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Operations on Rational Numbers

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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' is not equal to zero.

The operations performed on a rational number are addition, subtraction, multiplication and division.

Addition of Rational Numbers:
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.

Examples:
$\frac{1}{3}$ + $\frac{4}{3}$ = $\frac{5}{3}$

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

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.

Examples:
$\frac{4}{3}$ - $\frac{2}{3}$ = $\frac{2}{3}$

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

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.

Example:
$\frac{4}{3}$ 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.

Example:
$\frac{4}{3}$ $\div$ $\frac{2}{5}$ = $\frac{4}{3}$ x $\frac{5}{2}$ = $\frac{20}{6}$ = $\frac{10}{3}$