Question

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

Answer 1

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`.

Answer 2

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:
`color(white)("XXX")54/8=x/9`

`color(white)("XXX")rArr 8x=54xx9=486`

`color(white)("XXX")rArr x=486/8=243/4`

and `54/8 = (243/4)/9 = 60.75/9`