variable and expression before we start the study of the equations. By the term variable, we mean the values which are unknown and the different values can be placed to these variables. Now we will say that the expression can be formed by joining the terms with the operators + and -.
So we say that x , y , z are the variables. On the other hand we have 3x, 5y, 6z as the terms which are used as the units for the formation of the algebraic expressions. So we say that 3x + 5y – 2z is the expression. We can perform the mathematical operations on the expressions.

In order to add the expressions, we need to remember that the like terms of the expressions can be added together. So if we have the two expressions 3x + 6y and 4x – 2y so to add the given expressions we will proceed as follows:
(3x + 6y) + (4x – 2y),
= ( 3x + 4x ) + ( 6y – 2y),
= 7x + 4y.
Thus we say that the coefficient of the like terms are added up. In the same way the operation of subtraction can also be performed. So if we take the two expression: 3x + 6y and 4x – 2y . If we need to find the difference of the two expressions we will write it as follows: (3x + 6y) – ( 4x – 2y).
= ( 3x – 4x ) + ( 6y + 2y),
= -x + 8y.
We can also perform the operation of multiplication and division on the algebraic expressions. Different rules are followed for solving such expressions.
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Completing the Square

In this blog we will see how to Completing the Square. To find the complete square of any term first we need to take a quadratic equation. For example: as we know that the equation which has highest power is 2 is said to be quadratic equation. The general form can be written as: ax² + bx + c = 0, then change the general form into this given form:

a ( x + d)² + e = 0.

If we want to find the value of variable ‘d’ then we use formula: the formula to find the vaule of ‘d’ given as: d = b / 2a and formula to find the vlaue of ‘e’ is given as: e = c – b² / 4a. To calculate the complete square we need to follow some basic steps so that we can easily understand the process.

Step 1: First of all we have to take a simple expression. Suppose we have simple expression as: x² + bx. Here in this expression value of x is twice.

Step 2: Then complete square in the given expression. So it can be written as: x² + bx + (b / 2)² = (x + b / 2)², it means if we add (b / 2)² then we get the square.

Let understand all the steps with the help of small example:

For example: p² + 6x + 7, in this expression the value of b is 6,

Solution: Given expression is p² + 6x + 7, to find its complete square we need to follow the above mention steps:

First of all we have to find the complete square or value of d. we can find the vlaue of d using the above given formula:

d = b / 2a = 6 / 2

So it can be written as:

p² + 6p + (6 / 2)² + 7 – (6 / 2)²

So it can be written as:

(p + 6 / 2)² + 7 – 9 on further solving we get:

(p + 3)² – 2. in this way we can find out the complete square.

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Irrational Numbers List

In the previous post we have discussed about Is 0 a rational or Irrational number and In today's session we are going to discuss aboutIn mathematics, any number written in the form of simple fraction is said to be irrational number or the number which is not rational is irrational number.

The ‘pi’ is the example of irrational number because its value after the decimal point is:

⊼ = 3.1415926535897……….. So it cannot be expressed in form of rational number.

Now we will see the irrational numbers list. The irrational number list is given below: A list of irrational numbers includes numbers like: (know more about Irrational Numbers List, here)

 √2, √3, √5, √7, √11, √13, √17, √19, √23, √29, √31, √37, √41, √43, √47, √53, √57, √59, √61, √63, √67, √69, √71, √73, √79, √83, √87, √89, √93, √97, √101, √103, √107, √109, √111, √113, √117, √119, √123, √129, √131, √137, √141, √143, √147, √153, √157, √159, √161, √163, √167, √171, √173, √173, √183, √187, √189, √193, √197, √201, √203, √207,√211………...and so on. The List of Irrational numbers include many other numbers. Let’s study some facts about irrational numbers:

·         Negative of an irrational number is also irrational number, meaning of this sentence is: if ‘y’ is irrational then ‘–y’ is also an irrational number.

·         If we add an irrational number and rational number then the sum we get is also irrational. Let ‘p’ is an irrational number and ‘q’ is a rational number then the sum (p + q) is also irrational.

·         In case of roots also the above step is applicable, let √7 is irrational and ‘e’ is rational then the sum √7 + e is also irrational. This is all about the irrational number list. Now we will Units of Momentum. Momentum can be defined as the product of mass and velocity of given object. The unit of momentum is kg.m/s. If you are prepression for IIT then please prefer online tutorial of iit sample papers. It is very helpful for iit exam point of view.   

Is 0 a rational or Irrational number

Before comparing that Is 0 a rational or Irrational number, it is necessary to learn about the rational and irrational. Rational number can be defined as a number which is written in the fraction form or written in p/q (in ratio). For example: 1.2 the number is rational because it is also written in the fraction form. So we can write it as 6/5. An irrational number can be defined as a real number which cannot be written in the fraction form or cannot be written in p/q form. For example: pi the value of pi is 3.14 it is not in the ratios. So pi is included in the categories of irrational number. In word we can say that the numbers are not rational are all irrational numbers.
Now we will see Is 0 a rational or Irrational number? According to the definition of rational number and irrational number we can easily say that ‘0’ is rational number because it can be written in the form of p/q or in form of fraction. If we write 0 in fraction form then we can write it as:
⇨ 0 / 1 = 0
We can easily compare any number using the definition of rational number and irrational number.  Suppose we have given some number 9.5, 5, 1.75, √2, 0.111, √3, √99, now find which number is rational number and which one is irrational number. (know more about Is 0 a rational or Irrational number, here)
According to the definition of rational number and irrational number we can easily compare the given number.
9.5 can be written as 19/2, so it is rational number. 1.75 can be written as 7/4 so it is also rational number. √2, √3 and √99 cannot be written in the fraction form so these numbers are irrational number. And 0.111 can be written as 1/9 so it is also a rational number. So this is all about the rational and irrational number.
Now we will see the Units of Density, unit of density is given as kg/m³. Before entering in the examination of 10^th class please focus on 10th maths question paper. It is very helpful for exam point of view and In the next session we will discuss about Irrational Numbers List. 

How to Find Percentage

In the previous post we have discussed about Proportions and In today's session we are going to discuss about Percentage, It defines how a number is present in form of fraction. It is define as a ratio that is based on the whole number. We can describe percentage as a value occurred on per 100. As the name describe per cent in which cent means hundred. In this blog we are going to know about how to find percentage. When we define any number in terms of percentage as 25% means 25 / 100 or 25 per 100. It also express the method of changing any percent value in the whole number.

We can easily express a number in form of percentage , first generate a fraction that have numerator as the value for which we want to calculate percentage and denominator define as the whole value and then multiply this fraction with 100 .It gives the percentage as if there is part x and its whole value is y then percentage is expressed as x / y * 100.

We can describe whole process of generating percentage in form of some steps as:

(1): Find the whole value

(2): define the portion for which percentage will be calculated.

(3): Generate the fraction

(4): calculate the percentage by multiplying the fraction value with the 100.

All the steps are described by an example as if the value is 25 and whole value is 50 than percentage is calculated as put the whole value and partition value in form of fraction as 25 / 50 and then multiplied it with 100 as 25 / 50 * 100 = 50 % that means 25 is 50 % of 50 that means 25 is just half of 50.

Cognitive Bias describe as a deviation in the judgment that is generate in specific situation. It is express as the inherent errors in thinking.

