Question

Find five rational numbers between

(i) 4÷5

and

7÷8

(ii) -3÷7

and
-5÷11​

Answer 1

Correct Question : ↧

Part 1. ↧

Find five rational number between  $\frac{4}{5} \: and \: \frac{7}{8}$

Part 2.↧

Find five rational number between  $\frac{-3}{7} \:and\:\frac{-5}{11}$

Solution : ↧

Part (1) ↧

In this question we need to find five rational number between  $\frac{4}{5} \:and \: \frac{7}{8}$

First of all We need to take the LCM of 5 and 8

$\begin{array}{c|c}\sf 2 & \sf 5\ -\ 8\\\cline{1-2} \sf 2 & \sf 5\ -\ 4\\\cline{1-2}\sf 2 & \sf 5\ -\ 2\\\cline{1-2}\sf 5 & \sf 5\ -\ 1\\\cline{1-2} & \sf 1\end{array}$

So, the LCM of 5 and 8 is 40.

$\frac{4}{5} \times \frac{8}{8} = \frac{32}{40}$

$\frac{7}{8} \times \frac{5}{5} = \frac{35}{40}$

Now, ↧

$\frac{32}{40} \times \frac{10}{10} = \frac{320}{400}$

$\frac{35}{40} \times \frac{10}{10} = \frac{350}{400}$

$Now, \: our \: Answer\: is\: \frac{321}{400}, \frac{322}{400}, \frac{323}{400}, \frac{324}{400}, \frac{325}{400}.$

Part (2) ↧

In this question also we need to find five rational number only.

$\frac{-3}{7} \:and\:\frac{-5}{11}$

First of all We need to take the LCM of 7 and 11

$\begin{array}{c|c}\sf 7 & \sf 7\ -\ 11\\\cline{1-2} \sf 11 & \sf 1\ -\ 11\\\\\cline{1-2} & \sf 1\end{array}$

So, our LCM of 7 and 11 is 77.

$\frac{-3}{7} \times \frac{11}{11} = \frac{-33}{77}$

$\frac{-5}{11} \times \frac{7}{7} = \frac{-35}{77}$

Now, ↧

$\frac{-33}{77} \times \frac{10}{10} = \frac{-330}{770}$

$\frac{-35}{77} \times \frac{10}{10} = \frac{-350}{770}$

$Now, \: our \: Answer\: is\: \frac{-331}{770}, \frac{-332}{770}, \frac{-333}{770}, \frac{-334}{770}, \frac{-335}{770}.$

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