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Given:-
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To Find:-
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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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[tex]\begin{gathered}\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}\end{gathered}[/tex]
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Hence, The LCM of 5 & 8 is [tex]\sf{\red{2\times 2 \times2\times 5 = 40}}[/tex]
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Now, We have to make the denominators = 40 by multiplying the given values
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[tex]\begin{gathered}:\implies\sf\dfrac{1}{5} \times \dfrac{8}{8} = \dfrac{8}{40}\\\\\end{gathered}[/tex]
[tex]:\implies\sf\dfrac{1}{8} \times \dfrac{5}{5} = \dfrac{5}{40}[/tex]
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For 4 Rational Numbers, We will again multiply the rational Numbers to another one.So,
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[tex]\begin{gathered}:\implies\sf\dfrac{5}{40} \times \dfrac{2}{2} = \dfrac{10}{80}\\\\\end{gathered}[/tex]
[tex]:\implies\sf\dfrac{8}{40} \times \dfrac{2}{2} = \dfrac{16}{80}[/tex]
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The four rational Numbers between:
[tex]\sf\dfrac{1}{5} \: \sf and \: \: \dfrac{1}{8} \: are : \dfrac{11}{80}, \: \dfrac{12}{80}, \: \dfrac{13}{80}, \: \dfrac{14}{80}[/tex]
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