Question

Find five rational numbers between $\frac{1}{4}$and $\frac{1}{2}$

Answer 1

To find rational numbers between given numbers a and b-

a+d, a+2d, a+3d, a+4d, a+5d where, $\mathrm{d}=\frac{\mathrm{b}-\mathrm{a}}{\mathrm{n}+1}$

Step 1

Find d- $\mathrm{d}=\frac{{\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{4}}}{5+1}$

$$\begin{gathered} \mathrm{d}=\frac{{\displaystyle \frac{2-2}{4}}}{6} \\ =\frac{{\displaystyle \frac{1}{4}}}{6} \\ =\frac{1}{24} \end{gathered}$$

Step 2

Required terms- a+d, a+2d, a+3d, a+4d, a+5d

$$\begin{gathered} \frac{1}{4}+\frac{1}{24},\frac{1}{4}+\frac{2}{24},\frac{1}{4}+\frac{3}{24},\frac{1}{4}+\frac{4}{24},\frac{1}{4}+\frac{5}{24} \\ \frac{6+1}{24},\frac{6+2}{24},\frac{6+3}{24},\frac{6+4}{24},\frac{6+5}{24} \\ \frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24},\frac{11}{24} \end{gathered}$$

Hence, Five rational numbers between $\frac{1}{4}$and $\frac{1}{2}$ are $\frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24},\frac{11}{24}$