Question

Find three rational numbers lying between \[\dfrac{3}{5} \,and\, \dfrac{7}{8}\]

Answer 1

Hint: here we are asked to find three rational numbers between the \[\dfrac{3}{5} \,and\, \dfrac{7}{8}\]
A rational number is the number which can be expressed In the terms of \[\dfrac{p}{q}\] where \[p\] and q are integers and \[q\] cannot be equal to zero .For solving such kind of question we need to convert the \[\dfrac{3}{5} \,and\, \dfrac{7}{8}\] firstly into the rational numbers having the same denominator which can be done by multiplying and dividing the both rational numbers by a common factor and later on finding the amount of the rational numbers asked In between them which is three in this question let us take a look on how to convert the given \[\dfrac{3}{5} \,and\, \dfrac{7}{8}\] and find the required amount of rational numbers

Complete step-by-step answer:
Now we are given with \[\dfrac{3}{5} \,and\, \dfrac{7}{8}\] and we are asked to find the three rational numbers in between them
Now rational numbers are those numbers that can be expressed In the terms of \[\dfrac{p}{q}\] where \[p\] and q are integers and \[q\] cannot be equal to zero.
To find the rational numbers between the \[\dfrac{3}{5} and \dfrac{7}{8}\] we have to convert the given rational number with different denominator into rational numbers with same denominator that can be done by multiplying the both denominator with the same factor
But as we can the given rational numbers are \[\dfrac{3}{5} \,and\, \dfrac{7}{8}\] which means the denominator are \[5\] and \[8\] so we would find the LCM that is \[40\] and we would multiply and divide \[\dfrac{3}{5}\] by \[8\] and \[\dfrac{7}{8}\] by \[5\] so the resulting rational numbers be –
\[\dfrac{3}{5}*\dfrac{8}{8} = \dfrac{{24}}{{40}} \,and\, \dfrac{7}{8}*\dfrac{5}{5} = \dfrac{{35}}{{40}}\]
So now the rational numbers becomes –
\[\dfrac{{24}}{{40}}and\dfrac{{35}}{{40}}\]
So now the three rational numbers between \[\dfrac{{24}}{{40}} \,and\, \dfrac{{35}}{{40}}\] can be \[\dfrac{{26}}{{40}},\dfrac{{30}}{{40}},\dfrac{{31}}{{40}}\]
So the required three rational numbers are \[\dfrac{{26}}{{40}},\dfrac{{30}}{{40}},\dfrac{{31}}{{40}}\].

Note: While solving such kind of questions the common factor should be found correctly while converting the rational numbers having the same denominator .Also there can be infinite number of the rational between two given numbers