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5.Find five rational numbers between
(i)\(\frac { 2 }{ 3 }\) and \(\frac { 4 }{ 5 }\)

(ii) \(\frac { -3 }{ 2 } \)and \(\frac { 5 }{ 3 }\)

(iii) \(\frac { 1 }{ 4 }\) and \(\frac { 1 }{ 2 }\)

Answer :

(i) We have rational numbers as: \(\frac{2}3\) and\(\frac{4}5\)

Making the denominator same for both the rational numbers:

\(\frac{2}3=\frac{2}3×\frac{20}{20}=\frac{40}{60}\) and \(\frac{4}5=\frac{4×12}{5×12}=\frac{48}{60}\)

So now we have to see five rational number between \(\frac{40}{60}\) and \(\frac{48}{60}\)

These can be, \(\frac{41}{60},\frac{42}{60},\frac{43}{60},\frac{44}{60},\frac{46}{60}\)

(ii) We have rational numbers as: \(\frac{-3}2\) and\(\frac{5}3\)

Making the denominator same for both the rational numbers:

\(\frac{-3}2=\frac{-3×3}{2×3}=\frac{-9}{6}\) and \(\frac{5}3=\frac{5×2}{3×2}=\frac{10}{6}\)

So now we have to see five rational number between \(\frac{-9}{6}\) and \(\frac{10}{6}\)

These can be, \(\frac{-8}{6},\frac{-7}{6},\frac{-6}{6},\frac{3}{6},\frac{4}{6}\)

(iii) We have rational numbers as: \(\frac{1}4\) and\(\frac{1}2\)

Making the denominator same for both the rational numbers:

\(\frac{1}4=\frac{1×8}{2×8}=\frac{8}{32}\) and \(\frac{1}2=\frac{1×16}{2×16}=\frac{16}{32}\)

So now we have to see five rational number between \(\frac{8}{32}\) and \(\frac{16}{32}\)

These can be, \(\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}\)