# Does 54/8 have an equivalent fraction with a denominator or 9? If so, what is it?

May 3, 2016

No. This fraction cannot be changed to an equivalent one with denominator of $9$.

#### Explanation:

The original denominator is $8 = {2}^{3}$, it is impossible to change the denominator to $9 = {3}^{2}$. The only oerations allowed are multiplying or dividing by the same number, but you would have to reduce the fraction by $8$ (there are no $2 ' s$ in prime factorization of $9$), but the numerator is not a multiple of $8$.

May 4, 2016

It does not have an equivalent version (with a denominator of 9) and an integer numerator.

#### Explanation:

Occasionally you may find a teacher looking for (or accepting) fractions with numerators (or denominators) which are themselves fractions.

In this case, we would have the required ratios:
$\textcolor{w h i t e}{\text{XXX}} \frac{54}{8} = \frac{x}{9}$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 8 x = 54 \times 9 = 486$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow x = \frac{486}{8} = \frac{243}{4}$

and $\frac{54}{8} = \frac{\frac{243}{4}}{9} = \frac{60.75}{9}$