Question

$\text{Insert five ratinal numbers between}\frac{3}{5}and\frac{2}{3}.$

Answer 1

$\text{LCM of denominators 5 and 3 is 15}\text{Make, denominator of each given ratinal number equal to 15 i.e , the LCM}\frac{3}{5}=\frac{3\times 3}{5\times 3}=\frac{9}{15}and\frac{2}{3}=\frac{2\times 5}{3\times 5}=\frac{10}{15}\text{Since, five ratinal numbers are required, multiply the numerator and denominator of each rational by 5+1=+6}\therefore \frac{9}{15}=\frac{9\times 6}{15\times 6}=\frac{54}{90}and\frac{10}{15}=\frac{10\times 6}{15\times 6}=\frac{60}{90}\therefore \text{Required rational numbers between}\frac{3}{5}and\frac{2}{3}are=\frac{55}{90},\frac{56}{90},\frac{57}{90},\frac{58}{90},and\frac{59}{90}=\frac{11}{18},\frac{28}{45},\frac{19}{35},\frac{29}{45}and\frac{59}{90}$