Answer:
(a) We have,\[\to \] Now, factors of \[\frac{9\times 2}{10\times 2}=\frac{18}{20}\] and factors of \[\frac{9\times 3}{10\times 3}=\frac{27}{30}\] Common factors = 2, 2 and 3 HCF of 48 and \[\frac{660}{990}\] \[=\times 2\times \times 5\times \] \[990=\times 3\times \times 5\times \] Hence, simplest form of the fraction \[990=2\times 3\times 5\times 11=330\]is \[\therefore \] (b) We have,\[\frac{660}{990}=\frac{660\div 330}{990\div 330}=\frac{2}{3}\] Now, factors of \[\frac{660}{990}\] and factors of \[\frac{2}{3}\] Common factors = 2, 3 and 5 HCF of 150 and \[\to \] \[\frac{2\times 2}{3\times 2}=\frac{4}{6}\] \[\frac{2\times 3}{3\times 3}=\frac{6}{9}\] Hence, simplest form of the fraction \[\frac{180}{360}\]is \[180=\times \times \times \times \] (c) We have,\[360=\times \times \times \times \times 2\] Now, factors of \[360=2\times 2\times 3\times 3\times 5=180\] and factors of \[\therefore \] Common factors = 2 and 7 HCF of 84 and \[\frac{180}{360}=\frac{180\div 180}{360\div 180}=\frac{1}{2}\] \[\frac{180}{360}\] \[\frac{1}{2}\] Hence, simplest form of the fraction \[\to \]is\[\frac{1\times 2}{2\times 2}=\frac{2}{4}\] (d) We have, \[\frac{1\times 3}{2\times 3}=\frac{3}{6}\] Now, factors of \[\frac{220}{550}\] and factors of \[220=\times 2\times \times \] Common factors = 2 and 2 HCF of 12 and \[550=\times 5\times \times \] \[550=2\times 5\times 11=110\] \[\therefore \] Hence, simplest form of the fraction\[\frac{220}{550}=\frac{220\div 110}{550\div 110}=\frac{2}{5}\] is\[\frac{220}{530}\] (e) We have, \[\frac{2}{5}\] Now, factors of \[\to \] and factors of \[\frac{2\times 2}{5\times 2}=\frac{4}{10}\] Common factor = 7 HCF of 7 and 28 = 7 \[\frac{2\times 3}{5\times 3}=\frac{6}{15}\] \[\frac{1}{5}\] Hence, simplest form of the fraction\[\frac{1}{3}\]is \[\frac{1}{3}>\frac{1}{5}\]
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