question_answer 1)

Which of the following pairs represent the same number? (i) \[\frac{-7}{21}\] and \[\frac{3}{9}\]                    (ii) \[\frac{-16}{20}\] and \[\frac{20}{-25}\]           (iii) \[\frac{-2}{-3}\] and \[\frac{2}{3}\] (iv) \[\frac{-3}{5}\] and \[\frac{-12}{20}\]              (v) \[\frac{8}{-5}\] and \[\frac{-24}{15}\]               (vi) \[\frac{1}{3}\] and \[\frac{-1}{9}\] (vii) \[\frac{-5}{-9}\] and \[\frac{5}{-9}\].

Answer:

                (i) \[\frac{-7}{21}\] is a negative rational number and \[\frac{3}{9}\] is a positive rational number. So, the given pair does not represent the same rational number. (ii) \[\frac{-16}{20}=\frac{-16\times -1}{20\times -1}=\frac{16}{-20}=\frac{16\div 4}{-20\div 4}=\frac{4}{-5}\] \[\frac{20}{-25}=\frac{20\div 5}{-25\div 5}=\frac{4}{-5}\] So, the given pair represents the same rational number. (iii) \[\frac{-2}{-3}=\frac{-2\times -1}{-3\times -1}=\frac{2}{3}\] So, the given pair represents the same rational number. (iv) \[\frac{-3}{5}=\frac{-3\times 4}{5\times 4}=\frac{-12}{20}\] So, the given pair represents the same rational number. (v) \[\frac{8}{-5}=\frac{8\times -3}{-5\times -3}=\frac{-24}{15}\] So, the given pair represents the same rational number. (vi) \[\frac{1}{3}\] is a positive rational number and \[\frac{-1}{9}\] is a negative rational number. So, the given pair does not presents the same rational number. (vii) \[\frac{-5}{-9}=\frac{-5\times -1}{-9\times -1}=\frac{5}{9}\] Thus, \[\frac{-5}{-9}\] is a positive rational number and \[\frac{5}{-9}\] is a negative rational number. So, the given pair does not represent the same rational number.