Closure & Commutative Prop. of Rational Numbers

The video tutorial explains rational numbers, which can be expressed as fractions or decimals. It covers the closure and commutative properties of whole numbers, integers, and rational numbers. The closure property is discussed in terms of addition, subtraction, multiplication, and division, highlighting that rational numbers are closed under addition, subtraction, and multiplication but not division. The commutative property is also examined, showing that addition and multiplication are commutative for rational numbers, while subtraction and division are not.

What is a rational number?

• A number that can be expressed as a fraction where the denominator is zero.

• A number that can be expressed as a fraction where both numerator and denominator are integers and the denominator is not zero.

• A number that cannot be expressed as a fraction.

• A number that is always positive.

Which operation is not closed for whole numbers?

• Addition

• Subtraction

• Multiplication

• None of the above

Are rational numbers closed under division?

• Yes, always

• No, because division by zero is not defined

• No, because division is not defined for rational numbers

• Yes, except when the numerator is zero

Which property is not commutative for whole numbers?

• Multiplication

• Subtraction

• Addition

• All of the above

For integers, which operation is commutative?

• Division

• None of the above

• Addition

• Subtraction

Is addition commutative for rational numbers?

• No, the order changes the sum

• Yes, the order does not affect the sum

• Only when both numbers are negative

• Only when both numbers are positive

What happens when you subtract two rational numbers in different orders?

• The result is always positive

• The result is always zero

• The result is the same

• The result is different

Is multiplication commutative for rational numbers?

• Yes, the product remains the same

• Only when both numbers are negative

• No, the product changes

• Only when both numbers are positive

What is the result of dividing two rational numbers in different orders?

• The result is the same

• The result is different

• The result is always one

• The result is always zero

Which property is not commutative for rational numbers?

• Multiplication

• Addition

• Subtraction

• None of the above