Exemplar exercise problems III — task. Mathematics CBSE, Class 8.

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1. \(-\frac{3}{8} + \frac{(1)}{7} = \frac{(1)}{7} + \left(\frac{-3}{8}\right)\) is an example to show that

addition of rational numbers is associative.
rational numbers are not closed under addition.
rational numbers are distributive under addition.
addition of rational numbers is commutative.

2. Which of the following expressions shows that rational numbers are associative under multiplicaion?

\(\frac{2}{3} \times \left(\frac{-6}{7} \times \frac{3}{5}\right) = \frac{2}{3} \times \left(\frac{3}{5} \times \frac{-6}{7}\right) \)
\(\frac{2}{3} \times \left(\frac{-6}{7} \times \frac{3}{5}\right) = \left(\frac{2}{3} \times \frac{-6}{7}\right) \times \frac{3}{5}\)
\(\left(\frac{2}{3} \times \frac{-6}{7}\right) \times \frac{3}{5} = \left(\frac{-6}{7} \times \frac{2}{3}\right) \times \frac{3}{5}\)
\(\frac{2}{3} \times \left(\frac{-6}{7} \times \frac{3}{5}\right) = \left(\frac{3}{5} \times \frac{2}{3}\right) \times \frac{-6}{7}\)

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