Question

If a,b,c are integers, then
(A\b)/c not equal to a/(b/c) unless c=?

Answer 1

If $a,\:b,\:c$ are intergers, then $\dfrac{\dfrac{a}{b}}{c}\neq \dfrac{a}{\dfrac{b}{c}}$ unless $c=1.$

Explanation:

• The two fractions are:

• $\dfrac{\dfrac{a}{b}}{c}=\dfrac{a}{bc}$

• $\dfrac{a}{\dfrac{b}{c}}=\dfrac{ac}{b}$

• Clearly, these fractions are not the same in general.

• Let them be equal. Then,

• $\quad \dfrac{a}{bc}=\dfrac{ac}{b}$

• $\Rightarrow \dfrac{1}{c}=c$

• $\Rightarrow c^{2}=1$

• $\Rightarrow \bold{c=1}$

Thus we can conclude that $c=1$ is the only condition for the given fractions to be equal.