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Proportions

In algebra proportion is define as the special form used for comparison of two ratios . When we talk about the ratios it define as relationship between two or more things. But when we talk about the proportion it is the method of setting two ratios equal. We can say it in other words as when two ratios are equal to each other then their proportion are also equal. It is explained as 1 / 2 is equal to the 2 / 4 or 14 / 28.

Proportions is used when there is one part is missing in the given ratio as if a ratio is equal to other ratio means there proportion are equal then we can easily find the missing value. (want to Learn more about Proportions, click here),

As if there are two ratios a / b that is equal to x / y then these are stated as

a / b = x / y means these ratios have same proportions.

Sometimes values are missing from ratios but having the same proportion as x / 10 and 1 / 2 have these ratios are stated as x / 10 = 1 / 2, so for finding the value of x we use the proportion as

x = 10 * 1 / 2

x = 10 / 2 = 5.

We can also depict the proportion as the comparison that shows the relative relation between two or more things in terms of quantity , quality and any other sort of measurement.

Topic on How to Graph a Circle will describe all the methods of graphing a circle in easy manner.

icse sample paper that is provided by the icse board that helps the students to understand the pattern of paper come in the exam and In the next session we will discuss about How to Find Percentage. 

Consecutive Odd Integers

In the previous post we have discussed about How to solve Consecutive Integers and In today's session we are going to discuss about Consecutive Odd Integers. Let us first talk about the integers. The numbers which can be expressed in the form of the whole numbers and their additive inverse are called integers. All the integers can be expressed on a number line. A number line contains the series of all positive and negative numbers marked at the equal interval, where we could observe the number zero at the center, positive numbers at the right of the number line and negative numbers at the left of the number line.  Now we will learn about the Consecutive Odd Integers. By the consecutive numbers, we mean the numbers appearing one after another. Thus 1, 2, 3 . . .  are consecutive integers.  Now if we talk about the consecutive odd integers, we mean the series of odd integers which occur one after another but are odd.  So we say that the series of odd consecutive integers are 1, 3, 5, 7, 9 , . . . . . . etc.  In case of writing the series of odd integers in the form  of general series we will assume any number x. We know that 2 * x will always be the odd number. Now on another hand we say that if we add 1 to the odd number, it becomes the odd number. For this we say that the number 2x + 1 is any odd number. Now to write the series of the odd consecutive integers, we write 2x + 1, 2x + 3, 2x + 5, 2x +7 . . . . etc. (know more about Integer, here

 In order to learn about the Variance Calculator, we will visit online math tutor and learn more about the related topics. Central Board of Secondary Education Sample Papers is also available in all the subjects and they can guide us to understand the   pattern of the question papers in the previous years. It will guide the students to prepare for the fore coming examinations.

How to solve Consecutive Integers

Integers are the numbers which can be expressed in the series from minus infinite to plus infinite. Now let us look at the consecutive integers. Two integers which exist one after another when they are expressed on the number line are called consecutive numbers. If we have any number n, then the successor  and the predecessor of the number n forms the series of the consecutive numbers. So if we have n = 5, then we have n-1 = 5 – 1 = 4 and  n + 1 = 5 + 1 = 6. Thus the series 4 , 5 , 6  are called consecutive numbers.   There series of consecutive numbers can be used to solve many word problem related to linear equations.  In case we talk about any 3 consecutive integers, we say that series will be x, x + 1 and x + 2. On the other hand if we need to write the series of even numbers, then we know that each even number is the multiple of 2, so the first number will be 2 * x. (know more about Integers, here

Thus the series of consecutive integers will be  2x , 2x + 2, 2x + 4. Now we will assume the series of odd consecutive integer numbers. For this we will assume the first odd integer as  2x + 1. The next odd integer will be  2x + 3, 2x + 5. Thus the series of consecutive odd numbers will be  2x + 1, 2x + 3 and 2x + 5.
 If we have the problem that the sum of 3 consecutive integers is 36, find the integers. Then we will first assume the three numbers as x , x + 1 and x + 2. Thus we represent the sum as :
X + x + 1 + x + 2  = 36
Or 3x + 3 = 36
Or 3x = 36 – 3
Or 3x = 33
Or x = 33/ 3 = 11
SO  the three numbers are 11, 12 and 13.
 In order to learn How do you Find the Circumference of a Circle, we can take online help from math tutor and learn  the concepts in details. CBSE physics syllabus is also available online and we can download the curriculum for different grades from it and In the next session we will discuss about Consecutive Odd Integers.

Problem solving strategies

To become a better problem solver you need to analyze the problem in deep first and it require a systematic approach. Problem solving strategies requires practice, the more you practice, the better you get.
 Strategies of problem solving are:
1.      Look for the clues: In problem solving strategies, first read the problem carefully and underline the clue words. Look for the facts given and what do you need to find out.

2.      Make a plan: In strategies of problem solving, firstly set a plan. Or if you have done any problem like this before then do what you did.  You can use formulae, sketches, tables or any pattern.

3.      Now solve: In problem solving strategies, whatever plan you have thought of, just solve the problem according to it.

4.      Checking your answer: In strategies of problem solving, look over the solution. Check if it is the probable answer and also check for the units to be used in the answer.

In problem solving strategies, the first thing you do is looking for a clue, for which you need to a skills in solving problems and practice is most important here.
For example: In strategies of problem solving, if we are looking for clues in addition.
Then clues can be total, sum, in all, perimeter and so on.
Now in problem solving strategies, if you are looking for the subtraction clues, then they can be difference, exceed or how much more.
Similarly, in strategies of problem solving, if we are looking for the clues of multiplication, then you should look for the words: total, area, times, product, etc.
And in problem solving strategies, if you are looking for the clues related to division, then you should look for the words: distribute, quotient, average, share, divide,etc.


In strategies of problem solving, after all of the above points , one point which you need to remember is practice as much as you can to become a good problem solver.
In The Next Session We Are Going To Discuss Grade VI, Tools To Solve Problems.

Multiplying Mixed Numbers

In the previous session we discuss about Prime and Composite Numbers and now today we will discuss about Multiplying Mixed Numbers. In the mathematic a whole number is combined with a fraction is known as mixed number.
For example: 4 1 and 3 5
                        5          8
These are the examples of mixed fraction.
Now we will see process multiplying mixed numbers.
For multiplication of mixed fraction we have to follow some steps which are:
Step1: For the multiplication of mixed fraction firstly take a mixed number.
Step2: Then after change the mixed number into an improper fraction.
Step3: Then we write the number in multiplication order.
Step4: Then we will see the fraction values, if the values are divisible then we cancel the value otherwise we have to multiply numerator value of one fraction into another and multiply the denominator value to the other fraction.
Step5: At last again we get the result.
Suppose we have any mixed number 16 14/12 multiply to 10 8/14.
For the multiplication mixed numbers we have to follow all the above following steps:
Step1: firstly write the mixed number which is given:
   16 14/12 * 10 8/14;
Step2: Now we have to convert mixed number into improper fraction.
 = 206 * 148,
     12        14
Now multiply the numerator value of one fraction by another value and multiply denominator by other denominator value.
 = 206 * 148,
     12 * 14
On further solving we get:
⇒ 30488,
     168
Now divide the numerator value to the denominator value.
On dividing we get:
⇨ 181.47
On multiplication we get the 181.47.
Suppose we have any mixed number 8 7/10 multiply 4 8/9.
For multiplication of mixed numbers we have to follow all the above following steps:
Step1: firstly write the mixed number which is given:  
   8 7/10 * 4 8/9;
Step2: Now we have to convert mixed number into improper fraction.
 = 87 * 44,
    10     9
 = 87 * 44,
       90
Step4: Now multiply both the numerator and denominator values.
On multiplication we have:
⇒ 3696,
      90
On multiplication we get the 3696/90.
A trigonometry calculator is a mathematical tool which makes the calculation so easy. For more detail see the Andhra Pradesh board of secondary education.

