# Q 1.     List five rational numbers between:      (iii) $\frac{-4}{5}and \frac{-2}{3}$

D Divya Prakash Singh

To find five rational numbers between $\frac{-4}{5}and \frac{-2}{3}$ we will convert each rational numbers with the denominator as $5\times3 =15$, we have  $\left ( \because LCM\ of\ 5\ and\ 3 = 15 \right )$

$\frac{-4}{5} = \frac{-4\times3}{5\times3} = \frac{-12}{15}\ and\ \frac{-2}{3} = \frac{-2\times5}{3\times5} = \frac{-10}{15}$

Since there is only one integer i.e., -11 between -12 and -10, we have to find equivalent rational numbers.

$\frac{-12}{15} = \frac{-12\times3}{15\times3} = \frac{-36}{45}\ and\ \frac{-10}{15} = \frac{-10\times3}{15\times3} = \frac{-30}{45}$

Now, we have five rational numbers possible:

$\therefore \frac{-36}{45}<\frac{-35}{45}<\frac{-34}{45}<\frac{-33}{45}<\frac{-32}{45}<\frac{-31}{45}<\frac{-30}{45}$

Hence, the required rational numbers are

$\frac{-7}{9},\frac{-34}{45},\frac{-11}{15},\frac{-32}{45}\ and\ \frac{-31}{45}.$

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