Among the following, an associative under addition property is

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2 (\frac{1}{3} \times \frac{2}{3}) = (2 \times \frac{1}{3}) + (2 \times \frac{2}{3})

2 (\frac{1}{3} + \frac{2}{3}) = (2 \times \frac{1}{3}) + (2 \times \frac{2}{3})

2 + (\frac{1}{3} + \frac{2}{3}) = (2 + \frac{1}{3}) + \frac{2}{3}

None of these

answer is A.

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Detailed Solution

If a, b and c any three rational numbers we can added in any order give the same sum then it is called associative under addition.

Example : $2 + (\frac{1}{3} + \frac{2}{3}) = (2 + \frac{1}{3}) + \frac{2}{3}$

$\Rightarrow 2 + 1 = \frac{7}{3} + \frac{2}{3}$

$\Rightarrow 3 = 3$

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