Prime and Composite Numbers

Having learnt about factors of numbers, we will learn about another classification of numbers on the basis of factors. This is classification of numbers as prime and composite numbers. Before we try to know about this concept, let us recall factors. Factors of a number are the numbers which divide the given number completely or we can say that if a number is completely divisible by some other number, then the latter is called the factor of the former number. It is also important to note here that any number is always completely divisible by 1 & itself.
Turning to our topic of discussion here, let us define prime and composite numbers.
A number which has exactly two factors is called prime number. Such numbers are completely divisible by 1 & itself only, no other number completely divides such numbers. If we take 5 & list its factors, we get only 2 factors of 5, viz.,1 & 5; so 5 is a prime number. Similarly, 2, 3, 7, 11, 13, 17,19, 23, 29,etc are all prime numbers.
A number which has at least 3 factors, i.e., other than 1 & itself, it is divisible by at least 1 other number is called a composite number. If we take 4 & list its factors, we get 3 factors of 4, viz.,1 , 2 & 4 itself; so 4 is a composite number. Similarly, 6, 8, 9, 10, 12, 14, 16, etc are composite numbers.
In listing the examples of prime & composite numbers, we notice that our numbers begin with 2; not 1. It is because 1 is the only number which has only 1 factor, i.e.,1. It is 1 itself, hence, it does not fit either of the definitions of prime or composite numbers. Thus, we say that 1 is neither prime nor composite.
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What is a Ratio

In the previous post we have discussed about Fractions and In today's session we are going to discuss about What is a Ratio, When we need to compare the two quantities, we say that we are going to find the ratio of the two numbers. Now let us learn what is a Ratio? We say that a ratio shows the relative sizes of two or more values. We can represent the ratio of the two quantities in different ways. First method to show the ratio is by colon sign “:”. Here we write two items separated by a colon. Another way to represent the ratio is as a single number by dividing one value by the total. If we take the examples of both the cases, we say that:
If there are 25 boys and 17 girls in the class and we need to represent the ratio of boys: girls, we write  25  ratio 17 or it can be expressed as 25 :17
 In case we write there is one boy and 3 girls, then we represent the ratio as 1 : 3 and we write  that for every 1 boy, there are 3 girls.
The above mentioned statement tells that there are in all 1 + 3 students, so we can also represent the above ratio as ¼ are boys and ¾ are girls. Here we can say that out of total of 4 children, we have 1 out of 4 as boys and 3 out of 4 as girls.
 So on dividing ¼, we get  0.25 are boys and 0.75 are girls. This statement leads us to the conclusion that  25 % of all the students are boys and 75 % of all the children are girls.
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Fractions

In mathematics fraction means the numbers are in the form a/b. In fraction ‘a’ is called numerator part and ‘b’ is called denominator part and in fraction both the parts numerator and denominator are integer numbers.
Now we are going to explore fractions. Basically fractions are of three types and they are given as:
1. Proper fraction.
2. Improper fraction.
3. Mixed fraction.
Proper fraction: Fractions whose numerator is smaller than denominator is called proper fraction.
For example: - 1/3, 3/5, 6/9 etc are proper fraction.
Improper fraction: Fractions in which numerator part is larger than the denominator part is called as improper fraction.
For example: - 4/2, 8/4, 7/4 etc are improper fraction.
Mixed fraction: When the numbers consist of whole number as first part and second part as fraction are called mixed fraction.
For example: - 2(1/2), 7(3/9) etc are mixed fraction.
Now see how to add fractions and there are some rules which we have to follow while adding fraction numbers. Suppose we have two fraction numbers 2/5 and 4/5 now we want to add these two numbers before adding two fractions we have to take LCM (least common factor) of both denominators
        2/5 + 4/5 = (2+4)/5
Now it is clearly seen that both the denominators are same so denominator become 5 and we add both the numerator and get:
(2+4)/5 = 6/5,
So after adding two fractions we get the result and that is 6/5.
Now take another example where both denominators are different. Two numbers are 3/2 and 5/4, now taking the LCM of denominators and the LCM is 4.
Then, 3/2 + 5/4 = (6+5)/4,
          (6+5)/4 = 11/4,
So the final result is 11/4 and by this way we are going to solve the fractions.
You can learn different math topic online like Box and Whisker Plot.  For cbse class 12 sample papers you can take help of online eduational portal boards.edurite.com.
And In the next session we will discuss about What is a Ratio.

add unlike fractions calculator

The use of add unlike fractions calculator, will help us to learn how to add the unlike fractions, which means to add the fractions which have different denominators. We observe that if the denominators of the two fractions are not same, then we will first try to make the denominators of the two fractions same, so it is done by making the two fractions like. In order to make the denominators of the two fractions same, we need to find the LCM of the two denominators and thus once we will find the LCM of the two denominators same, we will convert the two fractions into their equivalent fractions. For this we will multiply the numerator and the denominator of both the fractions with certain number to get the denominator as the LCM which we have calculated earlier. Now we observe that the denominators of the two fractions have become same and so it becomes the problem of addition of like fractions. Now we will add the numerators of the two like fractions and thus get the sum of two unlike fractions. Finally we convert the resultant fraction into the standard form. To understand it more clearly we look at the following example:
3/5 + 5/4
Here we have 5 and 4 as the denominators, so LCM of 5 and 4 is 20. Now we convert 3/5 and 5/4 with denominator 20, so they are written as
 = 12 / 20  + 25 / 20
= ( 12 + 25 ) / 20
= 37 / 20
Now they are in the standard form, so 37 / 20 is the solution.

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online tutor

To learn about  the use of  online tutor, in  day to day update of the academics, we feel that the child make use of online tutor to learn about the  topics which he feels that he is not able to understand by his own and you can take help of gujarat secondary education board. So in such a case a child uses the facility which is provided by the online tutor to get online support and get the solution to the problems where you find any type of difficulty to understand it.  In case we are living in a rural area or any locality isolated from the main city and we do not have any mentor to guide us at each step we are held up, in such cases, we have online tutor to guide us and  help us time  and again we require guidance at some stage or the another. So  if a child is a keen learner and wants  a guide to help him to make the topics clear time to time, he / she must register himself  for the use of online tutor and  make the use of the  online tutor  24 hours, 7 days a week. Online tutor is at your disposal any time, any moment you require the guidance and assistance. It provide us creative and innovative ways to learn and understand the units of the chapter the child feels difficult to learn and understand. Online tutors also provides the support and help so that the  chapter becomes interesting and based on the units learned, a child is provided online worksheets  to test his learning ability.
This is all about the online tutor  and if anyone want to know about z score then they can refer Internet and text books for understanding it more precisely and Read more maths topics such as online tutoring in the upcoming sessions here and In the next session we will discuss about add unlike fractions calculator.

