Question

closed under rational number addition yes or no

Answer 1

yes closed multiplication addition but not in subtraction under rational number .

Answer 2

hai friend..........
"yes"

●under division. You have seen that wholenumbers are closed under addition and multiplication but not under subtraction and division. However, integers are closed under addition, subtraction and multiplication but not under division.


●a/b + c/d = (ad+bc)/bd, so closed under addition.
a/b - c/d = (ad-bc)/bd, so closed under subtraction.
a/b * c/d = (ac)/(bd), so closed under multiplication.

a/b / c/d = (ad)/(bc), so closed under division.

Wait!! but what if bc = 0?

b cannot be zero, because a/b is rational. But, c can be 0, so bc might be zero, and if so, then (ad)/(bc) is not rational, so

NOT closed under division, unless you add "except for division by zero".

Wait!! but what if bd = 0 in the first three examples for addition, subtraction, and multiplication? That is impossible, because you are given that a/b and c/d are rational so neither b nor d can be zero.

it may be helps you frnd......