rational numbers are always associative under division true or false

Open in App

Solution

Dear student,

Associative property does not hold good for subtraction and division of rational numbers.

$Let a, b and c are 3 rational numbers . Now, a \div (b \div c) \neq (a \div b) \div c Consider the rational numbers \frac{64}{729}, \frac{16}{81} and \frac{2}{3} Now, \frac{64}{729} \div (\frac{16}{81} \div \frac{2}{3}) = \frac{64}{729} \div (\frac{16}{81} \times \frac{3}{2}) = \frac{64}{729} \div \frac{8}{27} = \frac{64}{729} \times \frac{27}{8} = \frac{8}{27} and (\frac{64}{729} \div \frac{16}{81}) \div \frac{2}{3} = (\frac{64}{729} \times \frac{81}{16}) \div \frac{2}{3} = \frac{4}{9} \div \frac{2}{3} = \frac{4}{9} \times \frac{3}{2} = \frac{2}{3} So, \frac{64}{729} \div (\frac{16}{81} \div \frac{2}{3}) \neq (\frac{64}{729} \div \frac{16}{81}) \div \frac{2}{3} Hence, the given statement is false .$

Regards

Suggest Corrections

Similar questions

- (\frac{- 7}{8}) = \frac{7}{8} .

$\frac{1}{2}$ divided by $\frac{5}{3}$ gives us a rational number. That means rational numbers are closed under division. Say true or false.

Division of 2 irrational numbers can be rational .(true or false)

Join BYJU'S Learning Program