The set of rational numbers form an Abelian group under addition. That is, if x, y and z are any rational numbers, then
You need the rules of multiplication as well as of addition. But multiplication of integers can be viewed as repeated addition. Thus, if p/q and r/s are two rational numbers then their sum is(p*s + q*r)/(q*s)
Yes.
Yes.
Yes, the set of rational numbers is closed under addition.
For addition, 0 and for multiplication, 1.
You need the rules of multiplication as well as of addition. But multiplication of integers can be viewed as repeated addition. Thus, if p/q and r/s are two rational numbers then their sum is(p*s + q*r)/(q*s)
A rational number is not. But the set of ALL rational numbers is.
The rules are the same.
Because both of those numbers are rational. The sum of any two rational numbers is rational.
No. The set of rational numbers is closed under addition (and multiplication).
Yes.
Yes, they can.
Yes.
Yes.
Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.
Yes, the set of rational numbers is closed under addition.
For addition, 0 and for multiplication, 1.