Closed Under Addition, Subtraction, Multiplication and Division

Front

What does it mean for a set of numbers to be closed under an operation?

Back

A set of numbers is closed under an operation if performing that operation on members of the set always produces a member of the same set.

Front

Are rational numbers closed under addition?

Back

Yes, rational numbers are closed under addition.

Front

What is the closure property for integers?

Back

The closure property for integers states that when you add, subtract, or multiply integers, the result is always an integer.

Front

True or False: Integers are closed under subtraction.

Back

True.

Front

True or False: Rational numbers are closed under multiplication.

Back

True.

Front

What is an example of a set that is not closed under division?

Back

The set of integers is not closed under division, as dividing two integers can result in a non-integer.

Front

What is the associative property?

Back

The associative property states that the way in which numbers are grouped in addition or multiplication does not change the result.

Front

True or False: The sum of two rational numbers is always a rational number.

Back

True.

Front

What is an example of a closure property in multiplication?

Back

The product of two counting numbers is always a counting number.

Front

What does it mean for a number set to be closed under multiplication?

Back

It means that multiplying any two numbers from the set will yield a number that is also in the set.