Normal teachings for thinking about fractions like 4/8 or 8/4 goes something like:
Use the denominator to tell you the amount of equally sized parts in a whole, and use the numerator to tell you the amount of those equally sized parts selected. Cool.
Often this approach to thinking about fractions is accompanied by visualizations of pizza or collections of rectangles. No simplification is required for a result.
But, when you have a complex fraction such as 8/(1/4), the teaching above becomes very difficult to apply and incorrect results are common (at least for me).
Every teaching I find on this says to simplify the problem first and then solve using the normal teaching above. But, one might ask whether simplification is required before applying the normal teaching, and if so…why? Can we apply the normal teaching for thinking about complex fractions, without simplifying? Perhaps the normal teaching only works when the numerator is greater than or equal to 1?