Question

Which is greater in each of the following:
(i) \(\frac{2}{3}\),\(\frac{5}{2}\) (ii) -\(\frac{5}{6}\),-\(\frac{4}{3}\) (iii) -\(\frac{3}{4}\),\(\frac{2}{-3}\) (iv) \(-\frac{1}{4}\),\(\frac{1}{4}\) (v) \(-\frac{32}{7}\),\(-\frac{34}{5}\)

Answer 1

(i) \(\frac{2}{3}\), \(\frac{5}{2}\)
By converting these into like fractions,
\(\frac{2}{3}\) = \(\frac{2\times 2}{3\times 2}\)= 4/6
\(\frac{5}{2}\)= \(\frac{5\times 3}{2\times 3}\) =\(\frac{15}{6}\)
As 15 > 4, therefore, \(\frac{5}{2}\) is greater.

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(ii) -\(\frac{5}{6}\), -\(\frac{4}{3}\)
-\(\frac{4}{3}\) = -\(\frac{4\times 2}{3\times 2}\) = -\(\frac{8}{6}\)
As -5>-8, therefore, -\(\frac{5}{6}\) is greater.