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# Operations On Rational Numbers

Rational numbers are terminating or recurring decimal numbers written in the form of fraction    $\frac{a}{b}$ in which 'a' and 'b' are integers and the denominator 'b' not equal to zero. The operations performed on a rational number are addition, subtraction, multiplication and division.

To add two or more rational numbers the denominator of all the rational numbers should be the same. If the denominators of all rational numbers are same then you can simply add all the numerators and the denominator value will the same. If all the denominator values are not the same then you have to make the denominator value as same by multiplying the numerator and denominator value by a common factor.

e.g.,
$\frac{1}{3}$    +   $\frac{4}{3}$   =  $\frac{5}{3}$

$\frac{1}{3}$  + $\frac{1}{5}$ = $\frac{5}{15}$ +  $\frac{3}{15}$ = $\frac{8}{15}$

Subtraction of Rational Numbers
To subtract two or more rational numbers the denominator of all the rational numbers should be the same. If the denominators of all rational numbers are same then you can simply subtract the numerators and the denominator value will the same. If all the denominator values are not the same then you have to make the denominator value as same by multiplying the numerator and denominator value by a common factor.

e.g.,
$\frac{4}{3}$ - $\frac{2}{3}$ = $\frac{2}{3}$

$\frac{1}{3}$ - $\frac{1}{5}$ = $\frac{5}{15}$ - $\frac{3}{15}$ = $\frac{2}{15}$

Multiplication of Rational Numbers
Multiplication of rational numbers is very easy. You should simply multiply all the numerators and it will be the resulting numerator and multiply all the denominators and it will be the resulting denominator.

e.g,
$\frac{4}{3}$ x $\frac{2}{3}$ = $\frac{8}{9}$

Division of Rational Numbers
Division of rational numbers requires multiplication of rational numbers. If you are dividing two rational numbers then take the reciprocal of the second rational number and multiply it with the first rational number.

e.g,
$\frac{4}{3}$ / $\frac{2}{5}$ = $\frac{4}{3}$ x $\frac{5}{2}$ = $\frac{20}{6}$ = $\frac{10}{3}$

## Multiplications of rational numbers

Rational numbers are 'p / q' type, with one condition that here 'q' is not zero. We perform basic operations like addition, subtraction, multiplication, and division on the Rational Numbers. All the operation on the rational numbers are quiet same as the operations we have performed on the normal numbers. All the operations are very much similar wit...Read More

Rational number is represented by Q. Q is any real number which can be expressed in the form of x/y, provided that y is not equal to zero and x and y are integers. Addition of Rational Numbers play a very important role in various mathematical calculations.

Steps for addition of rational numbers:

1. Write the rational numbers and check whether the ...Read More

## Subtraction of Rational Numbers

Subtraction of Rational Numbers plays a very important role in various mathematical calculations, here are some steps for subtracting two or more rational numbers:

1. For subtraction we need to check whether the denominator of the given numbers are same or not

2. If both the rational numbers have same denominators then we can ...Read More

## Division of Rational Numbers

Rational Number is any real number which can be represented in the form of x/y if y is not equal to zero and x, y are integers. It is very necessary to understand all the operations that can be performed on Rational Numbers such as addition, subtraction, multiplication, and division. The division of Rational Numbers is a bit complex operation and we need t...Read More