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# A Rational Number that is not an Integer

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Here, we have to prove for a rational number that is not an integer number. A rational number is the number of the form p / q and an integer is the number that has an integer value and always comes in the whole number. Now, any number which is a rational number but not integer. For example taking in consideration 3 / 4 that is a rational number but is not an integer. Converting this number in to integral part, so we can write it as: 3 / 4 = 0.75 0.75 is not an integer number. Similarly, in mathematics of numbers, we have a number of rational numbers (like 1/5, 6/8 and many more) that are not integer numbers. Each and every integer number can be written in the form of rational number but it is always not possible that all the rational number can also be represented in the form of integer number.
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A Rational Number that is not an Integer
A Rational Number that is not an Integer
Here, we have to prove for a rational number that is not an integer number. A rational
number is the number of the form p / q and an integer is the number that has an
integer value and always comes in the whole number.
Now, any number which is a rational number but not integer. For example taking in
consideration 3 / 4 that is a rational number but is not an integer.
Converting this number in to integral part, so we can write it as: 3 / 4 = 0.75 0.75 is
not an integer number.
Similarly, in mathematics of numbers, we have a number of rational numbers (like
1/5, 6/8 and many more) that are not integer numbers.
Each and every integer number can be written in the form of rational number but it is
always not possible that all the rational number can also be represented in the form of
integer number.

Tutorcircle.com
PageNo.:1/5

To check that a rational number that is not an integer number we have to only check
that whether the number can be written in the form of integer or a whole number
format.
Example Of Rational Number
For addition of these two quantities we just need to equalize the denominator first
then we have to add them. We don't need to do any application with the numerator.
For equalizing the denominator we need to follow some specific rules:
We have to multiply both the denominator and numerator with the same integer so
the value of fraction doesn't change and we have to multiply the integer in a manner
so that the value of both the denominator will be same or for simplification you can
multiply the first value by denominator of second and second value with the
denominator of first.
Now, let's see how to multiply 3*5/4*5+4*4/5* 4, the denominator of first number is 4
and we have multiply it on both the numerator and denominator.
The denominator of second number is 5 and we have multiplied it on both the
numerator and denominator.
Now, the result will be: 15/20 +16/20, Now it's very easy we just have to add the
numerator denominator remains the same so, required answer will be: 15/20 +
16/20=31/20.

Tutorcircle.com
PageNo.:2/5

-2.6 is a rational number which can be written-26/10. 3.26 is a rational number which
can be written 326/100.
In the above mentioned examples, the first example shows the negative value and
the other shows the positive value.
So, second one is positive rational number. This is all about Positive Rational
numbers.
Some more examples of positive rational number is :4, 1/4, 6 There are numbers you
can possibly get when you divide one positive whole number by another one, or one
negative whole number by another one.
Negative Rational Numbers
The numbers which are written in form of a/b where a and b are integers such that
b0 all comes in the family of Rational Numbers.
Positive Rational Numbers are those which have both numerators and denominators
as positive or negative. Example: 5/7, 6/5 or (-3/-4) are positive rational numbers.
Negative Rational Numbers are the numbers which have either numerator or
denominator as negative.
Example: -3/7, -5/8 0r 5/-8 are negative rational numbers. Negative rational number
must have at least one negative value that can either be numerator or denominator.

Tut
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3 3
/5

Introduction to Rational numbers
Today, I will tel you a story. Once there was a family of Natural numbers where al counting
numbers used to live. One day a guest named zero visited the house and requested for a
permission to stay there.
Al were happy; they requested the eldest member of the family Mr. infinite () to grant the
permission for 0. The permission was granted and the name of the house was changed to
house of Whole numbers.
Now, after some time negative numbers also visited the house and requested for the
permission to be the part of the family. They were permitted and now the family became the
family of Integers i.e. - . ........-3,-2,-1,0,1,2,3,........ On seeing the family living together,
some numbers which were in form of p/q, where p and q are natural numbers also asked for a
permission to stay there. They were cal ed fractions.
Some fractions are 4/7, 2/5 ...etc. The family of fractions also told that if you al see the
denominator with you, which is not usually visible, then you wil also become the part of
fractions family. All the numbers started trying it and realized that they all are the part of
fractions. But this was not true for negative integers.
The meeting was held, in which it was decided that a name Rational number will be given to
the family. A family of Rational Numbers consists of all the numbers which can be expressed
in form of p/q, where p and q are integers, but q 0.

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4/3
/5

ThankYou
TutorCircle.com

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