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Express each ...

Question

Express each of the following rational numbers as the sum of an integer and a rational number:
(i) $\frac{12}{5}$
(ii) $\frac{- 11}{7}$
(iii) $\frac{- 25}{9}$
(iv) $\frac{- 103}{20}$

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Solution

We have
(i) $\frac{12}{5} = 2 \frac{2}{5} = 2 + \frac{2}{5}$ [ $∵ a \frac{b}{c} = a + \frac{b}{c}$ ]
(ii) $\frac{- 11}{7} = - \frac{11}{7} = - 1 \frac{4}{7} = - 1 + \frac{- 4}{7}$
(iii) $\frac{- 25}{9} = - \frac{25}{9} = - 2 \frac{7}{9} = - 2 + \frac{- 7}{9}$
(iv) $\frac{- 103}{20} = - \frac{103}{20} = - 5 \frac{3}{20} = - 5 + \frac{- 3}{20}$

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