Make generalizations

Hello students,Previously we have discussed about verifying trigonometric identities and In this blog I am going to tell you about the generalizations which comes under 12th state board syllabus tamilnadu. We can understand the generalization as the means of conclusions. Here a important point is that all generalization can be conclusions but it is not necessary that all conclusions may be generalizations. In generalization we extend the concept pf concept in more precise form.
Generalization may be faulty and valid generalization. The simple definition of the generalization is that, it is that type of broad statement that comes from the various valid resources like from observations, experiences and by doing surveys of the entire group of people    A valid generalization follows some properties: -
(I) There should be some facts to support the particular generalize statements.
(II) There should be various types of examples to support that generalize statements
(III) There should be some past facts, surveys and experience.
(IV) There should be valid logic and reasoning.
If any statements do not the follow the above properties then it is said to be faulty generalization.
Below are some examples to make generalizations.
Simple type of information - Government schools, Colleges, courts, offices are closed on the second of October.
In generalize form – Most of the government buildings are closed on national holiday.
Simple type of information – My brother sneezes every time of second when Diwali comes.
In generalize form – My brother is allergic to crackers.
Some predefined generalizations are: - Asians are bad drivers? And white men can’t jump?
Generalization means either the word all or every. Below are the some generalization’s clue words, they are: -
All                    None
Most                Many
Always             Some
Usually            Seldom
Never               Sometimes
Few                 Generally and last Overall.
The above mention words support instruction for the generalization.
In the next session we will discuss about online tutor and You can visit our website if you need help with algebra.

Mathematics in daily life

In our daily routine life mathematics play an important role to fulfill our most of the task that can’t be possible without the help of mathematics. Mathematics provides lots of concept, rules, methods and properties to accomplish the task which is related to the maths. People have been using the mathematical principal and tool form thousands of years, across several countries and continents. In our daily routine life, mathematics work as a body part to solve the problem by providing solving equations with fractions and other problems. Mathematics is a universal concept, which did not invent. Mathematics in daily life is discovered by the human being across the world and is an important part of tamilnadu education board.
There are several applications of mathematics in daily life that belongs to our daily routine activities. Suppose a man went to the market to buy something. He had $ 50 in his pocket. He bought many things for his house. Now the question arises that how he calculate, “how much money he spends?” and “how much he saves?” the solution of these problem are provided by the mathematics. In mathematics various types of operation are defined to solve the calculative problem in terms of money or more things, like addition, subtraction, multiplication division and so on. The importance of mathematics is not limited to the calculative part, they are widely used in various filed like several field of science, in the field of space research or many more fields that are related to the human being.
Suppose a man wants to paint their house. The cost of paint the house will be $ 3 per m². At that time there are various formula provided by the mathematics to calculate the geographical surface of the earth. These formulas are very helpful in estimating the cost of painting the house or any type of maintenance work.  According to my view the importance of Mathematics in daily life can’t be explain in words because it is concept which are used by everybody in each and every moment of life.
In the next session we are going to discuss about how to Make generalizations
and You can visit our website for getting information about math word problem solver.

Steps in problem solving

Previously we have discussed about verifying trigonometric identities worksheet and In today's session we are going to discuss about Steps in problem solving which is the most important part of secondary school education andhra pradesh, The problems that looks very complex initially are not solve directly so there are basically some Steps in problem solving that are use in solve math problems as follows:
Step no (1): Problem understanding – In this step first states the problem in your own words then find the main problem or thing you want to solve.
Then find the all unknown variable into the given problem and check the other information you need to find the solution for main problem.
Step no (2): After writing the problem into own understanding way make a plan to solve the problem – There are some steps or strategies that helps in making a plan:
First of all check the pattern of the problem then research for the other problems that are solved before having the same pattern .After getting the all results then make the tables and diagram according to the given problem and at last make the suitable expression for the problem that have the same pattern as before solved problems
Step no (3) : act according to the plan – After making a useful plan implement according to the plan means perform the necessary actions and computations that are helping us in solving problem .when getting the answer check them that these are according to the expected answer or not and if these are not according to them then apply other plan for problem solving .Maintain the record for each and every calculations .
Step no (4) : Back track :Check the Result by putting in the original problem and find another method to cross check the answer and also find the other related problem that are in more general form by solve with the existing technique or method .
In the next session we are going to discuss about Mathematics in daily life and You can visit our website for getting information about online math help.

equally likely events

Hello students,Previously we have discussed about inverse function worksheet and In today's session we are going to discuss about equally likely events which is a part of board of intermediate education andhra pradesh, In the mathematics we deals with the probability and their events such as exhaustive, dependent, independent, mutually exclusive, favorable and many more. Equally likely events are one of them. Let’s talk about the equally likely events definition : - In some experiments we know the results in advance but actually do not know the exact result, this type of results are called the random experiments and the result of random experiments are called equally likely events if the different outcomes have the same chance of occurrence.
For example when a die is thrown, each of the faces bearing one, two, three, four, five or six dots is equally like to appear.
Another example when we toss a coin then we have a chance to get either a Head or Tail.
Means it includes all those experiments in which we know the all results but we do not know the actual or exact results.
Let’s take examples -
Which of the following experiments have equally likely outcomes or events.
I) A driver attempts to start a car. The car start or does not start.
II) A players attempts to shot a basketball. she/he shoots or misses the shot.
III) A trial is made to answer a true false question. The answer is right or wrong.
IV) A baby is born. It is a boy or girl
Solutions : - (I) A driver attempts to start a car. The car starts or does not start, is not equally like events.
(II) A players attempts to shot a basketball. she/he shoots or misses the shot are not equally like events.
(III) A trial is made to answer a true false question. The answer is right or wrong is an equally like to occur.
(IV) A baby is born. It is a boy or girl is an equally like occur event.


In the next session we are going to discuss Grade VI, Steps in problem solving and You can visit our website for getting information about free math tutor.

Mathematical Reasoning

Previously we have discussed about difference between rational and irrational numbers and In today's session we are going to discuss about Mathematical Reasoning which is a part of ap secondary education board, Mathematical reasoning explained by solving the problem without knowing that what is to be done but when you know how to solve the problem then it is not consider as mathematical reasoning .For the question about what is mathematical reasoning the answer is that collection of the problems that are not in routine life and they are not solved by using any normal procedure and these problems are solved by making own strategies and by making own methods , also these are not based on the single strategy but based on the variety of strategies are known as the mathematical
There are some mathematical reasoning examples to understand the way of solving the problems of mathematical reasoning: Example: If Jon have 23 chocolates and he put equal number of chocolates in two bags and after putting seven chocolates are left then how many chocolates he put into each bag? The problems will need only little bit of attention to solve are considered as mathematical reasoning problems.
These types of problems are helping the students to make their mathematical concept strong as well as they helps the student to save their extra time that is spend in problem solving as for example If we want to multiple the number 36 * 18 then it will solved in more easy way as add 4 to 36 that is equal to 40 (36 + 4) and add 2 in 18 to make it 20 as (18 + 2) and multiply them that is much easier then multiply 36 * 18 and answer for multiplication 40 * 20 = 800 and subtract 4 and 2 that is totally 6 from 800 that is 794 that is the actual answer for multiplication of 36 * 18 .
In the next session we are going to discuss Grade VI, equally likely events and You can visit our website for getting information about free online tutor.

