Let us first do additive modular arithmetic. This system has only the following elements. $\{0,1,2,3,4\}$. But note that $4+1=\pmod 5$ in this system. So $1$ works like $-4$ of familiar all integers (infinite) number system.

Also in this system non-zero elements $\{1,2,3,4\}$ is closed for multiplication modulo 5. And we see $2\times3$ is $1\pmod 5$ So $3$ behaves like $\frac12$ of our familiar rational number system. So we can interpret $3$ as $1/2$ assuming multiplication is interpreted as mod 5.

If the time is 9pm now 23 hours from now it would be 7pm. To find this answer very few people would add 23 to 9. Most people subtract 1 from 9. That is because in mod 24 number system $23$ is $-1$.

Let us first do additive modular arithmetic. This system has only the following elements. $\{0,1,2,3,4\}$. But note that $4+1=0\pmod 5$ in this system. So $1$ works like $-4$ of familiar all integers (infinite) number system.

Also in this system non-zero elements $\{1,2,3,4\}$ is closed for multiplication modulo 5. And we see $2\times3$ is $1\pmod 5$ So $3$ behaves like $\frac12$ of our familiar rational number system. So we can interpret $3$ as $1/2$ assuming multiplication is interpreted as mod 5.

If the time is 9pm now 23 hours from now it would be 8pm. To find this answer very few people would add 23 to 9. Most people subtract 1 from 9. That is because in mod 24 number system $23$ is $-1$.