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 $$\frac { 1 }{ 2 }$$

(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, $$\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}$$