Informal and mathematical language

Hello students, in daily to daily life we use language to telling something to anyone not only we use but everyone use the language for the communication. The language may be anyone like English, Hindi, Latin and many more. But have you ever think about the language of Maths.  Here we are going to discuss the language of maths especially for the informal and mathematical language. In mathematics we use so many types of methods, theorems, expressions, symbols, proofs and many things, the all are comes in mathematical language. It is true that mathematics language is not used for the communication but without this we can nothing understand in math. Like algebra which is totally written in symbolic form.
We assumes math as a language and generally mathematical language is used for the better understanding, to represents the mathematical theorems more clearly, give their reason very logically so that everyone can easily understand. Mathematical language have own grammar, syntax, symbols and conventions. Like we use x for expressing theorems. The vocabulary words for the logic are ‘and’, ‘or’, ‘not’, ‘if…then’, ‘for all’, and ‘if and only if’. Symbols for operation are +, -, *, /, ∏, ∟, ∞, √, ∑, and ⌠ many more. Mathematical language is only used by the mathematicians for the communicating mathematical thoughts among themselves. (know more about cbse books for class 11, here)
Mathematical language also gives precise information for English like statements like we write a is equal to b in English language but the same statement in mathematical form will be a = b. The informal language in math is only used for understanding the concepts and proofs. Generally this language is not written; usually it is used for spoken and used according to the situations or conditions. In the next session we will discuss about Mathematical Reasoning. 

dependent

Probability can be considered as a branch of mathematics that deals with the calculation of likelihood of a given event’s occurrence. The occurrence of an event can be described in terms of number between the 1 and o. In the terms of probability, an event with a probability of 1 can be describe as certain or in the same aspect the probability of .5 can be specify as a half odd or half even. In the probability, an event is word which can be defined as a particular work which is performed in continues time period. When an event is performed in a particular time period then to estimate the outcome of that event, we use the concept of probability.
In the simple form we can say that when the number of occurring events is divide by the total number of events plus the number of failure of occurrence are known as probability. In the probability, some of the cases occur which has the two events. It means that in the probability some time two events are performed together at a time. On the basis of probability we can categorized the events in two ways, which are given below:
A)      Dependent event
B)      Independent event
Dependent events = Dependents are those events in which outcome of the one event affects the outcome of another event. It means to say that the output of the one event depends on the output of another event.
Independent events: independents events are those events which are independent to each other. It means that the outcome of one event not affect the outcome of another event. (know more about cbse sample papers for class 10, here)

Example: Suppose there is pack of playing card. If in case we pick card of king of heart. In the next time if we pick the card then it is obvious that card is not same to the king of heart. So, we can say that here both events are dependent to each other because in a Dependent Events Probability of the pack of card, there is only one king of heart exists.  In the next session we will discuss about Informal and mathematical language. 

Tools to solve problems

In mathematics, we know that various types of tools are provided to solve the problem that is related to calculation. Problem solving is the logical process which includes the process of finding the problem and estimate there solution. In the process of solving problem, mathematics provides lots of tools like addition, subtraction, multiplication, division, various types of concept like equation and various types of formulas and theorems. Here we are going to discussing about the most popular Problem Solving Model that are used to solving problem.
Addition: addition is the most basic tool of the mathematics which is used to perform the sum of the different objects like total money in the account, total amount of bill etc.
Example: 4 + 3 = 7
Subtraction: this operation is also a most basic tool to perform the difference between two given objects like how money was left after spending in the market and so on.
Example 15 – 5 = 10
Multiplication and division: these are the most popular that helps in to overcome form the problem of repetitive calculation.
The above are the most basic tools that are used in our daily routine life without applying any concept or rule. But in mathematics, sometime we need to solve to solve those types of problem, where we need to find the value of the unknown variable. On the basis of unknown variable the solution of the problem depends. To solve that kind of problem we required the concept of mathematics that is known as algebra. Algebra is the mathematical concept, which is used to change the problem into equation then by finding the value of variable to solve the problem. (know more about cbse sample paper for class x, here)
Example: a + 5 = 9
In the above we can say that there is an example of equation, where we need to fill the value of a by the appropriate number which satisfy the given equation true. In the various field of science mathematical Tools To Solve Problems, are most widely. In the next session we will discuss about dependent. 

predictions

Hello students, in this blog we are going to learn about the predictions mean guessing for something. The simple definition of the Predictions is that, it is statement that is made about the future or act of predicting (as by reasoning about the future). The act of foretelling and that which is foretold is predictions. In other words when we predict anything that means that those things will be happen in the future and generally all forecasting is based on the experience or knowledge.
A very suitable synonym for the predictions is the Forecast. But between the prediction and the forecast, there is a overlap and why it is? Let’s see....
In prediction we expect some output while forecast contains the possible outcomes.
Predictions is made for the future means we planned for future that what will be happen when several types of conditions will arises. It is not necessary that every prediction will be right some may be wrong. It can also be defined in the terms of uncertainty.
The most important example about the predictions is that some astrologers said before few years that the world will be no more after the 12 December 2012, and everyone heard this statement, but nobody knows the truth, because it is also a prediction that is based on the some knowledge and books.
Predictions can be done in every field like in science, finance, fiction, politics and in many more.
And it can be done by collecting the past and current data of that particular field that which we want to predict and for collecting data there is several methods.


I hope this information that I gave above will be truly useful for the Grade VI students.

In the next session we are going to discuss Measures of central tendency and dispersion

Measures of central tendency/dispersion

Measures of central tendency are define in the statistics in the form of Mean ,median and mode .Measures of central tendency defines the single value for the group of values .Sometimes these are known as the average of the bunch of values .When we talk about the Measures of central tendency it defines that which is the value repeated mostly or which value have the greater frequency .If we take some examples as in a class what is the average height of the students or in a group what is the average age of peoples so these type of questions are solved with the help of Measures of central tendency that are describe as mean , median or mode as gives the single value that define the whole group of values .
Measures of central dispersion is denoted as the gap of the values from the center means it is define the
spreadness of the values .It is defined in terms of Range or variance or standard deviation .If we take some examples to understand the Measures of central dispersion as if the age of students in the class is 9 or 15 then there is lot of variation in the group of values so these are calculated through the Measures of central dispersion .This is helps the students of grade VI for understand how we can measure the central tendency of bunch of data or central tendency of dispersion. (know more about cbse syllabus for class 10 , here)
There are some examples as if in a group there are 5 students and their age is 8 , 7 , 6 , 9 , 7 then the central tendency is define as the value having the maximum frequency that is 7 then the answer is 7 or sometimes we talk about the mean that is define also as the average value then it is calculated as
( 8 + 7 + 6 + 9 + 7) / 5 = 37 / 5 = 7 .4 years that is about the 7 in round figures.
In the next session we will discuss about predictions. 

