Online free math tutor

-->In the previous post we have discussed about decimal to percent and In today's session we are going to discuss about Online free math tutor.

Learning Mathematics has become fun with introduction of use of teaching tools and aids in the field of education. Though it never means that class room can go ahead without a teacher, but the presence of computer in a classroom makes the teaching learning process very interesting and enjoyable.

With time methods of teaching of any subject are also changing. The problems of students can be sorted by the Free Online Math Tutor, which can support the children to get the solution of problems any time they need.

Further we observe that there are many websites which provide Free Online Math Tutor support for different topics. Thus a child can easily access the solution to any type of the problem faced while he study, without taking into consideration, the grade and the topic to be studied. These online tutors are boon for the learners and thus it clears the doubts of students time to time. They simply clear the hurdles faced by the students at the time of revision done by them. Basically we find that the  exercises are followed by the multiple choices questions and the quiz based on different topics.

All this helps children to create interest in the subject. We call it as an innovative method of teaching learning process. This online tutor helps to provide instant support for the students and thus the solutions to sums are provided by the math online tutors without taking much of the time.

To learn about the Kinetic Molecular Theory Of Gases, we can also take the online support for chemistry.

Icse Books Download can be done, in case the books are not available in the market.

decimal to percent

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There are several mathematical operations that we can do with decimal numbers. If we are asked to find the percentage for any given decimal, then decimal is multiplied with 100 to get the desired %. Position of the decimal in the number is shifted to right of the original position skipping two digits after decimal. For instance, suppose we have a decimal number 00.4887, then equivalent percent is calculated as follows:

00.4887 x 100 = (4887 /10000) x 100 = 4887 /100 = 48.87 %.

Let us take one more example of decimal to percent conversion: Convert 2.02 to its equivalent %. We multiply 2.02 and 100: 2.02 x 100 = 202 %

Application of this is found in many mathematical problems where the rate or percentage evaluation is needed to be done.

Linear equations are those expressions in maths which when plotted result into a straight geometrical line. The commonly used form of any linear equation is the slope – intercept form that is given as: y = m x + c. Where, m denotes the slope and c denotes the intersection point of the line when it is graphed. On the basis of the slope and the intercept of the line we can decide whether the two lines are intersecting, parallel or coinciding. If the two lines have different slopes, then only we can use the linear equation solver to find the intersection point. There can be just one intersection point between two lines. In case the slopes are equal, the lines can be either coinciding or parallel.

If the intercepts of the lines are also equal, then the lines are said to be coinciding and for lines with different intercepts we call them parallel. These concepts form the base of algebra and geometry of maths and have been briefed in the cbse sample papers 12.

Imaginary Number definition

There are so many types of a number in mathematics such as real numbers, whole numbers, imaginary numbers, complex numbers etc. But here we will only discuss imaginary number definition which says that an imaginary number is a number which will always remain less than or equal to zero whenever you square the number. Imaginary numbers are always represented in the form of iy where y is any real number and i is the imaginary unit.

In other words imaginary number can be defined as when an imaginary number, let us suppose iy, is being added to any real number like x, it results into a complex number which is of the form x + iy, where x and y are the real part and imaginary part of that complex number respectively.
And as you can see that complex number will become equal to the imaginary number whenever the real part of the complex number, which is x, will be zero.

In imaginary number definition there is one more point which is yet to be discussed. The point is, whenever we see any number under the square root with a negative sign ahead, we cannot solve it, but we could have solved it if there was no negative sign so that’s why we put an imaginary unit i before the square root because of the property i² = -1 and then we can just solve the number in square root.
For example, we have a number √ -25, which is an imaginary number and its square is -25 but we can also represent an imaginary number as a real number by just putting an imaginary unit i before the square root as i² = -1,so we have i √ 25 which is equal to i5.

In order to get help in the topics: representative elements and cbse latest sample papers, you can just visit our next article.

Perfect Numbers

In the previous post we have discussed about What are Ordered Pairs and In today's session we are going to discuss about Perfect Numbers. Perfect Numbers that define in the number theory describe as a positive integer number which is equal to the sum of its divisor that gives the remainder zero means they would be proper divisor but in this sum discard the number itself that is also a proper divisor  but could not included in the calculation of perfect number.

We can also explained perfect number as a half of the sum of total positive divisors but in this case include the number itself.

We can easily define the perfect number by an example as 6 is a perfect number because the sum of all the divisor excluding itself equal to 6 that is 1 , 2 and 3 are the proper positive divisor of number 6 and their sum as 1 + 2 + 3 = 6.

According to the second definition of the perfect number if half of the sum of its all proper divisor is equal to the given number then that number is called as perfect number as (1 + 2 + 3 + 6) / 2 = 12 / 2 = 6.

We can also categorize the perfect numbers as even perfect number and odd perfect number.

According to the definition of the even perfect number, 2 > n-1( 2 >n – 1) shows an even perfect number in which n shows the prime number. (know more about Perfect Numbers, here)

We can calculate perfect numbers as 2 is prime number so put it into the given formula as 2 > (2 – 1).(2 > 2 – 1) = 2 > 1. 4 – 1 = 2 .3 = 6 , that shows 6 as a perfect number.

Systematic Sampling is a statistical method that describes as a method of random selection of elements from an ordered sampling frame. It is very popular because of its simplicity and its periodic quality.

