Saturday, July 24

Least Common Multiple

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Least Common Multiple: In arithmetic number of theory is the least common multiple or lowest common multiple (LCM) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both of a and of b. Since it was a multiple, it can be divided by a and b without a reminder.If either a or b is 0, so that number is no such positive integer, then LCM(a, b) is defined to be zero.Now let us find least common multiple,Multiples of 4 are:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, ......................Multiple of 7 are:7, 14, 21, ................These were some examples of least common multiple lcm.ope you like the above example of Least common Multiple.Please leave your comments, if you have any doubts.

Probability

What is probability:Let us now understand what is a Probability.An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a probability.Usually questions are asked on how to calculate probability.In the future blogs we will learn about probability calculator.

Matrices Determinants


Matrices Determinants:Let us learn matrices determinants.Matrices :A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket.Determinants : Let A = [aij] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is denoted by the symbol det.A or |A|.The above explanation speaks about deteminants and matrices,in the coming Blogs we will learn about determinants of matrices.

Friday, July 16

Binomial Theorem


Let us learn about Binomial Theorem in this Blog.The binomial theorem explains the power of the binomial. Binomial coefficient is the resulting coefficient of the expression. By using binomial theorem we can raise the power. For example, (x+y) is a binomial. Binomial Distribution is a statistical experiment which means the number of successes in n repeated trials of a binomial experiment. It is also called as Bernoulli distribution or Bernoulli trial.For example:For a clinical trial, a patient may live or die. Here the researcher faces the number of survivors and not how much time the patient lives after treatment.H

Measuring Angles:


In this blog I will help you understand about Measuring angles: In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the circle r, and possibly multiplied by a scaling constant k (which depends on the units of measurement that are chosen).The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered.Let us now learn about measuring angles Worksheet,it deals with the problems related to identifying the angles and example problems.

Wednesday, July 14

Binomial Distribution

Binomial Theorem:The binomial theorem explains the power of the binomial. Binomial coefficient is the resulting coefficient of the expression. By using binomial theorem we can raise the power. For example, (x+y) is a binomial.With the help of this binomial theorem ,for example we can expand any power of x + y into a sum of terms forming a polynomial.
(x+y) n = nc0. Xn.y0 + nc1 .x (n-1) y1 + nc2 .x (n-2).y2 +……..+ nc (n-1) x1.y (n-1) + ncn. x0. yn

Where the corresponding binomial theorem coefficient example is in the form ‘nCk’.

nCk = [(n!) / [k! (n-k)!]]
We know that (x+y)0=1
(x+y)1=1x+1y
(x+y)2=x2+2xy+y2


Let there be n independent trials in an experiments and let the random variable X denote the number of successes in the trails . Let the probability of getting a positive possible in a single trail be p and that getting a failure be q so that p + q = 1. then

P(X = r) = nCr * Pr * q(n-r).

This is called Binomial distribution.Hope you like the above example of Binomial Theorem.Please leave your comments, if you have any doubts.

Sunday, July 11

Integers

Integers:

When ever we learn about any new topic we learn from the basic,similarly lets see the concept of Integers.........and let us first understand the concept and meaning of Integers.The most common thing is what do we mean by Integers??? We can explain this with the help of a simple definition of Integers.

Integers are the whole numbers, negative whole numbers, and zero. For example, 43434235, 28, 2, 0, -28, and -3030 are integers, but numbers like 1/2, 4.00032, 2.5, Pi, and -9.90 are not. We can say that an integer is in the set: {...3,-2,-1,0,1,2,3,...} Positive numbers, zero and negative numbers together form an Integer. A fraction is a part or parts of a whole. Decimal fraction is the special fraction whose denominators are 10, 100, 1000 etc. These fractions are called decimal fractions. Let us see about Integers, Fractions and decimals in this article.

The numbers 0, 1, −1, 2, −2, … are called integers of which 1, 2, 3, … are called positive integers and −1, −2, −3,… are called negative integers. The collections of all integers are denoted by the letter Z


Thus Z = {…, −3, −2, −1, 0, 1, 2, 3…}.Let us now learn about the origin of the term "Integers".The integers (from the Latin integer, literally "untouched", hence "whole": the word comes from the same origin, but via French) are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}. For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers.
The integers (with addition as operation) form the smallest group containing the additive monoid of the natural numbers. Like the natural numbers, the integers form a countably infinite set.




About Integers:

The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.

Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10, which is even.

Every positive integer can be factored into the product of prime numbers, and there's only one way to do it for every number. For instance, 280 = 2x2x2x5x7, and there's only one way to factor 280 into prime numbers.

Introduction about Integer Fraction:

If two numbers are in a / b form, where the two numbers are integer then it said to be a integers fraction,

Here, a (numerator)/ b (denominator) à both ‘a’ and ‘b’ not equal to zero.

Types of Integer fraction:

1. Proper Fraction.

2. Improper Fraction.

3. Mixed Fraction.

Proper Fraction:

In the proper fraction is the fraction in which the numerator (the top number) is less than the denominator (the bottom number).

Example:

1/2, 2/3, 5/7.

Improper Fraction:

An improper fraction is the numerator (the top number) is greater than or equal to the denominator (the bottom number).

Example:

4/3, 5/2, 7/5.

Mixed Fraction:

Mixed Fraction is the combination of whole number and proper fraction.

In mixed fraction addition we do the following steps,

1. First convert mixed fraction into the proper fraction.

[Multiply the denominator (Bottom of the number) of the fraction by the whole number and then add the numerator (top of the number) keep the answer over the original denominator.]

2. Add the numerators if the denominators are same.

3. If the denominators are Unequal make the common denominator by using LCM method.

4. Then simplify the answer that is divided the numerator and denominator by the same number.


Hope you like the above example of Integers.Please leave your comments, if you have any doubts.