Collect/organize/graph data

Hello students, in this session we are going to discuss the collecting data, organize it and graphing data. Let’s take a look step by step. To organize and graph data, firstly it should be properly collected. And there are various methods to collect the data according to our requirements.
Data collections mean store the data at a particular place and also describing that how it was collected. And in data collection we get the information from many source such as from persons. By the data collections we store the information at a particular place so that we can use this information for further use. Before data collection you should know about the types of data. Data may be primary and secondary, after finding the types of data we apply the collection methods, and they are also two types grouped and Un grouped.
Methods for primary data collection are: - Data collection through investigation, Data collection through telephones and Personal investigation methods.
Methods for secondary data collection are: - Official methods include the data collection from the ministry of finance and industry by using some tools. (know more about icse board , here)
Semi official methods include the data collection from the banks, board of railway.
After collecting data we need to organize the data. To organize the data generally we use tables. Because the retrieval and insertion of data and information in table is easy than any other.
Let talk about the graph of data, to do this we use several types of graphing methods such as : - pie chart, line plot, box plot, pictograph, map chart, bar graph, line graph, stem and leaf plot, frequency polygon and histogram that are mainly used.

I hope this information that i gave above will be truly useful for the Grade VI students.
In the next session we will discuss about Measures of central tendency/dispersion. 

Independent

In probability, two events are said to be independent when the occurrence of one event does not make any effect on the other event. It means that any two related events that have no effect on each other. Here an event refers to any type of activity that is performed manually. In mathematical definition two events are independent if the outcome of one event does not make any influence in the outcome of second event. In the process of finding the probability of two independent events requires to multiply the probabilities of the two events. After obtaining the outcome, if needed then simplifies the final result.
Suppose the event of getting a Red heart in first attempt and the event of getting a black heart in second event are independent event. So, we can say that any two random variables are independent if the conditional probability distribution of either given the observed value of the other is the same as if the second event’s value had not been observed. The concept of independent event is most widely used in probability to give knowledge to the students of Grade VI. (know more about syllabus of cbse board, here)
In the form of standard definition independent events can be defined as:
Suppose we have two independent events x and y then they can be represented as
 P (x ∩ y) = P (x) . P (y),
In the above notation ‘x ∩ y’ can be defined as intersection of ‘x’ and ‘y’. It means that it is an event where both events ‘x’ and ‘y’ occur. In probability of independent events we can apply the multiplication rule that is given below:
Rule for probability of independent event:
If two events ‘x’ and ‘y’ is independent then probability of occurrence is:
   P (x and y) = P (x) . P (y),
In the next session we will discuss about Collect/organize/graph data. 

Representing probability

This unit is for the students of Grade VI; here we are going to learn probability representation. We come across the situations in our daily life when the results are unpredictable, like the toss of a coin, where we are not sure whether we will get a head or the tail. In day to day life we come across the statements like “Probably I may get the job next month”, “USA might win this one day cricket match series”. Such cases involve the elements of uncertainty or chance. A numerical measure of such   uncertainties is provided by a very important branch of statistics called the theory of probability. (know more about icse board syllabus, here)

Today this subject has been developed up to such extent that its use is seen in almost every field of life. This tool of measuring probability is used in social, physical science and in the quantitative analysis of all business and economics related problems. Statistics forms the basics of decision theory which means making decisions under the conditions of uncertainty. Representing probability basically means representation of the chances of probability of any event in forms of figures and numbers. When we want to find the probability of occurrence of any event, we must know the possible outcomes and the total number of outcomes of the experiment. It will be clearer with the following example. If you toss a coin and you need to know the probability of getting a head. It is absolutely uncertain event. When we flip a coin, we do not know if it will be a head or a tail. Now we know that there may be two possible outcomes H, T. So the possibility of getting a HEAD is 1 /2.
So the probability of getting a head is P (H) = ½.
 In the next session we are going to discuss Independent.

Estimating probability

Hello students, in this section we are going to discuss the estimating probability, Probability means predictions. Estimating probability means finding the probability. In this we are using favorable event, it means the cases which ensure the occurrence of an event.
Mathematically we have,
Probability of an event ‘A’ that is P (A) = m / n.
Where m = possible outcomes favorable to the occurrence of ‘A’.
n = total number of possible outcomes.
And n - m = possible outcomes unfavorable to the occurrence of ‘A’.
We also notice that
P (A) + P (A)' = m / n + n – m / n = 1,
That is P (A) + P (not A) = 1.
 Probability sum of events in an experiment is equal to one, means if there is an experiment in which three events are occurring, as x , y , z then the probability p (x) , p (y) and p (z) are denoted as p (x) + p (y) +p (z) = 1.
Let us take an example to estimate the probability.
-Estimate the probability of getting the number less than 6 in throwing a die once.
Solution: - Total number of events are: 1, 2, 3, 4, 5, 6.
n (s) = 6,
Favorable events = a number than less than 6 = A = 1, 2, 3, 4, 5,
n (A) = 5,
Hence P (A) = n (A) / n (s) = 5 / 6.
Like this we can solve any examples for probability of Estimating.
I hope this information will be valuable for the Grade VI students.
 In the next session we are going to discuss Representing probability.

Possible outcomes

Hello students, in this section we are going to discuss the possible outcomes in probability. Probability means predictions. Possible outcomes means when we are performing a task then its results will be there, so the total number of expected results are called as the possible outcomes for an event. Let us take a look to understand the possible outcomes for the various experiments.
i) When we toss a coin, we get either a Head (H) or a Tail (T). Thus, all possible outcomes are H, T.
ii) Suppose two coins are tossed simultaneously. Then, all possible outcomes are HH, HT, TT and TH.
Remarks:- HH means head on first coin and head on second coin.
HT means head on first coin and tail on second coin.
iii) When we toss a three coin simultaneously. Then, all possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. (know more about cbse board, here)

Remarks: - HHH means head on first coin, head on second coin and head in third coin too.
HHT means head on first coin, head on second coin and tail on third coin.
iv) In drawing a card from a well shuffled deck of 52 cards, total number of possible outcomes is 52.
v) On rolling a die, the number on the upper face is the outcome. Thus all possible outcomes are 1, 2, 3, 4, 5, 6.
The collection of all or some of the possible outcomes is called the event.
The all possible outcomes are also known as the sample spaces and we denote the sample spaces as ‘s’ = the total number of possible outcomes
 I hope this information will be valuable for the Grade VI students.
 In the next session we are going to discuss Probability Help.

complement

In Grade VI, while studying about set theory, we come across different types of sets. Here we are going to define complement of a set.
If we say that U is the universal set and A is any set, which is the subset of set  U, then the complement of set A will be all the elements which belong to set  U but  does not belong to set A.  Complement of set A can be written as U – A. We express complement of set A as A’.  Thus we can say that
 A’ = U – A
 Also we can say that the elements of set A and the elements of set A’ ( which is the complement of set A, when U is the universal set ) join together to form the universal set  U. mathematically it can be expressed as follows: A  + A’ = U
It will be more clear by the following example: Let U = 1, 2, 3, 4 , 5, 6, 7, 8 , 9, 10 we say that set U is the universal set which represents the natural numbers from 1 to 10. Also let the  set A = 1, 3, 5, 7, 9 which is the set of all odd numbers from 1 to 10. (know more about free download cbse books, here)
 Now A’ = U – A
= 1, 2, 3, 4 , 5, 6, 7, 8 , 9, 10 -   1, 3, 5, 7, 9  = 2, 4, 6, 8, 10
 SO we observe that it will contain all the elements of the universal set U, which are not in A. Also if we add together set A and set A’ , then the resultant set will be the universal set itself.
Another important thing about  a complement is  that  a complement of any complement is the original set itself. It means: ( A’)’ = A
In the next session we will discuss about Possible outcomes. 

