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Class – 8 : Rational Numbers
Mention the commutativity, associative and distributive properties of rational numbers. Also, check a × b = b × a and a + b = b + a for a = ½ and b = ¾.
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The properties of rational numbers are as follows:
Commutativity: The commutative property states that the order of the numbers does not affect the result of addition or multiplication. For addition: a + b = b + a For multiplication: a × b = b × a
Associativity: The associative property states that the grouping of numbers does not affect the result of addition or multiplication. For addition: (a + b) + c = a + (b + c) For multiplication: (a × b) × c = a × (b × c)
Distributive: The distributive property states that multiplication can be distributed over addition. For multiplication and addition: a × (b + c) = a × b + a × c.<div>Now, let’s check the commutativity property for a = ½ and b = ¾:
a × b = ½ × ¾ = 3/8
b × a = ¾ × ½ = 3/8
As we can see, a × b and b × a both yield the same result of 3/8. Therefore, the commutativity property holds for these values.
Similarly, let’s check the commutativity property for addition:
a + b = ½ + ¾ = 5/4
b + a = ¾ + ½ = 5/4
Once again, a + b and b + a both result in 5/4, confirming that the commutativity property holds for these values.
Thus, both the commutativity property and the commutative property hold for a = ½ and b = ¾.
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