Solve Rational Numbers Problem

Hello friends rational number is an important for grade VI student karnataka secondary education board. They can be written as a ratio of two integers in the form a/b where a and b are integers, b is not zero. Rational Numbers are whole numbers, math fractions and decimals - the numbers we use in our daily life. The set of rational numbers is denoted by Q, and represents the set of all possible integer-to-natural-number ratios a/b. A rational number a/b is said to have numerator a and denominator b. If the numerator or the denominator of a rational number is a negative integer, then the rational number is called a negative rational number. Numbers that are not rational are called irrational numbers. The real number line consists of the union of the rational and irrational numbers. The set of rational numbers is a of measure zero on the number line. So it is small compared to the irrationals and the continuum. The elementary algebraic operations for combining rational numbers are exactly the same as for combining fractions. Positive rational numbers are represented to the right of 0 and Negative rational numbers are represented to the left of 0.

Simply any number that can be made by dividing one integer by another is called rational number. The word comes from "ratio" and is called rational number. Zero divided by any other integer equals zero, therefore zero is a rational number (but division by zero is undefined).

Now let us discuss about solving rational number problem. We will take some examples for explanation.(Learn more about rational numbers here),

1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2)

0.75 is a rational number (3/4) = 075/100 = 3/4

1 is a rational number (1/1) =1/1 =13.32 is a rational number =(1332/100)

-5.2 is a rational number = (-52/10)

Any rational number is trivially also an algebraic number. It is always possible to find another rational number between any two members of the set of rationales. Therefore, rather counter intuitively, the rational numbers are a continuous set, but at the same time countable.

The elementary algebraic operations for combining rational numbers are exactly the same as for combining fractions

For a,b and c any different rational numbers, then

1/(a-b)² +1/(b-c)² +1/(c-a)²

is the square of the rational number

a²+b²+c²-ab-bc-ca /(a-b)(b-c)(c-a)

Now let's move to an example of adding rational numbers

Two fractions are added as follows

¼ + ¼= 1+1/4 =2/4 =1/2

a/b +c/d =ad+bc/bd 

Now we will move towards subtraction of natural numbers

3/4 - 1/4 = 3-1/4 =2/4 = 12

a/b - c/d= ad-bc/bd

Now let us see the multiplication of rational numbers

2/3 × 2/5 =4/15

a/b .c/d =ac/bd

Finally we are here with division of rational numbers

½ ÷1/4 =1/2×4/1 =2

A recurring decimal is one which has one or more digits after the decimal point and they repeat endlessly in a specific pattern. Any recurring decimal can be expressed as a fraction. Hence it is a rational number. The pattern of rational numbers which is repeated is denoted by a line above the pattern called “bar” or “vinculum”.

Example

1/3 = 0.333…. or 0.3

-2/3 = -0.666…..

A terminating decimal is one which has limited number of digits after the decimal place. Any terminating decimal can be expressed as a fraction. Hence it is a rational number.

Example

5/8 = 0.625

3/4 = 0.75

So here we end with rational numbers. I hope that this article will help you in solving problems related to rational numbers and if you want to learn about inequalities and also on Proportions then refer Internet.