1.

Verify associativity of rational numbers for 1/2,2/3,5/6​

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Answer:

According to associative PROPERTY of RATIONAL numbers,

a + (B + c) = (a + b) + c,

where a, b and c are rational numbers.

\dfrac{1}{2} + ( \ \dfrac{2}{3} + \dfrac{5}{6} \ )

= \dfrac{1}{2} + ( \ \dfrac{4}{6} + \dfrac{5}{6} \ )

= \dfrac{1}{2} + \dfrac{9}{6}

= \dfrac{3}{6} + \dfrac{9}{6}

= \dfrac{12}{6}

= 2

( \ \dfrac{1}{2} + \dfrac{2}{3} \ ) + \dfrac{5}{6}

= ( \ \dfrac{3}{6} + \dfrac{4}{6} \ ) + \dfrac{5}{6}

= \dfrac{7}{6} + \dfrac{5}{6}

= \dfrac{12}{6}

=2

Since we get the same result, ASSOCIATIVITY of rational numbers for 1/2, 2/3, 5/6 is verified.


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