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# Are rational numbers closed under division?

Yes, rational numbers are closed under division. The definition of a rational number is: a/b where "a" and "b" are integers and b is not equal to zero. Because of this defini…tion, you will never encounter a situation such as (5/6) / (4/0) because 4/0 is not a rational number. 0/0 is also not a rational number.

# Are rational numbers closed under multiplication?

Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which… is good to keep in mind.

# What numbers are closed under multiplication?

Yes: Multiplying any two counting numbers will produce a counting number.

# Are rational numbers are closed under addition subtraction division or multiplication?

The set of rational numbers is closed under all 4 basic operations.

# Is the set of odd numbers is closed under multiplication but is not under addition?

Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b Ďµ S, we also have a + b Ďµ S. Let 3, 5 Ďµ the set of odd num…bers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set of the odd numbers is not closed under addition.

# Why are odd integers closed under multiplication but not under addition?

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

# Is the set of rational numbers closed under division and Why?

No. Zero is a rational number, but division by zero is not defined.

# Are real numbers closed under addition and subtraction?

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

# Are odd numbered sets closed under addition and multiplication?

No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.

Answered

# Is a rational number closed for addition and for multiplication?

A rational number is not. But the set of ALL rational numbers is.

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# Is this set of negative numbers closed under multiplication or addition?

Yes. The empty set is closed under the two operations.

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# Are the rational numbers closed under multiplication?

Yes.

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In Algebra

# Are rational numbers closed under division mutiplication adddition or subtraction?

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excludin…g the zero are closed under division.

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In Science

# What does it mean for a polynomial to be closed under addition subtraction and multiplication?

If you perform any of those operations on a polynomial, the result will be a polynomial.