Icse board papers helps students for assessment of their knowledge.

What are Ordered Pairs

In the previous post we have discussed about ratio definition and In today's session we are going to discuss about Ordered pair, It can be consider as any pair of object that are related to the mathematics. Usually the concept of ordered pair deals with the real number of number system. A pair of ordered pairs popularly used for denoting a point on a coordinate plane. Usually this concept deals with two values that are written in the form (a, b ), In the given notation the value of “a” denotes the pixel position of x- axis and value of b denotes the pixel position on y axis. (Know more about Ordered Pairs in broad manner, here,)

It means to say that in the ordered pairs first value denotes the value of x coordinate and second value denotes the value of y coordinate.  In a graph, the concept of ordered pair with value (0, 0) denotes the origin point of graph. An ordered pair can simply be considered as a pair of two no. in a certain aspect. The one more thing we need to remember that ordered pairs can also contain the same number two times like (2, 2) or (4, 4).

In the real world an ordered pair is very popular in the field of graph or map where this concept is used for locating a position. It is also helpful in creating a road map, world map and so on. In mathematics, these ordered pairs used to show the actual position in a rectangular grid form. The concept of ordered pairs can also deal with three variables or values with in a three dimensional coordinate graph or map. If any ordered pair contains negative values it means that coordinate point showing the position below the origin point. Otherwise if both pixel position is positive then coordinate are shown in upper side of origin point. In the concpet of solving algebraic equation we basically deals with how to solve the equation. The central board of secondary education provide the cbse sample papers for class 10 in the begining of new session of 10th and 12th garde.

ratio definition

In mathematics, there are various ways which provide the relationship between different concepts of mathematics. Ratio in mathematics is also a concept that shows the relationship between two numbers of the same nature. It means to say that ratio is a mathematical concept which is used to express how many times a number contains in comparison of other or first number. Generally the concept of ratio definition can be describe by taking two variable x and y as “ x to y” or in second form which is more popular i. e, x:y.

If we want to describe a concept of ratio in simple language then we express them as a relative size of two or more variables. The concept of ratio definition can be described by the ‘:’ symbol. This symbol shows the relationship between the same kinds of number by describing in what manner first number is related to another number. The concept of ratio can be performed by division of two numbers. As like there is a ratio of two numbers given like 2:10 which says that first number 2 is 5 times smaller than second number 10.

At the time of performing ratio analysis we can perform their task by follow the some of the step that are given below. Here these steps are express by solving a query. (Know more about ratio in broad manner, here,)

Suppose there are two variables x and y. if value of x is equal to the 5 and their ratio is 1 : 3 then calculate the value of y?

To perform the above given task x : y = 1 : 3 = 5 : ?

So,  first we need to perform the division of given variable with their corresponding ratio value. That is 5 / 1 = 5.

Now we need to multiply the same output with another ratio value. That is 5 * 3 = 15.

In the final step we can say that the ratio of x : y = 1: 3 = 5 : 15

In mathematics,  algebra 2 solver is a concept that helps the student by describing how to solve algebraic equation.  In board examination preparation, icse board sample papers helps the student to focus on important concept that has the higher possibility to come in exam and In the next session we will discuss about  What are Ordered Pairs.

How to perform Long Division

In the previous post we have discussed about Use Fraction to Decimal Converter and In today's session we are going to discuss How to perform Long Division. About Word division means equal distribution of the particular number of units in any number of parts.  We can divide any number n in x equal parts; by subtracting x form the number n. Then we say that again x is subtracted from the remaining units. This process is continued until the remainder is zero or less than x. In case we get the remainder equal to zero, we say that the number n is completely divisible by x, else not. (know more about Long division, here)
 This repeated method of subtraction for division is not possible for the larger numbers. So we say that in such case we use a Long Division.
In long Division method, we must first know the following terms. Divisor is the number by which we are dividing the given number. Dividend is the number which is being divided. The result we get after division in called the quotient and the number left at the end, which further cannot be divided by the divisor is called the remainder. Now we will place the dividend in the middle and check if the first digit of the dividend is smaller than divisor or not. In case it is not smaller, we will take first two digits of the number and divide them by the divisor.  The result is placed under the given digits and we find the difference between the two digits.
 In next step, the next digit is brought down from the dividend and the same process is repeated, until all the digits of the dividend are processed.

 In order to learn about What Is the Independent Variable, we can take online help of math tutor and understand the concept.  We can also download the syllabus of West Bengal Board of Primary Education which is available online on the website and can be used for the specific studies of a particular grade.

Use Fraction to Decimal Converter

In the previous post we have discussed about How to Work out Multiplying Fractions Calculator and In today's session we are going to discuss about Use Fraction to Decimal Converter. To learn about Fraction to Decimal Converter, we must first know about the fraction numbers and the decimal numbers. We say that the fraction numbers are the numbers which can be expressed in the form of p/q, where p and q are the whole numbers and q <> 0.  On the other hand we say that the numbers which are written in the form of the combination of the whole part and the decimal part are called the decimal number. The decimal part of the decimal number represents the part of the number which is less than 1.
Now let us take any fraction number say 2/5, we need to convert it in the form of the decimal number. For this we will try to convert the denominator in the form of the power of 10. So for this we will multiply the numerator and the denominator by 2 and thus we will get the fraction as:
( 2 * 2 ) / ( 5 * 2 )
= 4 / 10 (know more about Decimal, here)
 Now as we have the denominator as 10, so we can write the number in the form of decimal as 0.4
  In case the fraction is already in the form of the decimal fraction, then it can be easily converted in the form of the decimal number. So we can write the fraction number 124/100 in the form of the decimal number as 1.24. Here we will remove the denominator 100 and thus we will   place the decimal at the two places from the right. So we say that the fraction 124/100 is same as 1.24
To learn about the Negative Correlation, we will make the use of the online math tutor.  To get the CBSE History Syllabus, we can visit  the website and download all the necessary information.

