Question

find any four rational numbers between 1/5 and 1/8 ?​

Answer 1

Answer:

23/400, 22/400, 24/400, 21/400

Answer 2

Given:-

• Rational Numbers: 1/5 & 1/8

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To Find:-

• Any Four Rational Numbers

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Solution:-

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According to the Question, We have to find the LCM of Given Value.

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$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{2}}& {\sf{ \underline{ \: \: 5 \: , \: 8 \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \underline{\sf{2}}&{\sf{ \underline{\: \: 5 \: ,\: 4 \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{2}}&{\sf{ \underline{ \: \: 5 \: , \: 2\: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{5}}} & {\underline{\sf{ \: \: 5 \:, \: \: 1\: \: }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ {\underline{ \sf{}}}& \sf{ \: \: 1 \: , \: 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }\end{array}\end{gathered}\end{gathered}\end{gathered}$

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Hence, The LCM of 5 & 8 is $\sf{\red{2\times 2 \times2\times 5 = 40}}$

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Now, We have to make the denominators = 40 by multiplying the given values

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$:\implies\sf\dfrac{1}{5} \times \dfrac{8}{8} = \dfrac{8}{40}$

$:\implies\sf\dfrac{1}{8} \times \dfrac{5}{5} = \dfrac{5}{40}$

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For 4 Rational Numbers, We will again multiply the rational Numbers to another one. So,

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$:\implies\sf\dfrac{5}{40} \times \dfrac{2}{2} = \dfrac{10}{80}$

$:\implies\sf\dfrac{8}{40} \times \dfrac{2}{2} = \dfrac{16}{80}$

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The four rational Numbers between

$\sf\dfrac{1}{5} \: \sf and \: \: \dfrac{1}{8} \: are : \dfrac{11}{80}, \: \dfrac{12}{80}, \: \dfrac{13}{80}, \: \dfrac{14}{80} .$

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