This tweet has had many views and shares and has been much discussed
“x% of y = y% of x. So, for example, if you needed to work out 4% of 75 in your head, just flip it….”
Jen Rogers of Oxford University and the Royal Statistical Society was asked to comment on it on ‘More or Less’ (https://www.bbc.co.uk/sounds/play/m0004md0 at 17:25). It had come as a big shock to her and her fellow mathematicians.
This was certainly well known in my classrooms. I remembered being startled when a student first came up with it and, at first, I came up with the same explanation Jan gives.
But over time I found a much simpler and more elegant proof which is simply that ‘of’ is the same as multiplied by. So if you accept the commutativity of multiplication (so elegantly demonstrated through array – arranging objects in rectangles) then this is just obvious…….
If it doesn’t sound obvious then please be reassured that it did take me many long online discussions over several years to completely convince myself that ‘of is multiply’ throughout primary maths and well beyond and that array explains all multiplication and division at that level.
This understanding of multiplication and division was to form the basis of my PhD in maths education. But when it became clear that no research into maths education would be taken into consideration in the development of policy it seemed wiser to devote my time to political campaigning rather than on pushing back the frontiers of knowledge. Fortunately the former has not come at the expense of the latter, but sadly it has denied me my doctorate.