How to Work out Multiplying Fractions Calculator

Fractional number can be considering as a part of number system. Fractional number represents any whole number into any number of equal parts. Fractional numbers play an important role in our daily routine life like one-half of cake, one-fourth and so on. In the more basic way we can describe the fractional number as a number that is able to represent the integer value in the form of numerator and denominator. In the fractional number the value of numerator represents n number of parts which are same to other part. On the other hand the value of denominator shows how many parts are possible to generate a whole. (know more about Multiplying Fractions, here)
n / d
In the above given notation the variable ‘n’ refers to the value of numerator and the variable ‘d’ refers to the value of denominator. As we know that fractional numbers are part of mathematics then mathematical operations can easily be performed to solve various problems. With fractional number we can perform addition, subtraction, division and multiplication very easily. Here we are going to discussing about the multiplication of fractional numbers.
To perform the multiplication between the two fractional numbers, this can easily be performed by using the multiplying fractions calculator. The multiplying fractions calculator follows the some of the steps that are given below:
A ) First of all perform the multiplication between the numerator values of given fractional numbers.
B ) After that multiply the denominator ‘s value of given fractional numbers.
C ) This step is optional because if there is any need then simplify the obtained fractional into simple form.
During the multiplication of fractional numbers, if we follow the above steps then we get the right output for our problem. Geometric distribution is part of probability theory that able the user to get how many failures is possible before occurring single successful event. In the Tamilnadu state, Tamilnadu board conducts the board exam for students of secondary and senior secondary students. To accomplish their task board provides Tamilnadu board books to the students and In the next session we will discuss about Use Fraction to Decimal Converter.

How to Multiply Integers

In the previous session we discuss about How to Divide Integers and today we will discuss about How to Multiply Integers. A set of positive and negative numbers is known as integers. Decimal numbers and fractional numbers are not involves in integers.
For example: -6, -9, -58, -77, 0, 11, 25, 30, 110, 130, and160;
In the given example all are the integer number. The number 0 is also an integer number.
There are two types of integers which is shown below:
1.    Positive Integer
2.    Negative integer.
In the mathematics the numbers which are larger than zero are known as positive integer?
For example: 4, 10, 15, 22, 55, 510, 610, 790 and so on all are the positive integers.
The numbers which are smaller than zero, that number is known as negative integer.
For example: -10, -15, -17, -26, -32, -55, -89, -559, -670 and so on all are the negative integers.
Let’s see some steps of multiplying integers;
We have to follow some steps for multiplying integers which are shown below:
Step 1: To find the multiplying integers first we have to take the numbers, all the numbers be positive or negative number because fractional and decimal numbers are not involved in case integers.
Step 2: After that we multiply all the given positive and negative integers.
Let’s see how two numbers are multiplied, suppose we have two numbers are 300 and 250. Multiply both the integers?
Solution: Given, the two positive numbers are 300 and 250.
On multiplying we get:
300 * 250 = 75000,
When we multiply two positive integers we get positive number only.
When we have one integer is positive and the value of positive is 170 and one integer is negative and the values of negative integer is -115, and then see how the numbers are multiplied?
Solution: Given, Positive integer = 170 and negative integer = -155;
On multiplying both the numbers we get:
170 * (-155) = -26350, we get negative integer.
To get more information of Derivative Rules then follow the math online portal. To get better result than before examination solve the cbse question bank papers.

How to Divide Integers

We say that integers are the numbers which extend from minus infinite to plus infinite including zero. These numbers can be expressed on the number line.  Here we are going to learn about dividing integers. When we talk about  dividing integers properties, we say that the closure property does not hold true for the integers, which means that if we divide any integer number by another integer number, then the  result is not necessary an integer.
 Another property of integers is commutative property, which does not hold true for the division of the integer numbers.  Here we say that if a and b is any two integer numbers, then we say that a divided by b is not equal to b divided by a. mathematically we represent it as:
  A ÷ b  <> b ÷ a
 Now we say that  let us look at the  associative property of integers which also does not hold true for the division operation. We say that if we have a, b, c as any three integer numbers, then  we have :
( a ÷ b ) ÷ c <> a ÷ (  b ÷ c)

 Let us take another property of integers as division by 1: According to this property, we mean that if any integer number a is divided by 1, then the result is the original integer number so if we have a as any integer number, then we write it mathematically as  a ÷ 1 = a
 On the other hand, if any integer is divided by -1, then we write  a ÷ -1 = -a


 We will learn about the Trapezoidal Rule by taking online help from online math tutor. We can get CBSE sample papers online, which can help us to get the guide lines about how to prepare for the fore coming examination.

