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16% of 25? Easy!

The percentage calculation that 'blows minds'

What is 16% of 25?

Before you reach for a calculator, can you work it out mentally?

10% of 25 is 2.5....then 6%...urgh.  It's not simple.  Not in this form, anyway.

But suppose I'd asked: "What is 25% of 16"?   Many people would get this almost instantly:  "that's one quarter of 16, which is 4.  Easy!"

What's often missed is that the two calculations are identical.  25% of 16 is the same as 16% of 25.  And it is always true that A% of B is the same as B% of A.

How can this be?

We need to go back to what 'percent of' means.  25% of...   means (25/100) multiplied by....

The first calculation written out longhand is therefore 25/100 x 16, while the second is 16/100 x 25.  Changing the order in which you multiply two numbers together doesn't change the answer.  16 x 25 = 25 x 16, just as 3 x 5 is the same as 5 x 3  This is still true if you divide by 100.  The A% of B result follows from this.

The A% of B calculation tip was one of four that I tweeted last week, to help promote National Numeracy day, but the response to it was astonishing.  Reactions ranged from "Mind blown!" to "This is the best thing I've learned all year."

A similar calculation had featured on Radio 4's More or Less the previous week, and that in turn had been in response to a viral tweet stating that '4% of 75 = 75% of 4'.

Arithmetical shortcuts like this have always been popular, but were they ever so 'mind blowing'? I wonder if the ubiquity of calculators and spreadsheets has blunted society's arithmetical capabilities so far that we can now be amazed by something that would once have been familiar to anyone with a good O Level or School Certificate in maths.  My mum, for example.