Nice introduction on modulo arithmetic.
My father taught me this when I was young to check my calculations.

Here is an example of how I use it.
Let's say you multiply 53 by 47: Answer is 2491.
Here is how to check the answer:
5 +3 = 8
4 + 7 = 11 . Subtract 9 until you get a number below nine: 11-9=2
Now multiply the 2 numbers: 8 X 2 =16. Subtract 9 until you get a number below nine:
16-9 = 7

The answer now need to add up to 7 as well.

Add the digits of the answer:
2+4+9+1 = 16.
Subtract 9 until you get a number below nine:
16 - 9 = 7.

This is modulo arithmetic:
53 modulo 9 = 8
47 modulo 9 = 2
The multiplication of 8 and 2 modulo 9 is 7:
8X2 = 16. 16 modulo 9 = 7.

Now we know that the answer modulo 9 also needs to be 7.

Works with division too.

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Nice introduction on modulo arithmetic.

My father taught me this when I was young to check my calculations.

Here is an example of how I use it.

Let's say you multiply 53 by 47: Answer is 2491.

Here is how to check the answer:

5 +3 = 8

4 + 7 = 11 . Subtract 9 until you get a number below nine: 11-9=2

Now multiply the 2 numbers: 8 X 2 =16. Subtract 9 until you get a number below nine:

16-9 = 7

The answer now need to add up to 7 as well.

Add the digits of the answer:

2+4+9+1 = 16.

Subtract 9 until you get a number below nine:

16 - 9 = 7.

This is modulo arithmetic:

53 modulo 9 = 8

47 modulo 9 = 2

The multiplication of 8 and 2 modulo 9 is 7:

8X2 = 16. 16 modulo 9 = 7.

Now we know that the answer modulo 9 also needs to be 7.

Works with division too.