Question

Find three rational number between 3/5 and 5/7

Answer 1

3/5*7/7 and 5/7*5/5
=>21/35 and 25/35
three rational number between 3/5 and 7/5 are:-
22/35,23/35,24/35

Answer 2

Answer:

$\frac{85}{140} \: and \: \frac{86}{140}$ are required two rational numbers.

Step-by-step explanation:

$Given\\\: two \: rational \:</p><p>numbers \: \frac{3}{5}\: and \: \frac{5}{7}$

$i)\frac{3}{5}\\=\frac{3\times 7}{5\times 7 }\\ = \frac{21}{35}\\=\frac{21\times 4}{35\times 4}\\=\frac{84}{140}--(1)$

$ii)\frac{5}{7}\\=\frac{5\times 5}{7\times 5 }\\ = \frac{25}{35}\\=\frac{25\times 4}{35\times 4}\\=\frac{100}{140}--(2)$

Now,

Then the rational numbers between $\frac{3}{5} \: and \frac{5}{7}$

$\frac{3}{5}=\frac{84}{140}<(\frac{85}{140},\frac{86}{140})<\frac{100}{140}=\frac{5}{7}$

Note :

There exist infinite number of rational numbers between any two given rational numbers.

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