Thank you for the questions, Fred.

To your first question, there appear to be no rules prohibiting the combination of linear and spatial representation in the transcription of various parts of an expression in UEB. So, your sample transcription (which uses a spatial layout only for the fraction that includes cancellation) is not wrong. If you do use spatial arrangement for the part of the expression that includes cancellation, I would recommend transcribing the left side of the equation whose right side is spatial on the braille line with the equals sign that precedes that spatial material.

But really, I would recommend transcribing this simple cancellation in linear form, as is done in the last example in GTM 4.1.6.

I see what you're saying about numerators and denominators of a spatially arranged fraction starting in the same column as the second cell of the two-cell horizontal line mode indicator. First, I would note that GTM appears to be consistent with this treatment of spatial fractions; the fractions on page 23 of GTM are arranged in the same way. Second, I can only say that GTM does not tell us where to ... or where *not* to put numbers in relation to a horizontal line in a mathematical spatial arrangement. So, we are allowed to find our own consistency, with feedback from the braille user and/or teacher where possible.

Again, thank you for your astute questions.

–Kyle