Question

insert 5 rational numbers between 3/5 and 7/9​

Answer 1

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First take L.C.M. to make the denominators same.

L.C M. of 5 and 9=3×3×5=45

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$\large\mathtt\blue{ = > \frac{3}{5} \times \frac{9}{9} = \frac{27}{45} \:}$

$\large\mathtt\blue{ = > \frac{7}{9} \times \frac{5}{5} = \frac{35}{45} \:}$

So rational numbers between 3/5 and 7/9 are 28/45, 29/45, 30/45, 31/45, 32/45, 33/45 and 34/45.

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Answer 2

So to find 5 irrational number between the given nos. We Ned to make their denominator same..

$lcm = 5 \times 9 = 45 \\ = \frac{3}{5} \times \frac{9}{9} = \frac{27}{45} \\ = \frac{7}{9} \times \frac{5}{5} = \frac{35}{45}$

So, any 5 irrational numbers between them are -

$\frac{28}{45} . \frac{29}{45} . \frac{30}{45} . \frac{31}{45} . \frac{32}{45}$