How to solve Pattern Worksheets

We can see different patterns and series around us in our daily life. These patterns  can be the patterns drawn on the print of a  shirt, Pattern of the growth of the petals of a flower, patterns of the flooring  in your school. We must understand the methods of the formation of patterns and the logics used in it. The patterns  formed in such a way are called logical patterns. Now we look at the different mathematical patterns formed.
Let us look at some of the following series:
2 , 4 , 6 , 8, 10, 12, .. . . . . . This is the pattern of the even natural numbers. We say that these numbers are divisible by 2
1, 3, 5, 7, 9, 11, 13, 15, 17 , . . . . . . . . . . .  This is the pattern of the  odd numbers. We say that these numbers are not divisible by 2. Another series we take is the series of  prime numbers.
2, 3, 5, 7, 11, 13, 17, 19, . . . . are all prime numbers. We say that the prime numbers are the numbers which are having only 2 factors i.e. 1 and itself.
Now we will look at the series 1, 4, 9, 25, 36, 49, . . . . . . We say that this series is the series of the numbers which are the squares of the natural numbers 1, 2, 3, 4 ,5 , 6, . . . . . etc.
We can form infinite number of such series which can be in the form of Factorials, A.P. , G.P. etc.

 We can learn about Pattern Worksheets online and practice about the different types of patterns available or which can be formed. To learn about the Differential Equations we must go through CBSE Books for Class 11.

Subtracting Integers

In the previous section we have discussed about adding scientific notation calculator and In today's session we are going to discuss about Subtracting Integers.
We know that the subtraction operation is to be performed when something is to be reduced from the given unit. Now we will learn how to perform the operation of subtraction. Here we will learn it by the help of the following expression:
Subtract -5 from -7
 In this expression, we observe that both the terms are negative. So the given expression can be mathematically expressed as follows:
 = -7 – ( -5 ), so we come to the conclusion that the sign of the second term will be changed when we perform subtraction. So we get “
 = -7 + 5
= -2, here the sign of the second term becomes positive and thus we get the result by performing the addition operation between the two terms as -2.  When we need to learn about Quotient Rule, we must go through the cbse textbooks for class 11 and understand the basic concepts for the same. Now we will find that we perform the subtraction operation between the terms such the subtrahend is a negative number and the minuend is a positive number, then we proceed as follows:
 Subtract -4 from + 6, so this expression will be written as follows:
 = 6 – ( -4 ), so we write that the  sign of the negative number -4 will change to  + 4 and the expression will be written as follows :
= 6 + 4 = + 10
Thus we find the two terms will be added up and we get the result as  + 10, which is the difference of the  two numbers  where the  subtrahend is a negative number and the minuend is a positive number.

adding scientific notation calculator

In simple terms a scientific notation is a way of writing numbers which are too large or too small and can be written in standard decimal notation. Scientific notation has the number of useful properties which are more commonly used in calculators and also by the mathematicians, engineers and scientists. Exponential notation is the other name of scientific notation. In scientific notation all the numbers are written in the form of
  a * 10^b  ; where the b in the exponential form is the integer, the coefficient a is any real number in other words the number 10 is also known as base. Power of ten notation is used to save our efforts. If the decimal moved to the left this means base has the positive exponent. And if it has negative exponent it will move to the right.
There are few steps can be followed to add and subtract any two numbers in the adding scientific notation calculator.
Step 1 is to adjust the power of 10 in the 2 number so that they can form the same index.
Step 2 is to add or subtract the number
step 3 is to give the answer in the scientific notation.
Now we will understand this with the help of the following instance.
Evaluate 3 * 10³ + 6.3 * 10⁴ and give your answer in the scientific notation.
Solution : 3 * 10³ + 6.3 * 10⁴

= 0.3 * 10⁴ + 6.3 * 10⁴ ( convert them into the same indices)

= (0.3 + 6.3 ) * 10⁴ (add the numbers)

= 6.6 * 10⁴ ( answer in scientific notation.)

Few of the Algebra 2 problems are difficult to solve, algebra 2 tutor is available online to help you out. Work out TamilNadu board logic sample papers to score high in your examinations and In the next session we will discuss about subtracting integers worksheet.

subtracting integers worksheet

Previously we have discussed about antiderivative of e and In today's session we are going to discuss about subtracting integers worksheet, We know that integers are all natural numbers, their negative numbers & zero. Since we can do mathematical operations of addition, subtraction, multiplication & division, so we can do all these operations on integers as well. We can further improve our skills by working out subtracting integers worksheet.
Let us know how to subtract integers. We know that on a number line 0 is placed in the centre , all positive numbers on the right side of zero in increasing order & all negative numbers on left side of zero in decreasing order. To subtract any two integers, we can use a number line or can do the same by following the rules of signs associated with integers.(Know more about integers in broad manner, here,)
To subtract the given integers, we first consider their signs. If the two integers to be subtracted have positive sign, we subtract the smaller  number from the bigger & put +ve sign before the answer if smaller number is to be subtracted, while a –ve sign is put if the bigger number was to be subtracted. E.g., 3-7= -4 as 7, the bigger number was to be subtracted. But if it was 7-3, the answer would be 4 as the smaller number is to be subtracted.
While subtracting a –ve number, the –ve sign of the number & the minus sigh together become +, so we actually add the two numbers, e.g., 4-(-9)=4+9=13
To subtract a positive number from a negative number, the two numbers are actually added & a –ve sign is put before their sum, e.g.,(-8)-5=-8-5=-13.
Thus, we see that all the rules relating to addition of integers are followed in subtraction also with the only difference that the minus sign of subtraction combines with the sign of the number to be subtracted & for this combination of the sighs, we follow the following pattern:
-ve & +ve become –ve
-ve & -ve become +ve

We could also learn new topics like Binomial distribution and its also an important topic in andhra pradesh education board.
In the next session we will discuss about Properties of Numbers and  if anyone want to know about factor algebra calculator then they can refer to Internet and text books for understanding it more precisely.

