Find 5 rational numbers between 1/6 and 2/5. Class 9

Find 5 rational numbers between 1/6 and 2/5. Class 9

Question 1.

Find 5 rational numbers between $\frac{1}{6}$ and $\frac{2}{5}$. Class 9

Solution:

$\begin{aligned} & \frac{1}{6}=\frac{1 \times 5}{6 \times 5}=\frac{5}{30} \\ & \frac{2}{5}=\frac{2 \times 6}{5 \times 6}=\frac{12}{30}\end{aligned}$

Between 5 and 12, there are only 6 integers:

6, 7, 8, 9, 10,11

$\therefore \quad \frac{6}{30}, \frac{7}{30}, \frac{8}{30}, \frac{9}{30}, \frac{10}{30}$ are 5 rational numbers between $\frac{1}{6}$ and $\frac{2}{5}$

Question 2.

If [latex]\frac{x}{3}+\frac{x}{5}=\frac{16}{15}[/latex],find the rational number x. Class 9

Solution:

Given,

$\begin{array}{ll} & \frac{x}{3}+\frac{x}{5}=\frac{16}{15} \\ & \text { L.C.M. of } 3 \text { and } 5 \text { is } 15 \\ \therefore \quad & \frac{x \times 5}{3 \times 5}+\frac{x \times 3}{5 \times 3}=\frac{16}{15} \\ \therefore \quad & \frac{5 x}{15}+\frac{3 x}{15}=\frac{16}{15}\end{array}$

∴ $\frac{5 x+3 x}{15}=\frac{16}{15}$

∴ $\frac{8x}{15}=\frac{16}{15}$

∴ 8x = 16

∴ x = $\frac{16}{8}$

∴ x = 2