It never occurred to me that 7% of 50 is equal to 50% of 7 perhaps because they are equally easy to calculate? Multiply 7 by 5 and fix the decimal point.
What about 17% of 50? 17*5 isn’t so simple anymore, whereas 50% of 17 is 8.5.
To be fair, with most shortcuts, it’s possible to construct difficult cases (17% of 23 is difficult in either order) but where it applies (when one of the pairs is a common percentage), exploiting commutativity can be quite useful. Plus the mental overhead of remembering the rule is extremely minimal.
How can you discover that 50% of 17 is 8.5 if you can’t multiply 17*5? (If the answer is “by halving”, then my response is that halving and then multiplying by 10 is often the easiest way to multiply by 5!)
I’m not sure, but to me at least halving 17 to get 8.5 is an almost completely intuitive process, whereas multiplying 17 by 5 seems to require an extra cognitive step to reduce it to shifting the decimal point and then halving (or vice versa). Never mind the extra step when presented by the problem of taking 17% of 50.
