question_answer 28)

Find answers to the following. Write and indicate how you solved them. (a) \[\because \]equal to \[\frac{10}{20}=\frac{25}{50}=\frac{40}{80}=\frac{1}{2}\] (b) \[\frac{250}{400}\]equal to \[\frac{2}{3}\] (c) \[\frac{180}{200}\] equal to \[\frac{2}{5}\] (d) \[\frac{660}{990}\]equal to \[\frac{1}{2}\] TIPS To show that given fractions are equal or not. Firstly, we convert them into like fractions by multiplying numerator and denominator with same number and then compare.

Answer:

(a) LCM of 9 and 5 = 45 Now, \[\frac{180}{360}\] and \[\frac{5}{8}\] Thus, both fractions are like fractions but\[\frac{220}{550}\] \[\frac{9}{10}\] \[\frac{250}{400}\] (b) LCM of 16 and 9 = 144 Now, \[250=\times \times \times 5\] and \[400=\times \times \times 2\times 2\times 2\] Thus, both fractions are like fractions but \[400=2\times 5\times 5=50\] \[\therefore \] \[\frac{250}{400}=\frac{250\div 50}{400\div 50}=\frac{5}{8}\] (c) LCM of 5 and 20 = 20 Now, \[\frac{250}{400}\] and \[\frac{5}{8}\] Thus, both fractions are like fractions and \[\to \] \[\frac{5\times 2}{8\times 2}=\frac{10}{16}\] \[\frac{5\times 3}{8\times 3}=\frac{15}{24}\] (d) LCM of 15 and 30 = 30 Now, \[\frac{180}{200}\] and \[180=\times \times \times 3\times 3\] Thus, both fractions are like fractions but \[200=\times \times \times 5\times 2\] \[200=2\times 5\times 2=20\] \[\therefore \]