Question

Properties of addition, multiplication, subtraction and division of integers​

Answer 1

Answer:

There are four (4) basic properties of real numbers: namely; commutative, associative, distributive and identity. These properties only apply to the operations of addition and multiplication. That means subtraction and division do not have these properties built in.

The sum of two or more real numbers is always the same regardless of the order in which they are added. In other words, real numbers can be added in any order because the sum remains the same. Eg. a+b = b+a

The product of two or more real numbers is not affected by the order in which they are being multiplied. In other words, real numbers can be multiplied in any order because the product remains the same. Eg. a×b = b×a

The sum of two or more real numbers is always the same regardless of how you group them. When you add real numbers, any change in their grouping does not affect the sum. Eg. a+(b+c) = (a+b)+c

The product of two or more real numbers is always the same regardless of how you group them. When you multiply real numbers, any change in their grouping does not affect the product. Eg. a×(b×c) = (a×b)×c

Any real number added to zero (0) is equal to the number itself. Zero is the additive identity since a + 0 = a or 0 + a = a

Any real number multiplied to one (1) is equal to the number itself. The number one is the multiplicative identity since a × 1 = a or 1 × a = a

Maybe you have wondered why the operations of subtraction and division are not included in the discussion. The best way to explain this is to show some examples of why these two operations fail at meeting the requirements of being commutative.

If we assume that Commutative Property works with subtraction and division, that means that changing the order doesn’t affect the final outcome or result.

Since we have different values when swapping numbers during subtraction, this implies that the commutative property doesn’t apply to subtraction.

Just like in subtraction, changing the order of the numbers in division gives different answers. Therefore, the commutative property doesn’t apply to division.

If we want Associative Property to work with subtraction and division, changing the way on how we group the numbers should not affect the result.

Changing the grouping of numbers in subtraction yield different answers. Thus, associativity is not a property of subtraction.

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