You can
put this solution on YOUR website!You are asked to find a remainder.
A number n/5 leaves a remainder of 2.
What does (n+4)/5 leave as a remainder.
You took the approach of trying a few examples and then using that to deduce the answer. Not a bad way to go. But you made an early error.
You picked n = 10. If n=10, then n/5 does not leave a remainder of 2. 10 is evenly divisible by 5.
If you picked 12, then it would work. 12/5 leaves a remainder of 2.
What does (12+4)/5 leave as a remainder?
16/5 leaves a remainder of 1.
If you start with other numbers that when divided by 5 leave a remainder of 2, you'll quickly see that any integers that have either 2 or 7 in the ones place, leave a remainder of 2.
So any number then ends in either 6 (2+4) or 1 (7+4=11, which ends in 1) leaves a remainder of 1.
As you get farther into mathematics you'll be introduced to modulo arithmetic. When that time comes, remember this problem :)