Properties of Irrational Numbers

Previously we have discussed about factoring perfect square trinomials worksheet and In today's session we are going to discuss about Rational and irrational numbers which comes under board of andhra pradesh intermediate, They are the different type of number representation in the number system of mathematics. These are the number representations which help in solving the problem related to math. If we define the rational numbers then we can say that rational numbers are those numbers which represent the integer value in the form of numerator and denominator. For example, x / y, here x is numerator and y indicates the denominator which should be greater then 0.

In the same sense we can say that irrational numbers are those numbers which can’t be represented in the form of numerator and denominator format. In the general sense irrational numbers in the number system can be considered as real numbers but they can’t be shown in fractional format. The fundamental properties of irrational number is that they can’t be represented in ratio form.Through this topic we are going to discuss about the Properties of Irrational Numbers. Let's explain the concept to you with the help of some examples.

The famous example of irrational numbers is ∏. Generally this symbol is known as ‘ pi ‘. In the mathematics pi value is approximated as 22 / 7. It means ∏ = 3.141592653589 and so on. In the value of pi , we can see that the value is not accurate or they can’t be represented in standard fractional format. Thus, one of the Properties of Irrational Numbers is that the cannot be represented in fractional form. (Know more about  Irrational Numbers in broad manner, here,)

Another famous example of irrational numbers are √2. In the √2 there actual value is 1.41421356 and so on. As like the another fractional number √2 can’t be represented using ratio property of two numbers and they can’t be represented in any simple faction. That’s why this is irrational number.

Even the number e (symbol of Euler number ) can’t be represented in the ratio form and in simpler fraction from.

In the next session we are going to discuss subtracting integers worksheet 
and Read more maths topics of different grades such as Perfect Square Trinomials in the upcoming sessions here and You can visit our website for getting information about Rate of Change Formula.

 

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Binary Numbers

Previously we have discussed about how to solve limits and In today's session we are going to discuss about Binary numbers that comes under board of ssc education andhra pradesh, It deals with only two numbers 0 and 1.it is also known as base-2 number system. It has a radix of 2. In todays gadgets and computers, the circuits are implemented using binary coding that uses Binary Numbers.The main reason is that it is easy to manipulate the equations with 0 and 1.
We can define Binary Numbers as the ones that contain only two digits: 0's and 1's.
00000011001011011101010111 is a binary number. We can define Binary numbers as a sequence of 0's and 1's. The binary number can be converted into decimal numbers and hexadecimal numbers using the conversion formulas. Any number can be represented in the form of 0 and 1 and can be converted back into its original form .
Counting in binary number starts by taking rightmost digits and moving toward left. Conversion of binary number can be converted to decimal number by multiplying each digit by the corresponding power of 2.
for example,

0 0 1 1 can be converted to decimal number as,

[ 0 0 1 1 ]₂ =[ ( 2⁰ * 1 ) + ( 2 ¹ * 1 ) + ( 2² * 0 ) + ( 2³ * 0 ) ]₁₀
= [ 1 + 2 + 0 + 0 ]₁₀
=[3]₁₀

Similary, we can convert any binary number to a decimal number.
Following is the table which shows binary numbers and their corresponding decimal numbers.

Binary number decimal number

0 0
1 1
1 0 2
1 1 3
1 0 0 4
1 0 1 5
1 1 0 6
1 1 1 7
1 0 0 0 8
1 0 0 1 9

Now. Let us do addition in of binary numbers.
There are following rules,
1 + 1 =1 0
1 + 0 = 1
0 + 1 = 1
0 + 0 = 0

let us add two binary numbers,

1 0 1 0 + 1 1 0 0

1 0 1 0
+1 1 0 0
---------------------------------------------
1 0 1 1 0

we can implement a binary adder using this rule.
In the next session we are going to discuss Properties of Irrational Number and Read more maths topics of different grades such as Binomial Theorem
in the upcoming sessions here and You can visit our website for getting information about Normal Distribution Examples.

