Correct Answer - Option 4 : closure property
Multiplication represents the repeated addition of a number with itself. For example: 3 + 3 is represented as 3 × 2.
Addition: When two collections of similar objects are put together, the total of them is called addition.
Properties of addition in natural and whole numbers:
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Closure property: The sum of two natural/whole numbers is also a natural/ whole number.
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Commutative Property: p + q = q + p where p and q are any two natural/ whole numbers.
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Associative property: (p + q) + r = p + (q + r) = p + q + r . This property provides the process for adding 3 (or more) natural/whole numbers.
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Additive Identity in Whole Numbers: In the set of whole numbers, 4 + 0 = 0 + 4 = 4. Similarly, p + 0 = 0 + p = p (where p is any whole number). Hence, 0 is called the additive identity of the whole numbers.
Properties of Multiplication:
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Commutative Property: a × b = b × a. Example, 9 × 4 = 4 × 9 = 36
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Closure property: If p and q are natural or whole numbers then p × q is also a natural or whole number. Like in the above example, 4 and 9 are natural numbers, so is their multiple (36).
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Associative property: (p × q) × r = p × (q × r) (where p, q, and r are any three natural/whole numbers)
- Identity of multiplication: The number ‘1’ has the following special property in respect of multiplication. p × 1= 1 × p = p (where p is a natural number)
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Distributive property of multiplication over addition: p × (q + r) = (p × q) + (p × r).
Note: There is no distributive property for addition. One should not be confused (p + q) + r = p + (q + r) as distributive, the given property is associative property for addition.
