This is actually so useful, thanks! I feel I used head maths less and less (I'm an engineer and rarely need to do a calculation without a calculator) but this will be an excellent sanity check, or a quick calc when out and about with prices or something.

Many thanks for pointing out something that ought to be obvious haha

I don't see how that explanation makes sense. It's not showing the same thing.

The example in the title is saying .50 times 7 is equal to .07 times 50 which is not just changing the order like in your explanation.

Proof:

x/100 * y = xy/100 = y/100 * x

This isn't the only property that makes mental math easy. What is 3.5% of 62? Inverting the percentages doesn't really help but if we realized 3.5% = 1%+1%+1%+0.5% we have some easy math. This gives us 0.62+0.62+0.62+0.62/2=2.17

Also remember there isn't a teacher sitting over your shoulder to check your work, most of the time you do mental math, getting close is good enough. 62 is close to 60 and 3.5% is close to 4, and 60 x 4% is easy math to ger an answer that will be a little less than 2.4.