Selecting a sample

In the previous post we have discussed about Sampling errors and In today's session we are going to discuss about Selecting a sample.
Selecting a sample:
In this session, we will talk about selecting a sample from a group of samples for grade VI.
In terms of probability, sampling is a method that aids in random selection process.
The important condition is that all the events to be chosen must have same probability.
For example, the random numbers chosen by a computer program is a random selection process as all the numbers can be chosen with equal probability.
Sample size: sample size is the total sum of sizes of all its cases.
Before we continue, let us understand some basic notations,
N=total number of cases in the sampling space.
n=number of cases in a given sample
f=sampling fraction=n/N
Simple random sampling:
We have to select n units from N.
N is the total cases in sampling space.
All the n must have the equal probability to be chosen.
nCN=total number of subsets of n from N.
Let us make this concept clearer through an example.
Let us take an example that we have to do a survey of a company by selecting its past clients. We want 100 clients to be a part of the survey.
Company provides a list of 1000 employees whose records are in the database of the company.
Sampling fraction=n/N=100/1000=0.10
Hence sampling fraction is 10%.
We have several ways to select the 100 clients. An easy way is to put all the 1000 clients in a group, subdivide the group and randomly select any subgroup. This is a mechanical way to select but it is not as efficient as the quality of samples would depend on how we have subdivided the group and how randomly we choose the subgroups. (know more about  Sampling, here)
The computerized method is more efficient as compared to the mechanical method.
Principally, our main motive is to understand the selection of sample out of many. To know more about cbse syllabus.

The main point here to keep in mind is that the samples must have equal probability to be chosen.
If the selecting probability depends on the previous selection, then it is said to be conditional probability.
In the next topic, we are going to discuss Sampling errors.

Sampling errors

In sampling errors we take a number of samples of the given mode. The samples are the models on which an analyst is working to find the errors from the number of terms which are under examination. We use the numbers of samples and then find the mean to reduce the sampling errors of the data model. In this way we define sampling errors.
For example, population of the state (increasing or decreasing); now if we want the mean height of 5th standard youngsters then we measure all the heights of sample of 5th graders in the state.
The best parameter to estimate the population is sample mean. But, there is difference between the mean sample or observed sample and the true population mean. So that, the sampling method is good or bad, if the rate of sampling is bad then likely should be some errors occur in the sample static.

The sampling errors are not easy to reduce. For example, any state wants to contact people to know how many people are homeless, the number of senior citizens, etc. The state government wants to find the parameter information but this is not easy. Then there is an error due to imperfect data collection. To reduce the sampling errors we take a number of samples of the model and then find the mean value of these samples. There are some other errors like non sampling, standard error. (know more about icse syllabus 2013, here)

The non sampling error is caused by human error by which a statistical analysis is done. These errors are not limited and not eliminated. Standard error helps us to measure the sample accuracy of the sample model. The representative sample is an unbiased indication of the data model. This is the sampling errors for grade VI. In the next session we will discuss about Selecting a sample.

Constructing sample spaces

Constructing sample spaces:
Sample space is generally denoted by S, Ω or U. Fundamentally it’s the set of all random trials; like in tossing a coin the sample space is (head, tail). If we toss two coins then sample space for this random trial is (head, head), (head, tail), (tail, head), (tail, tail). In the trial of tossing a single sided die sample space s is (1, 2, 3, 4, 5, and 6). It’s not necessary that one trial should have only one sample space; like in a trial of drawing a card from a standard deck of 52 playing cards one probability of outcome is could be the rank (ace through king) and the another sample space could be suits i.e. (club, diamond, hearts or spades). The subsets of sample space are called event. Problems would be critical after increasing the number of sample spaces. So it would be problematic when there are infinite sample spaces means there are infinite events.
Sample space construction:
Sample space is the set of all possible outcomes and it’s necessary to consider all possibilities. It may be a difficult task and for this purpose counting principle can be used. If there is more than one event it’s important to determine all possibilities that exist. It can be stated that:
“If there are A ways of an event to occur and B ways for occurrence of second event then there are A.B ways for both to occur”. This is the concept of the counting principle.
An example is given below which can help to understand sample space better. (know more about cbse sample papers, here)
Example: one jar contains 1 red, 3 green, 2 blue or 4 yellow balls. Then what would be the probability of each outcome if a single ball is chosen from the jar.
Solution: Sample space for this random trial is
S = (red, green, blue, yellow)
Probability can be calculated as:
Probability:  P (red ball) = 1/10
P (green ball) = 3/10
P (blue ball) = 2/10 = 1/5
P (yellow ball) = 4/10 = 2/5
In the next session we will discuss about Sampling errors. 

Estimation of Solutions in Grade VI

In this session we are going to discuss Estimation of Solutions. Before we proceed for any project we need to find the estimated budget for the project to be attained. This is done by rounding the values to nearest tens, hundreds or thousands.  Suppose we go to buy some fruits and other purchase items. We make a rough budget of the articles to be purchased and take Rs 200 in my purse. This is called estimating solutions. Now when we buy the fruits, the seller tells the following costs:  Apples of Rs 84.00, Bananas of Rs 35 and grapes of Rs 18.
  The shopkeeper gives us the bill of Rs 84.00
                                                          Rs 35.00
                                                    +   Rs 18.00
                                                        _____________
                                                             137.00
We simply round off the figure to nearest tens and pay Rs 140 to him. Another way to make the payment will be to round off the above figure in nearest hundred and pay Rs 150.00 estimation of solutions is done in order to make any project a success, may it be a window shopping, budgeting for the parties big or small about how many expected guest will be attending the party or even organizing big projects.
In Grade VI We follow the following methods for estimating solutions:
To round off the value to nearest tens, we see the ones place digit, if it is less than 5, we make ones place 0. If it is greater than 5 we add 1 to tens place and make ones place 0. E.g.:
      47 round off to tens becomes 50
     32  round off  to tens becomes 30
    65 round off to tens becomes 70
In the next topic we are going to discuss Percentages

Proportions

Here we are going to learn about Proportions (some portion of this topic taken from ICSE class 10 syllabus).
When any two ratios are equal, we say that the two ratios are in proportion. It is the relationship between two ratios whose output is same and constant.
It is represented by a/b  :: c/d
or
a : b :: c : d
Here the ratio of a: b is proportion to c: d. Both symbols :: and = are used to represent the proportionality of two ratios.
If we have a : b : : c : d , it is read as a is to b as  c is to d
In the above statement we have 'a' as First  term, 'b' as second term , 'c' as third term and  'd' as the fourth term.
In this a and d are called extreme terms or extremes and b and c are middle terms and are also called means
If the given four numbers are in proportion, then the product of means is equal to the product of extremes.
In order to check that the two ratios are in proportion, we simply check if the product of extremes and the product of means are equal.
Let us see how to solve proportion with the help of an example:
Example: solve Proportion problem  60 : 105  :: 84 :147 .
Sol: We first take the product of means ie 105 * 84 = 8820
now we take the product of extremes i.e. 60 * 147 = 8820
Here we observe that the product of means = product of extremes. So the two ratios are in proportion.
This can also be checked by converting both ratios in lowest terms, if both the values are same, they are in proportion
Let us try it for the same data:
60 / 105  ,we divide numerator and denominator by 5 and get
= 12 /21 , again dividing by 3 we get
= 4 / 7
Similarly we write 84/147 , dividing & multiplying  by 3 we get
= 28 / 49
Now dividing & multiplying by 7 we get
= 4 /7
So they are in proportion.

