Question

Find 3 rational number between 2/3 and 3/4

Answer 1

solution:$find the rational numbers between \frac{2}{3}and\frac{3}{4},\\</p><p>first find the LCM of the denominators,3 and 4\\</p><p>LCM of 3 and 4=12\\</p><p>now,equalize the denominators of each fraction by equal to the LCM\\</p><p>\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}\\</p><p>\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$$multiplying \frac{8}{12}and\frac{9}{12} by \frac{10}{10}\\</p><p>\frac{8}{12}=\frac{8\times 10}{12\times 10}=\frac{80}{120}\\</p><p>\frac{9}{12}=\frac{9\times 10}{12\times 10}=\frac{90}{120}\\</p><p>so,the three rational number are \frac{81}{120},\frac{82}{120}and\frac{83}{120}$