Is this a thing?

M

Mijaedgetu

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Sep 2, 2020
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Hi,
Just wondered if anyone could help me with this... A friend posted this on facebook 1265 - 6.5 = 1258.5. I was intrigued by what he meant by it so did some poking around.

I found that if you add the digits of each number until you make each one a single digit, you get an equation that still works

So 1+2+6+5 = 14 / 1 + 4 = 5
6 + 5 = 11 / 1 + 1 = 2
1 + 2 + 5 + 8 + 5 = 21 / 2 + 1 = 3

5 - 2 = 3

I've tried it with a few other numbers (nothing particularly scientific or exhaustive) but I can't create the same effect as yet... I just wondered if this was a thing in maths that I haven't heard of and if so, does it have a name? Has anyone found any other sets of numbers that do the same?

Many Thanks in advance
Mike
 
What you've discovered is called "casting out nines" (because if you ignore all 9's you get the same result). You're right that it has long been known in mathematics (primarily as a way of checking your work); you might enjoy looking it up! (You'll find it everywhere, now that you know the name.)

We don't normally apply it to non-whole numbers, but it does work.
 
I see your 1st three lines but I do not see their relationship with the 4th line, 5-2=3. I do see where the 5, 2 and 3 come from but how were the three lines before it connected to the 4th line?
 
5, 2, and 3 are the "digital roots" of the original numbers, 1265, 6.5, and 1258.5 . So if 1265 - 6.5 = 1258.5, then 5 - 2 = 3.
 
firemath said:
It might be a thing.....just not a correct thing......
Click to expand...
Why not? If it has a well-known name, and has been used for centuries, doesn't that make it a thing? And it's true of ANY sum, so I'd call it "correct". It's just silly to think it's special to these numbers.
 
Mijaedgetu said:
… I've tried it with a few other numbers … but I can't create the same effect …
Click to expand...
Hi Mijaedgetu. You've tried it with other subtractions, yes? I think there's an additional rule, when casting nines from a subtraction: If we get a negative result, we need to add back one 9.

EG 1: 1265 - 6 = 1259

After casting nines, we get: 5 - 6 = 8

That simplifies to -1 = 8, which is incorrect. By adding back one 9 on the left-hand side, we get 8=8.

EG 2: 63 - 3 = 60

0 - 3 = 6

Adding back one 9 on the left-hand side gives 6=6.

If those other attempts that didn't work out involved something other than negative numbers or subtractions, then please post an example.

?
 
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