Question

Verify the following properties:
a) Commutative property of addition​

Answer 1

In mathematical computation, commutative property or commutative law explains that order of terms doesn’t matters while performing an operation. This property is applicable only for addition and multiplication process, such that a + b = b +a and a × b = b × a. But it is not applied to subtraction and division method, because, a – b ≠ b – a and a/b ≠ b/a.

Suppose two numbers A and B on addition gives a sum C, then if we interchange the position of A and B, the result will be C only, such as; A + B = B + A = C.  For example, 4 + 3 = 7 = 3 + 4; here, whether 3 come before or after the plus sign, the sum of 4 and 3 will be always 7 irrespective of their order.  

Although the official use of commutative property began at the end of the 18th century, it was known even in the ancient era. Apart from commutative, there are two more major properties of addition and multiplication of integers, they are associative and distributive. Let us discuss all the three properties or laws here.

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Answer 2

Commutative Property Of Addition

a + b = b + a

Example:

2 + 3 = 5 .... (1)

3 + 2 = 5 ...(2)

From (1) & (2)

2 + 3 = 3 + 2

Hence,

a + b = b + a

Hence Verified!