If a, b and c are rational numbers, then which of the following shows associativity for addition of rational numbers?

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$a + b + c = b + a$

$a + b + c = 0$

$a \times (b + c) = (a \times b) + (a \times c)$

$a + (b + c) = (a + b) + c$

answer is D.

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Detailed Solution

The associative property of addition for rational numbers states that the grouping of the terms being added does not affect the sum. In other words, if we add a set of rational numbers, we can regroup the terms in any way we want and still get the same sum.

For any three rational numbers, a,b, and c the associative property for addition is expressed as:

$a + (b + c) = (a + b) + c$ .

For example, let's consider the following expression:

(2/3 + 1/4) + 5/6

Using the associative property, we get (2/3 + 1/4) + 5/6 = 4/3.

Similarly, 2/3 + (1/4 + 5/6) = 4/3.

Hence, it is proved that rational numbers obey the associative property for addition.

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