In next post we will talk on Estimation of Solutions in Grade VI. For more information on Substitution Method, you can visit our website

Math Blog on Grade VI

Here we are going to discuss one of the most interesting and a bit complex topic of mathematics: operations on fractions, decimals, integers and exponents which are usually studied in grade VI.
Now we will first start with fraction:
Fractions can be defined as the part of whole numbers having both numerator and denominator. ¼, ¾  are some examples of fractions. Generally fractions are of three types i.e. proper fractions, improper fractions and mixed fractions. Let’s see some operations on fractions:

1.    Addition fractions:

While adding two fractions we must take care of that the denominators of the fractions to be added must be same. And if the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply add the numerators.

                     p/q + r/q = (p + r)/q

2.    Subtraction of fractions:

While subtracting two fractions we must take care of that the denominators of the fractions to be subtracted must be same. And if the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply subtract the numerators.

                     p/q - r/q = (p - r)/q

3.    Multiplication of fractions:

While multiplying two fractions multiply the numerators together and then multiply the denominator together and simplify them.

                     p/q x r/s = (p x r)/(q x s)

4.    Division of fractions:

While dividing the fractions take reciprocal of the second fraction and multiply both the fractions together.

           p/q ÷ r/s = p/q x s/r = (p x s)/(q x r)

Now move to the next topic i.e. decimals:
Decimal number can be defined as the number which contains decimal point. To understand the decimal numbers we must have knowledge about the place values, which is very important when we write the decimal numbers. (also try fraction to decimal converter)
In the number 234:

• The "4" is at the Units position.
• The "2" is at the Tens position.
• And the "3" is at the Hundreds position.
  

In a decimal number as we move left, each position becomes 10 times bigger and as we move right, each position become 10 times smaller.
Now we move to the next topic i.e. integers:
Integer can be defined as similar to the whole number but integers also contains negative numbers and do not contain fractions.
 Let’s see some examples of integers:

·         Negative Integers =   -1, -2,-3, -4, -5, …  

·         Positive Integers = 1, 2, 3, 4, 5, …  

·         Zero =   0

We can also put the integers like this ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... .
Now we move to the next topic i.e. exponents:
Exponents can be defined as the power or indices of a number. The exponent of a number represents that how many times the number will be use in multiplication. Let’s understand it by an example:
Example: 12² = 12 x 12 = 144
In words: 12² can be called as "12 to the second power", "12 to the power 2" or simply "12 square".

In upcoming posts we will discuss about Proportions. Visit our website for information on syllabus for class 10th ICSE

Percentages in Grade VI

Hello friends, in this math homework help session, I am going to discuss about the percentages, which you study in grade VI. The term percentage comes from Latin word and means for every hundreds. Another definition is percentages is a fraction with any numbers which divide by hundredths. Percentages mean divide by 100 or per hundred. Percentages are described in two ways. The first one is fraction form. Example:-26/100 =26% The second is decimal form. Example:-33=33%.
A model for percents is a square form divided into 100 equal parts.
some examples: 33 of the 100 parts in the square to show 33 hundredths means 33/100 or 0.33 or 33%.
Money is good example for percentages. There are 100 cents in a dollar. Five cents ($.05) are 5 hundredths or (5/100) or 5% of a dollar.
Any type of problems like fractions, decimals deal with the percentages and we can easily solve them as discussed below.
Formula for percentage is used to solve different percentages problems. It is given as:-
is/of=%/100, where formula start from the left side and we can use the cross multiply it means to one multiply numerator of one fraction by denominator of another fraction.
For example:- we can find out the 20 % of 100 is.....
step 1:- is =? of=100 ,%=?
step 2:-is/100 20/100
step 3:-let's assume that a is a single digit.
Step 4:-a/100=20/100
step 5:-now we have to do cross multiplication
a*100 and 100*20
a*100=2000
divide 2000 by 100 to get the a
step 6:-now 2000/100=20 and a=20
step 7:-so,20% of 100 is 20
In this way we can calculate percentages. In the next topic we are going to discuss Proportions.

In next post we will talk on Math Blog on Grade VI. For more information on class 10 ICSE syllabus, you can visit our website

Algebraic Expressions

In this section we will talk about the basic algebra1 like operations related to the algebraic expressions. We will learn here about the process for evaluating algebraic expression in the algebraic mathematics. All the algebra in this article will be around the level of grade VI of CBSE math Syllabus.

In the mathematics, pupils learn about some standard fractions, decimals, exponential, and some other algebraic math. We form the algebraic expressions with the help of these algebraic components. In algebra we generally learn about the linear equations, linear function, graphs, positive linear function, factors, greatest common factor (GCF) etc.  In the field of evaluation of algebraic expressions and equations we learn about balancing equation and also about the solution of them.For practicing you can refer number sets algebra 1 worksheets,
In algebra, if we add some thing with some other quantity then they also form an expression. Any of the expressions is the first step to solve an algebraic expression. The algebraic expressions are the way to show any problem in the word form which contains some variables in it and tells the story of the problem in the expression form. It’s not always necessary that an algebraic expression contains an operation in it. An algebraic expression may contains some of the variables, some operations (+, -, x, / ) applied on those variables or some times only variables within it. As per the naming is concerned, the variables are the components of the expressions, the elements whose products form a single term of the algebraic expression, are called as factors and the numerical factors present with the variables are called as the coefficient of the expressions.
A simple example: the algebraic expression 5x + 6y – 8z = xyz. While evaluating algebraic expression, we have four different terms in the expression. 5 is coefficient of the x and in the R.H.S. term x, y, z individually are the factors of that term.If you want more information on algebra, click here.
The elements whose product forms a term of an algebraic expression are called the factors of that term.  The numerical factor of a term containing a variable is called the coefficient of the term.
The evaluation of algebraic expressions includes the formation of simple algebraic expressions with the help of some data. For example, while evaluating algebraic expressions we write an algebraic equation. Let n be any number then we can write expressions of several type according to the condition given. For example:
1.      Number “n” is increased by 45 can be written as n + 45;
2.      Number is decreased by 36 as n - 36;
3.      Number is get multiplied by 6 as 6 * n;
In some other form If n = 4 then (- 4) n + n² = ?
If x = 3, y = 4 and z = 2 then expression 2 x + 3 y + z² =?.
Similarly we can make a number of algebraic expressions. The expressions are categorized according to the number of terms contained in them into monomials, binomials, and trinomials.

In above content we have discussed about algebraic expressions and if anyone want to know about Proportions then they can refer to Internet and text books for understanding it more precisely. You can also refer Grade 7 blog for further reading on inequalities