Question

Write the following rational numbers in ascending order:
(i) -\(\frac{3}{5}\),-\(\frac{2}{5}\),-\(\frac{1}{5}\)
(ii) -\(\frac{1}{3}\),-\(\frac{2}{9}\),-\(\frac{4}{3}\)
(iii) -\(\frac{3}{7}\),-\(\frac{3}{2}\),-\(\frac{3}{4}\)

Answer 1

(i) -\(\frac{3}{5}\),-\(\frac{2}{5}\),-\(\frac{1}{5}\)
As -3 < -2 < -1,
∴ -\(\frac{3}{5}\)<-\(\frac{2}{5}\)<-\(\frac{1}{5}\)

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(ii) -\(\frac{1}{3}\),-\(\frac{2}{9}\),-\(\frac{4}{3}\)
By converting these into like fractions,
\(\frac{-1\times 3}{3\times3}\), -\(\frac{2}{9}\), -\(\frac{4\times 3}{3\times 3}\)
-\(\frac{3}{9}\), -\(\frac{2}{9}\), -\(\frac{12}{9}\)
As -12<-3<-2
∴ -\(\frac{4}{3}\)<-\(\frac{1}{3}\)<-\(\frac{2}{9}\)

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(iii) -\(\frac{3}{7}\),-\(\frac{3}{2}\),-\(\frac{3}{4}\)
By converting these into like fractions,
-\(\frac{12}{48}\), -\(\frac{42}{28}\), -\(\frac{21}{28}\)
As - 42 < - 21 < - 12,
∴ -\(\frac{3}{2}\) < -\(\frac{3}{4}\) < -\(\frac{3}{7}\)