Any conjecture you want; a conjecture is merely an opinion or conclusion based on given information. Whether the conjecture is true or not is left to be proved (if provable at all).
One opinion (conjecture) could be that the sum is "blue". It's a totally nonsense conjecture, but its a conjecture none the less.
A sensible conjecture might be that the sum is odd.
This can be tested and found to be true or false by summing the first 46 odd numbers (a mechanical method that is fairly easy in this case), or by the mathematical manipulation of axioms via algebra (a mathematical proof).
Often, but not always. It depends upon what you do with them. If the numbers are not equal, and you subtract the larger from the smaller, the answer will be negative.
2 negatives make a positive
The numbers are the same as positive numbers, just the signs change. Write out the factor pairs as if the number were positive, but make one of the numbers positive and one negative. Now write the same pairs over again and reverse the signs. Negative numbers have twice as many factor pairs as positive numbers do.
The rules of integers state:~ two negatives make a positive number~one negative and one positive makes a negative number~ two positives are simply positive numbers
Any rational positive number is still rational when you make the same number negative.
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
You can make whatever conjecture that you want: it does not have to be true or even logical. You could conjecture that the relationship is like the one between the Sun and the Earth!
1+3+5+7+9+11 all the way to 100 = ?
You can make a conjecture by conducting research or experiments that come out to be unproven. It can appear to be correct but it is actually unproven.
No, a positive and a positive make a positive
Often, but not always. It depends upon what you do with them. If the numbers are not equal, and you subtract the larger from the smaller, the answer will be negative.
EVIDENCE
Pretend both the numbers are positive, find the quotient as normal and then make it negative.
2 negatives make a positive
A negative. If you have a string of positive and negative numbers multiplied together, all you need to find the sign of the answer is to find the parity of the negative numbers. If there are an odd number of negatives then the answer is negative and if there are an even number of negatives then the answer is positive. Remember, positive numbers make no difference to the sign of the answer.
Yes.