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Division of rational numbers is same as division of fractions. Division of fractions is the inverse of multiplication. In case of rational number also, division is the inverse of multiplication.
Division:
If x and y are two rational numbers such that y is not equal to 0, then the result of dividing x by y is the rational number obtained on multiplying x by the reciprocal of y. When x is divided by y, we write x ÷y = x X \(\frac{1}{y}\)
Some important terms to be noted in case of division are:
Dividend: The number to be divided is called the dividend.
Divisor: The number which divides the dividend is called the divisor.
Quotient: When dividend is divided by the divisor, the result of the division is called the quotient.
Example:
If \(\frac{a}{b}\) is divided by \(\frac{c}{d}\), then \(\frac{a}{b}\) is the dividend, \(\frac{c}{d}\) is the divisor, and is the quotient.
Division by 0 is not defined.
Division of Rational Numbers Example 1:
Divide \(\frac{3}{5}\) by \(\frac{4}{25}\)
Solution:
\(\frac{3}{5}\) ÷ \(\frac{4}{25}\) = \(\frac{3}{5}\) X \(\frac{25}{4}\)
= \(\frac{(3 X 25)}{(5 X 4)}\) = \(\frac{(3 X 5)}{(1 X 4)}\) = \(\frac{15}{4}\)
Division of Rational Numbers Example 2:
Divide \(\frac{-8}{9}\) by \(\frac{4}{3}\)
Solution:
\(\frac{-8}{9}\) ÷ \(\frac{4}{3}\) = \(\frac{-8}{9}\) X \(\frac{3}{4}\)
= \(\frac{(-8 X 3)}{(9 X 4)}\) = \(\frac{(-2 X 1)}{(3 X 1)}\) = \(\frac{-2}{3}\)
Division of Rational Numbers Example 3:
Divide \(\frac{-16}{21}\) by \(\frac{-4}{3}\)
Solution:
\(\frac{-16}{21}\) ÷ \(\frac{-4}{3}\) = \(\frac{-16}{21}\) X \(\frac{3}{-4}\)
= \(\frac{(-16 X 3)}{(21 X -4)}\) = \(\frac{(4 X 1)}{(7 X 1)}\) = \(\frac{4}{7}\)
Division of Rational Numbers Example 4:
Divide \(\frac{-8}{13}\) by \(\frac{3}{-26}\)
Solution:
\(\frac{-8}{13}\) ÷ \(\frac{3}{-26}\) = \(\frac{-8}{13}\) X \(\frac{-26}{3}\)
= \(\frac{(-8 X -26)}{(13 X 3)}\) = \(\frac{(8 X 2)}{(1 X 3)}\) = \(\frac{16}{3}\)