question_answer 1)

Find the equivalent fraction of \[\frac{7}{13}\]having (a) denominator 20 (b) numerator 9 (c) denominator 30 (d) numerator 27

Answer:

Let N stands for the numerator and D stands for the denominator. (a) Given, denominator of an equivalent fraction = 20 \[\frac{5}{11}\] \[\frac{48}{60}\] So, \[\frac{150}{60}\] [but \[\frac{84}{98}\]] \[\frac{12}{52}\] \[\frac{7}{28}\] On comparing, we get N = 12 \[\frac{48}{60}\] Required equivalent fraction of \[48=\times \times \times 2\times 2\] (b) Given, numerator of an equivalent fraction = 9 \[60=\times \times \times 5\] \[60=2\times 2\times 3=12\] \[\therefore \] \[\frac{48}{60}=\frac{48\div 12}{60\div 12}=\frac{4}{5}\] So, \[\frac{48}{60}\] [but \[\frac{4}{5}.\]] \[\frac{150}{60}\] \[150=\times \times \times 5\] On comparing, we get D = 15 \[60=\times \times \times 2\]Required equivalent fraction of \[60=2\times 3\times 5=30\] (c) Given, denominator of an equivalent fraction = 30 \[\therefore \] \[\frac{150}{60}=\frac{150\div 30}{60\div 30}=\frac{5}{2}\] So, \[\frac{150}{60}\] [but\[\frac{5}{2}.\]] \[\frac{84}{98}\] \[84=\times \times 3\times 2\] On comparing, we get N = 18 \[98=\times \times 7\] Required equivalent fraction of \[98=2\times 7=14\] (d) Given, numerator of an equivalent fraction \[\therefore \] \[\frac{84}{98}=\frac{84\div 14}{98\div 14}=\frac{6}{7}\] \[\frac{84}{98}\] \[\frac{6}{7}.\] So, \[\frac{12}{52}\]\[12=\times \times 3\] On comparing, we get D = 45 \[52=\times \times 13\] Required equivalent fraction of\[52=2\times 2=4\]