Prove that multiplication is commutative for rational numbers.

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Solution

To show that rational numbers are commutative under multiplication we verify the reult by using examples.
( $\frac{- 7}{3}$ ) × ( $\frac{6}{5}$ ) = $\frac{- 42}{15}$ .

( $\frac{6}{5}$ ) × ( $\frac{- 7}{3}$ ) = $\frac{- 42}{15}$ .

We find that multiplication is commutative for these two rational rational numbers. Similarly, it can be shown for other rational numbers. Therefore, in general, a × b = b × a for any two rational numbers a and b.

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The numerical expression $\frac{3}{8} + \frac{(- 5)}{7} = \frac{- 19}{56}$ shows that:
(a) rational numbers are closed under addition.
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(c) rational numbers are closed under multiplication.
(d) addition of rational numbers is not commutative.

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[4 MARKS]

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