Question

Verify the closure property of rational numbers addition, subtraction,division and multiplication

Answer 1

Answer:If a and b are two rational numbers and their difference c = a - b is also a rational number, then the two rational numbers a and b is said to satisfy Closure-Property of Subtraction. a - b = = = which is also a rational number. This means that the rational numbers are closed under subtraction.

Answer 2

Explain Closure property of rational numbers under addition subtraction multiplication and division

If a and b are two rational numbers and their difference c = a - b is also a rational number, then the two rational numbers a and b is said to satisfy Closure-Property of Subtraction. a - b = = = which is also a rational number. This means that the rational numbers are closed under subtraction.

• The closure property states that for any two rational numbers a and b, a × b is also a rational number. The result is a rational number. So rational numbers are closed under multiplication.

Commutative property:  

Commutative property states that there is no change in result though the numbers in an expression are interchanged. Commutative property holds for addition and multiplication but not for subtraction and division.

In summary, the Closure Property simply states that if we add or multiply any two real numbers together, we will get only one unique answer and that answer will also be a real number. The Commutative Property states that for addition or multiplication of real numbers, the order of the numbers does not matter.