question_answer 18)

Check whether the given fractions are equivalent. (a)\[\because \] (b)\[\frac{40}{80}=\frac{40\div 40}{80\div 40}=\frac{1}{2}\] (c)\[\because \] TIPS If the product of numerator of first fraction and denominator of second fraction is equal to the product of denominator of first fraction and numerator of second fraction, then given fractions will be equivalent otherwise not.

Answer:

(a) We have,\[\frac{10}{20}=\frac{25}{50}=\frac{40}{80}=\frac{1}{2}\] and \[\frac{250}{400}\] Now, \[\frac{2}{3}\] \[\frac{180}{200}\] \[\frac{2}{5}\] \[\frac{660}{990}\] [by cross product] \[\frac{1}{2}\] \[\frac{180}{360}\] and \[\frac{5}{8}\] are equivalent fractions. (b) We have, \[\frac{220}{550}\]and \[\frac{9}{10}\] Now, \[\frac{250}{400}\] \[250=\times \times \times 5\] But \[400=\times \times \times 2\times 2\times 2\] [by cross product] \[400=2\times 5\times 5=50\]\[\therefore \] and \[\frac{250}{400}=\frac{250\div 50}{400\div 50}=\frac{5}{8}\]are not equivalent fractions. (c) We have,\[\frac{250}{400}\] and \[\frac{5}{8}\] Now, \[\to \] \[\frac{5\times 2}{8\times 2}=\frac{10}{16}\] But \[\frac{5\times 3}{8\times 3}=\frac{15}{24}\] [by cross product] \[\frac{180}{200}\] \[180=\times \times \times 3\times 3\] and \[200=\times \times \times 5\times 2\] are not equivalent fractions.