Performance on fractions and long division predicts math "success" because those tasks embody math education's emphasis on procedural skills over conceptual understanding.
Tokenadult's comprehensive comment includes the 12/13 + 7/8 gem that sums up the problem. Kids see 12/13 + 7/8 and, if they're "good" at math, start turning the procedural crank they've been taught. (If they're "bad" at math, they freeze with a defeated feeling that there are too many procedural steps to remember.)
Get kids to see 12/13 + 7/8 primarily as "almost one plus almost one" (as thaumasiotes describes), and only secondarily as the beginning of a tedious procedure, to make substantive progress in math education.
A few years ago there was a long article about math education in USA by Russian math professor that immigrated. He blamed lack of "word problems" solved by intuition and guessing and substituting values at first, only then using algebra.
I can't find it now, but it showed exactly the same problems - math was just pattern mathing problem for most students - no real understanding.
Tokenadult's comprehensive comment includes the 12/13 + 7/8 gem that sums up the problem. Kids see 12/13 + 7/8 and, if they're "good" at math, start turning the procedural crank they've been taught. (If they're "bad" at math, they freeze with a defeated feeling that there are too many procedural steps to remember.)
Get kids to see 12/13 + 7/8 primarily as "almost one plus almost one" (as thaumasiotes describes), and only secondarily as the beginning of a tedious procedure, to make substantive progress in math education.