Question

taking, a=4/7, b= - 5/2 and c=4/3, show that a ÷ (b÷c) not equal to (a÷b)÷c, that is, division is not associative for rational numbers. ​

Answer 1

$\textbf{Given:}$

$a=\dfrac{4}{7},\;b=\dfrac{-5}{2},\;c=\dfrac{4}{3}$

$\textbf{To show:}$

$a{\div}(b{\div}c){\neq}(a{\div}b){\div}c$

$\textbf{Solution:}$

$\bf\,a{\div}(b{\div}c)$

$=\dfrac{4}{7}{\div}(\dfrac{-5}{2}{\div}\dfrac{4}{3})$

$=\dfrac{4}{7}{\div}(\dfrac{-5}{2}{\times}\dfrac{3}{4})$

$=\dfrac{4}{7}{\div}\dfrac{(-15)}{8}$

$=\dfrac{4}{7}{\times}\dfrac{8}{-15}$

$=\bf\dfrac{32}{-105}\;$.....(1)

$\bf(a{\div}b){\div}c$

$=(\dfrac{4}{7}{\div}\dfrac{(-5)}{2}){\div}\dfrac{4}{3}$

$=(\dfrac{4}{7}{\times}\dfrac{2}{(-5)}){\div}\dfrac{4}{3}$

$=\dfrac{8}{-35}{\div}\dfrac{4}{3}$

$=\dfrac{8}{-35}{\times}\dfrac{3}{4}$

$=\dfrac{2}{-35}{\times}\dfrac{3}{1}$

$=\bf\dfrac{6}{-35}\;$.......(2)

$\text{From (1) and (2), we get}$

$\bf\,a{\div}(b{\div}c){\neq}(a{\div}b){\div}c$

$\therefore\textbf{Division is not associative}$

Answer 2

Answer:

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