What are the properties of rational numbers?The word rational has evolved from the word ratio. In general, rational numbers are those numbers that can be expressed in the form of p/q, in which both p and q are integers and q≠0. The properties of rational numbers are:Closure PropertyCommutative PropertyAssociative PropertyDistributive PropertyIdentity PropertyInverse PropertyClosure propertyFor two rational numbers say x and y the RESULTS of addition, subtraction and multiplication operations GIVE a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example:(7/6)+(2/5) = 47/30(5/6) – (1/3) = 1/2(2/5). (3/7) = 6/35Do you know why division is not under closure property?The division is not under closure property because division by zero is not DEFINED. We can also say that except ‘0’ all numbers are closed under division.Commutative PropertyFor rational numbers, addition and multiplication are commutative.Commutative law of addition: a+b = b+aCommutative law of multiplication: a×b = b×aFor example:Commutative law exampleSubtraction is not commutative property i.e. a-b ≠ b-a. This can be understood clearly with the following example: Commutative law - subtraction LHSWhereas Commutative law - subtraction RHSThe division is also not commutative i.e. a/b ≠ b/a, since,Commutative law - Division LHS Whereas, Commutative law - Division RHSAssociative PropertyRational numbers follow the associative property for addition and multiplication.Suppose x, y and z are rational, then for addition: x+(y+z)=(x+y)+zFor multiplication: x(yz)=(xy)z.Example: 1/2 + (1/4 + 2/3) = (1/2 + 1/4) + 2/3⇒ 17/12 = 17/12And in case of multiplication;1/2 x (1/4 x 2/3) = (1/2 x 1/4) x 2/3⇒ 2/24 = 2/24⇒1/12 = 1/12Distributive PropertyThe distributive property STATES, if a, b and c are three rational numbers, then;a x (b+c) = (a x b) + (a x c)Example: 1/2 x (1/2 + 1/4) = (1/2 x 1/2) + (1/2 x 1/4)LHS = 1/2 x (1/2 + 1/4) = 3/8RHS = (1/2 x 1/2) + (1/2 x 1/4) = 3/8Hence, provedIdentity and Inverse Properties of Rational NumbersIdentity Property: 0 is an additive identity and 1 is a multiplicative identity for rational numbers.Examples:1/2 + 0 = 1/2 [Additive Identity]1/2 x 1 = 1/2 [Multiplicative Identity]Inverse Property: For a rational number x/y, the additive inverse is -x/y and y/x is the multiplicative inverse.Examples:The additive inverse of 1/3 is -1/3. Hence, 1/3 + (-1/3) = 0The multiplicative inverse of 1/3 is 3. Hence, 1/3 x 3 = 1Step-by-step explanation:hope it helps you PLEASE follow me and Mark me as brain list