Properties of Numbers

Hello students, Previously we have discussed about fourier transform of sine and Today we are going to discuss properties of numbers which is an important part of ap secondary education board. The numbers systems are a part of mathematics. Number systems have some basic properties like: commutative, distributive, and associative.
Associative property: associative word means to associate or to group; this property is a rule that refers to grouping. For addition, the rule is x + (y + z) = (x + y) + z. This property can be understood with the help of example: 4+ (5+7) = (4+5) + 7.
For multiplication, the operation x(yz)=(xy)z. We will understand this operation with the help of example 3(4*5)=(3*4)5.
Commutative property: commutative word means to move around or to commute; the commutative property is one of the parts that stated that you can rearrange digits in an expression. For addition, the commutative property rule is x + y = y + x; this means 6 + 4 = 4 + 6.
For multiplication, the commutative property rule is xy = yx this means 4*5 = 5*4. For example, we use the commutative property to restate 4 * 6 * a: 6*4*a, 6*a*4, a*6*4, 4*a*6, and 4*6*a
Why is it true that 4(6a) = (6a)(4)?
This is true by commutative property. (We can see that 4(6a) = (6a)(4) = 24a)
Distributive property: this property is easy to remember, this property can be stated as: x(y + z) = xy + xz. This means 3(4 + 5) = 3*4 + 3*5.
Why is it truethat3(a + b) = 3a + 3b?
This is true by the distributive property. Distributive Property operations can be performed in the real numbers.(Know more about Properties of Numbers in broad manner, here,)
The example of the number system properties: 4x - 5y + 6z (this is original statement).
4x - 5y + 6x: this is commutative property, (4x+6x)-5y: this is the associative property, x(4+6)-5y: this is distributive property.
In the next topic we are going to discuss about Binary Numbers
and Read more maths topics of different grades such as Binomial Experiments in the upcoming sessions here and and You can visit our website for getting information about Negative Correlation Coefficient.

Properties of Complex Numbers

Previously we have discussed about system of equations worksheet and Today we are going to discuss about the Complex numbers and their properties which comes under andhra pradesh education board. First of all we should know about the complex numbers. A complex number is a number which has a form of x + iy, here x and y are the real numbers and i is known as the imaginary part or unit of the complex number. The value of i is root of -1 or i>2= -1. In the form of the complex number the term x is the real part and iy is the imaginary part of the number. The complex number is known as purely imaginary number if its real part or x is equals to 0.(Know more about Complex Numbers in broad manner, here,)
Now here I will tell you about some of the Properties of Complex Numbers:
1.    Powers of   i = root of -1, i>2 = -1, i>3 = -1, i>4 = 1
2.     Equality of two complex numbers: Two complex numbers are said to be equal if their real and imaginary parts are equal say two complex numbers are

 x + iy = a + ib if x = a and y = b.

3.    Addition property: When we add two complex numbers then we have to add the real parts to one another and imaginary parts to one another of the numbers. Like if we have two complex numbers say a + ib and x + iy then their addition will be (a + x) + (b + y)i.
The subtraction is just opposite of the addition property of the complex numbers.
4.    Multiplication: To multiply two complex numbers simply use the FOIL method.

(a + bi)*(x + yi)= (ax - by) + (ay + bx)i.

5.     Complex Conjugation: The complex number x + yi can be conjugate and it will give value x –yi. One thing is to remember is that the product of a complex number and its conjugate is always a real value. That is (x + iy) (x - iy)= x2+ y2.
So these are the Complex Number Properties. In the next topic we are going to discuss Properties of Numbers and if anyone want to know about Solving Binomial Expansion then they can refer to Internet and text books for understanding it more precisely and if you need help with math you can visit our website.

How to do Estimate Quotients

Previously we have discussed about rational expressions calculator with steps and In today's session we are going to discuss about How to do Estimate Quotients which comes under school secondary board of andhra pradesh.
WHAT IS QUOTIENT??(Quotient Rule Derivatives)
Quotient is a result obtained by dividing one amount by another.
What is division?

The inverse process of multiplication is division. The number times a number can be broken into parts according to another number.
DIVISOR, DIVIDEND AND QUOTIENT:
    The number that is divided is called the dividend.
    The number that divides the dividend is called divisor.
    The number of times the dividend is divisible by the divisor is called the quotient.
    If the dividend is completely not divisible by the divisor it leaves behind a remainder.
10/2=5
Here,
10 is the dividend
2 is the divisor
5 is the quotient
Let us see how to find the dividend if we know the quotient, divisor and remainder
Dividend = Quotient x Divisor + Remainder
In the above example
Remainder=0
Quotient is 5
Divisor is 2
Dividend=2*5+0=10
Example:
5/4
Here divisor: 4
Remainder: 1
Quotient: 1
Dividend=4*1+1=5

Estimating is the process of finding the value of unknown quantity by proper steps.
How to do Estimate Quotients: Estimating of quotient means finding the value with which  a number can be divided with another number.(Know more about Quotients in broad manner, here,)

Compatible numbers:
What are compatible numbers:
Compatible numbers are numbers which we  can be divided  easily.
e.g.:
22 divided 2
2*1=2
again 2*1=2
=11
the quotient is 11
45/9
=5
The quotient is 5.
These are compatible numbers.
Now let us see how to estimate quotients for non compatible numbers:

315/5

Let us take 31..
Now 31 divided 5, we get 6
we get a remainder of 1
15 divided by 5 is 3
therefore the quotient is 63
Solve estimate quotients:
294/7
What number times 7 has a product close to 29?
? *7 = 28
4 * 7 = 28
So,
29 divided by 7 is about 4
Now ?*7=14
Answer here is 2
Therefore the quotient is 42

In The Next Session We Are Going To Discuss Properties of Complex Numbers
and if anyone want to know about Binomial Expansion then they can refer to Internet and text books for understanding it more precisely.

