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.

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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.