Question

Given that an equation is 1/54x = 1/9, what would x be?

Answer 1

If two fractions are equal to each other, then their inverses must be equal as well:

$\dfrac{a}{b} = \dfrac{c}{d} \implies \dfrac{b}{a} = \dfrac{d}{c}$

So, we have

$\dfrac{1}{54x} = \dfrac{1}{9} \implies 54x = 9$

Now divide both sides by 54:

$x = \dfrac{9}{54} = \dfrac{1}{6}$

Note:

Given the slightly ambiguous way the question is written, you may also mean

$\dfrac{1}{54}\; x = \dfrac{1}{9}$

In this case, simply multiply both sides by 54:

$x = \dfrac{54}{9} = 6$