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.