Natural Numbers

Number theory : The set of it integers and its properties are at  the  root of all mathematical disciplines. In fact , it is impossible to do mathematics without making use of integers in some form or another. Number theory which involves the study of integers  itself , is a rich and fascinating branch o mathematics .many volume have been written on this subject and some of the best mathematician in history have devoted much of their time to the study of number theory.

We can subdivide the number theory as follow :
(i) Combinatorial Number Theory
(ii) Algebraic Number Theory
(iii) Analytic Number Theory
(iv) Transcendental number theory
(v) Geometric number theory
(vi) Computational number theory

What is a Natural Number?
Introduction To natural number : Since our childhood we are using numbers 1 , 2, 3, 4,………………………..t count and calculate. For example 3 banana , 5 apples , 7 mangoes , 2 books etc. here banana , apples , mangoes are objects whereas three , five , seven , two etc indicates about the quantities of theses objects .

To define natural numbers we might put these in this way, as when we count objects in groups of objects , we start counting from one and then go on to two, three , four etc . there is a  natural way of counting  objects .Hence 1 , 2 , 3 , 4 , …………………are called natural numbers .In fact number from 1 to 1crore are all natural numbers.Let us see what  is  a natural numbers ?We start counting from1  , so 1 is the first natural number , if we add1 to the first natural number , then we get 2  the second natural number/.by adding 1 to any natural number , then we get 2 , the second natural number. In fact adding 1 to  any natural number , we get the next natural number let us take few  examples of natural numbers  , 1000 is the natural number next to 999 , 10001 is the natural number, next to 10000 and so on .Thus if we think of any natural number , there is always a natural number next to it .Consequently there is no last  or greatest natural number consequently there is no last or greatest natural number. now in simple word , let  us define natural numbers: natural numbers are number from 1 onwards, ie , 1 , 2  3  4 , 5 , 6 ……………………..and are used for counting

Properties of natural numbers :Following are some properties of natural number (i) The first and smallest natural number is 1.(ii) Every natural number (except 1) can be obtained by adding to 1 to the previous natural number(iii)For the natural number 1, there is no previous natural number (iv)There is no last or greatest natural number (v)We cannot complete the counting of all natural number .

Ratios and Scale drawings

A ratio is a comparison of one thing with another.  It shows the relative size of two or more quantities. The order of the ratio is very important. a:b is not equal to b:a. Now let us find how to do ratios? A ratio can be expresses in three different ways:-

1. Fractional notation : 2/5
2. Odds notation: 2:5
3. Using the word “to” : 2 to 5

How to find ratios? Ratios can be solved by reducing them.  We can multiply or divide both the terms of ratio by the same number; it makes no change to the ratio. So this clearly answers how to solve ratios?

For example: - In a class of 20 students, 5 are girls and 15 are boys. What is the ratio of girls to boys?
Solution: - There are 5 girls and 15 boys.
The ratio of girls to boys will be 5:15
We can reduce this fraction by dividing both the terms by number 5
The ratio will be 1:3
Let us learn about ratio word problems now. Ratio word problems are problems that require use of ratios to relate the different quantities.
Following points should be kept in mind while solving ratio word problems:-

• Convert all the quantities to same units if required
• Write the quantities in the ratio as a fraction
• Remember to keep same quantities in numerator and denominator

Example:- There are blue and red ball in a bag, the ratio of blue balls to red balls is 5:6. If the bag contains 60 red balls, how many blue balls are there?
Solution: -
Let x be blue balls
Red/Green = 5/6 = x/60
X = 50 balls.
Let us learn about scale drawings. If any ratio is expressed in 1:n  form, then n is called the scale factor. It is not possible to draw on paper the exact size of real- life objects. Therefore we make use of scale drawing to draw such figures like a car, a building or any map.

Example: -A figure has a scale of 1:10 that means anything drawn with the size of “1” would have a size of “10” in real world.

How to Convert Fractions to Decimals

Let's learn about How to Convert Fractions to Decimals.

In order to Convert Fractions to Decimals, the proper or improper fraction has to undergo division. The numerator has to be divided by the denominator and the resultant will be a decimal value. Below is an example:
Example:
5/2
= 2.5

For more help, get it from an expert free math tutor. Next time i will help you with the concept of solving equations with decimals.

Do post your comments.

Bias Statistics

Let's learn about bias in the study of statistics.

There are four different types of bias in statistics and these are listed below:

• Spectrum bias
• Omitted Variable bias
• Systematic bias
• Cognitive bias  

 Next time i will help you with some other concept of statistics such as inference statistics. For more help you can also connect with an online tutor and get your help. Not just in statistics but in other topics such as geometry tutoring as well.

Do post me back your feed backs.

Critical Value

Let's learn about Critical Value in statistics in today's learning.

Critical value is an important concept of statistics which is used in calculus as well. The point where a function has its maxima and minima is called the critical value.

This cutoff value determines the boundary between the samples, on the basis of which , it is determined, whether to reject the null hypothesis or whether to not reject the null hypothesis. If the calculated value from the statistical information is greater than the critical value, then the null hypothesis is rejected in favor of the choice hypothesis and vice versa.

Next time i will share with you about statistics data graphs. For more help connect with a calculus tutor and get your help.

Do post your comments.

types of quadrilaterals

Let us learn about types of quadrilaterals

Quadrilaterals are 1 of the types of polygon. In geometry all quadrilaterals have 4 sides. All quadrilaterals are 2-Dimensional figures or polygons. The 4 sides figures are known as quadrilaterals. Quadrilaterals main property has width & length of 2 dimensions.
Types of quadrilaterals & their properties:

1. Parallelogram

2. Trapezoids.

In our next blog we shall learn about what causes pollution I hope the above explanation was useful.Keep reading and leave your comments.

make sentences using words

Let us try to make sentences using words

Math: Math is the study of quantity, space, structure, & change.

Addition: Addition is a basic operation in mathematics; addition has simple rules. Addition role in math problems are important in most of the problems.

Subtraction: Subtraction is the operation which finds the difference between the given two numbers

Multiplication: Multiplication means times or repeated addition. The symbol used for multiplication is '×'.

Fraction: A Fraction means a part of a group or a region or a whole.

In our next blog we shall learn about metallic character I hope the above explanation was useful.Keep reading and leave your comments.