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In mathematics, the clock system is usually referred to as modular arithmetic. This comes from the fact that mathematicians write down clock numbers as x mod m. For example 15 mod 4. The x (15) is the number and m (4) the system. In our case that would mean that we want to express the number 15 in a finite system with four characters (that would be the same as Smart Joe's watch we looked at above) When the number you want to express is positive you can calculate x mod m by taking m from x until x is smaller than m. If you have 15 mod 4, you can take 4 from 15 three times to equal 3; 15-(3×4)=3. Let's look at another example: 3 mod 4. Since 3 is already smaller than 4, you can't subtract 4 from it. In this case, the result is 3.
In modular systems you can solve equations like we did on the clock before.
For example 5+4=2 in modulo 7. Can you fill in the the addition table above for modulo 7?
Of course we can't only solve additions in modular systems, but also subtractions, multiplications, etc. Can you fill in the multiplication table for modulo 7 above?