Math Blog on Estimating Quotients

Previously we have discussed about measures of central tendency worksheets and In today's session we are going to discuss about Estimating quotients of numbers which is  a part of board of secondary education ap, Its defined by some rules that help the students in understanding how to estimate quotients .The rules for defining the estimate the quotient are as follows with their examples:
Rule no 1 # Decimal number is rounded to the nearest whole number means if the decimal number is approximately equal or near to the its nearest whole number then it will change into that whole number .
Example : 5 . 9 / 3 = ?
6 / 3 = 2 so 5 . 9 / 3 is near about to 2.
Rule no 2 # Decimal number(learn how to divide decimals) may be renamed means if the decimal number is not exactly calculated in terms of easier calculation then it will be change into its close decimal number that makes the calculations easy.(Know more about Quotients in broad manner, here,)
Example : 2 .8 / 3 = ?
2 .7 is easily divided by the 3 that is equal to the .9 so rename the 2 .8 into the 2 .7 to make the calculation more easy and fast so in place of 2 .8 / 3 we can write 2 .7 / 3 = 0 .9 .
Rule no 3 # Division problems can be rewrite as Multiplication problems .
Example : 7 .7 / 6 = ?
6 * _ = 6 .0
6 * 1 .0 = 6 .0
6 * 1 .1 = 6 .6
6 * 1. 5 = 9 .0
Here 7 .7 / 6 is lies in between 1 .1 and 1. 5 that is near about 1 .3 .
Rule no 4 # When divide the number by 10 , 1000 , 1000 or 10000 and so on move the digits of the number to the right side by one , two or three places .
Example : 554 / 10 = 55 .4
554 / 100 = 5 .54
554 / 1,000 = 0 .554
554 / 10,000 = 0 .0554
In the next topic we are going to discuss How to do Estimate Quotients
and Read more maths topics of different grades such as Math Blogs on Solving Trinomial Multiplication in the upcoming sessions here.
.

Types of Numbers

Number is the basic and very important object of mathematics. Today we are going to discuss about the numbers and their various types. Whenever we apply any mathematical operation then we need to take one or more numbers as an input and that produces an output which is also a number. We can apply many operations on numbers such as multiplication, division, subtraction, addition etc. Numeral is the notation which represents the numbers. (To get help on cbse boards click here)

Now I am going to tell you about the various types of the numbers.
NUMBER TYPES:
1.       Natural Number: These numbers are represented by “N”. Also known as counting numbers. These numbers start from one like: 1, 2, 3, 4, …..
2.       Integers: These numbers are represented as “Z”. These are of two types:

 a) Positive integers

                                                                         b) Negative integers
These are ………-4, -3, -2, -1, 0, 1, 2, 3, 4……………
3.       Rational Numbers: A rational number is represented by a fraction which is consisting of an integer numerator and denominator which is not equal to zero. These numbers are represented by Q. x/y where x is an integer and y is not equal to 0.
4.       Real Numbers: These numbers are all measuring numbers and written with decimal numerals. To represent them we use “R” notation. Example: 2.5342, 5.32 etc.
5.       Complex Numbers: A complex number consists of a number of the form x+iy where x, y are real numbers and i represents the imaginary part of the number and square root of -1. Represented as “C”.

Each number system is a proper subset of the other number set such as: C is the subset of R, R is subset of Q, Q is subset of Z and Z is subset of N (which in turn is Superset of Z).

Here I explained about the Numbers and types of numbers, in next session we will discuss about the various properties of the numbers and In the next session we will discuss about Math Blog on Estimating Quotients. 

How to perform Estimating and Rounding Numbers

Estimating and rounding is the basic need of math. These two things are used frequently in most of the math problems. Rounding and estimating comes in various physical quantities such as money, length of time, etc. Rounding off of any number is kind of or similar to estimation.
Here we will first learn rounding of the whole numbers.  In this, first we find the place value we want that is the rounding digit and then search the immediate digit to its right. If the immediate right digit is less than 5 then without changing the rounding digit just change the remaining right digit of it to zero. If that digit is greater than or equal to 5, then we will add 1 to the rounding digit and change all the right digits to zero.
Here are some examples to show estimating and rounding
1.       367 is the given number here then for estimating and rounding it we first look at the rounding digit that is 6. Now we will take the right digit of this rounding digit 6 that is 7. Here 7 is greater than 5 so we will add 1 to the rounding digit as 6 +1 = 7 and then we move to the right digit and make it 0. So we will get 370 that is the round up value. (To get help on icse text books click here)
Similarly
2.       Round off of 342 will be: 340 because here the rounding digit is 4 and the right digit is 2 that is less than 5 so we will place a zero at its place without changing the rounding digit.
So here I tell you about a very interesting part of math. Using this we can correctly answer the question by estimation. We should get it into habit so that we may be able to frequently solve estimation and round off based problems.
In next time we will discuss about Estimating Quotients and In the next session we will discuss about Types of Numbers. 

