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Which of the following is/are the property (ies) of multiplication in integers? I. Multiplication is associative II. Multiplication is closed III. Multiplication distributes over addition

Which of the following is/are the property (ies) of multiplication in integers? I. Multiplication is associative II. Multiplication is closed III. Multiplication distributes over addition Correct Answer I, II and III

Multiplication represents repeated addition of a number with itself. For example: 3 + 3 is represented as 3 × 2.

Properties of Multiplication:

  • Commutative Property: a × b = b × a. Example, 9 × 4 = 4 × 9 = 36
  • 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).
  • 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)
  • Distributive property of multiplication over addition: p × (q + r) = (p × q) + (p × r).

Note that 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.

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:

  • Closure property: Sum of two natural/whole numbers is also a natural/ whole number.
  • Commutative Property: p + q = q + p where p and q are any two natural/ whole numbers.
  • Associative property: (p + q) + r = p + (q + r) = p + q + r . This property provides the process for adding 3 (or more) natural/whole numbers.
  • 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.

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