question_answer 15)

Replace \[[\text{but}\,27=3\times 9]\] in each of the following by the correct number. (a) \[\therefore \] (b) \[\frac{3}{5}=\frac{N}{D}=\frac{27}{45}\] (c) \[\frac{36}{48}\] (d) \[\therefore \] (e) \[\frac{9}{D}=\frac{36}{48}\]

Answer:

(a) We have, \[\Rightarrow \] \[9\times 48=D\times 36\] \[\Rightarrow \] So, \[D=\frac{9\times 48}{36}=12\Rightarrow D=12\]\[\therefore \] or \[\frac{36}{48}=\frac{N}{D}=\frac{9}{12}\] On comparing, we get \[\therefore \] Hence, \[\frac{2}{7}=\frac{8}{}\] (b) We have, \[\Rightarrow \] \[N\times 48=4\times 36\] \[\Rightarrow \] So, \[N=\frac{4\times 36}{48}=3\Rightarrow N=3\]\[\therefore \] or \[\frac{36}{48}=\frac{N}{D}=\frac{3}{4}\] On comparing, we get \[\frac{5}{9},\frac{30}{54}\] Hence, \[\frac{3}{10},\frac{12}{50}\] (c) We have, \[\frac{7}{13},\frac{5}{11}\] \[\frac{5}{9}\] \[\frac{30}{54}\] So, \[5\times 54=270\] \[9\times 30=270\] or \[\because \] On comparing, we get \[270=270\] Hence, \[\therefore \] (d) We have, \[\frac{5}{9}\] \[\frac{30}{54}\] \[\frac{3}{10}\] So, \[\frac{12}{50}\]\[3\times 50=150\] \[10\times 12=120\] On comparing, we get \[150\ne 120\] Hence, \[\therefore \] (e) We have, \[\frac{3}{10}\] \[\frac{12}{50}\] \[\frac{7}{13}\] So, \[\frac{5}{11}\] \[7\times 11=77\] \[13\times 5=65\] On comparing, we get \[77\ne 65\] Hence, \[\therefore \]