Question

In you opinion, which one is the correct way?
(1) $\frac{\frac{a}{b}}{x} = \frac{a}{bx}$
(2) $\frac{\frac{a}{b}}{x} = \frac{ax}{b}$
Also give the reason. ​

Answer 1

Option - 1 is correct....

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Answer 2

Let us Consider a fraction $\sf{a/b}$ and divide it by a number, say $\sf{x}$, Then it can be written as : $\sf{\frac{a\!/_b}{x}}$. Now this can also be noticed at : $\sf{\frac{a\!/_b}{x\!/_1}}$  (∵ n/1 = n)

Simplify $\sf{\frac{a\!/_b}{x\!/_1}}$

$\to\sf{\displaystyle\frac{a}{b}\div \frac{x}{1}}$

$\to\sf{\displaystyle\frac{a}{b}\times \frac{1}{x}}$

$\to\sf{\displaystyle\frac{a}{bx}}$

∴ $\to\sf{\displaystyle\frac{a\!/_b}{x}=\:\frac{a}{bx}}$ , So Option 1) is correct