Number System Problems

Some of the real number examples are natural, positive and negative integers, fractions, decimal numbers, cube roots and square roots of any number. To solve the Number System Problems, we will first diagnose the type of problem and check which arithmetical calculation is to be done and this is a part of CBSE Board Syllabus.
We have some clues which help to analyze the type of problem.
If a word Add, Combine, sum, Join, together, all together, in all or total exist in the math problem then we add the numbers.
eg. :  Find the sum of 2.43, 23.09, and 3.9.
      What is the result if you Add 23.6 and 12.8 ?
      If you Join the line segment of 3.5 cm and 4.67, what is the total length?
      I have Rs34.65 and my sister has Rs 45.80, how much money do we have in all?
Similarly to diagnose the problem of difference we must look into following keywords
Left, subtract, difference, More, much and other such words.(want to Learn about Number ,click here),
 eg. : I had 24.500 kg sugar from which 12.470 kg sugar is used, how much sugar is left with me?
         Find the difference between 124.6 and 34.67.
        Subtract    34.67 from 56.34 and give the answer.
      I have Rs34.65 and my sister has Rs 45.80, how much money more does my sister have?
 Now we look into the keywords of multiplication:
      Product, multiply, To find the value of more than one when value of one is given. In all such cases we multiply.
Eg. Find the product of 34.6 and 32.90.
     What is the result , if you multiply 12.9 with 4.98?
     If the cost of 1 pen is Rs 45.00, find the cost of 23 pens.
Now we discuss the cases where division is done.
   To check the problem for division we must see divide, distribute, equally , and the problems where we need to find the unit value.
 Eg: Distribute 35 apples equally among 5 children.
       Divide 500 books on 25 shelves equally.
      If 5050 gms of grapes are to be distributed equally among 10 persons how much will each child get?

So students this is all about number system problem. In the next article we will discuss about How to perform Estimating and Rounding Numbers
and if anyone want to know about Simplifying Rational Expressions

then they can refer to Internet and text books for understanding it more precisely. 
.

number system and conversion

Hello friends,Previously we have discussed about probability examples and today i am going to teach you Number system in mathematics which constitutes a large space in cbse text books. As we talk about computers it works on only two digits 0 and 1, called binary numbers. Computer can only capable of manipulating binary numbers. If we want to understand how computer works, we should be able to use binary number system. But in order to work well as a computer professional we should know all types of number systems and way to convert between each other, If anyone wants they can take help of online tutoring. Because many times we need to convert one number system into other.

Types of Numbers
1.      Decimal System
2.      Binary System
3.      Octal System
4.      Hexadecimal System

Decimal System
            Base 10
            Digits - 0 to 9

Also called the positional number system. In decimal number system each digit is multiplied by the power of 10 depending on the position of the digit, which increases as we move from right to left, where first right most digit has power 0.

Example: 786₁₀
            786 = 7 * 10² + 8*10¹ + 6*10⁰
                       = 700 + 70 + 6

Binary System
            Base 2
            Digit – 0 and 1
In Binary  number system there can be only two possible values 0 and 1, often called as “bit”. Number of bits used in binary number represents the number. Power of 2 is used rather than 10 as in decimal number.

Example: 10010₂ number of bits =5_, 111011₂  number of bits =6

Octal System
            Base 8
            Digits – o to 7
Power of 8 is used to represent or convert from any number system into octal.

Example : 223₈, 456₈,557₈


Hexadecimal Number
            Base 16
            Digits – 0 to 9 and a to f

Power of 16 is used to represent number in this number system. Hexadecimal is the grouping of binary number that is hexamdecimal no can be broken into two parts of 4bits.

Example:  2AF4₁₆, 456AF_{16 (know more about numbers, here),}


Conversion

We will see how to convert one number system into other number system.

          Example: 11101 = ?₁₀
                Binary to Decimal

            1*2⁵    +  1*2⁴           +    1*2³         +    1*2²         +   0*2¹          +    1*2⁰                             
            32        +   16            +      8               +        4          +      0           +      1
        
            61

93₁₀ = ?₂
Decimal to Binary

93/2 =  46  remainder  1                   (Least significant bit)
46/2 = 23   remainder  0
23/2 = 11   remainder  1
11/2 =  5    remainder  1
5/2    = 2    remainder  1
2/2    = 1    remainder  0
1/2    = 0    remainder  1                   ( most significant bit)

We write it from msb to lsb
Result = 1011101

 Octal to decimal
754₈ into ?₁₀

=7x8² +          7x8¹                    +          7x8⁰
=448    +             56                          +             7
=511

Decimal to Octal
264₁₀  = ?₈
264/8 = 24 remainder 3
24/8   =  0 remainder 3
Result = 33

Hexa to Decimal
2CD₁₆ = ?₁₀
2x16²  +          Cx16¹              +          Dx16⁰
64        +          12x16             +          13x1
64        +          192                 +          13
269₁₀

Decimal to hexa
192₁₀ = ?₁₆

192/16 = 57 remainder 9
57/16  = 3   remainder  9
  3/16  =  0  remainder 3
Result = 399

We can use a table to show the relation between all the number system we have.

Decimal	Hexadecimal	Octal	binary
0	0	00000000000	0000
1	1	00100000001	0001
2	2	00200000010	0010
3	3	00300000011	0011
4	4	00400000100	0100
5	5	00500000101	0101
6	6	00600000110	0110
7	7	00700000111	0111
8	8	01000001000	1000
9	9	01100001001	1001
10	A	01200001010	1010
11	B	01300001011	1011
12	C	01400001100	1100
13	D	01500001101	1101
14	E	01600001110	1110
15	F	01700001111	1111

This table can be simply use to convert one number system into another .
This is all about number system and conversion and if anyone want to know about Properties of Irrational Numbers then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Rationalizing the Denominator  in the next session here.