Find ten rational numbers between


Find ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$.


The L. C.M of the denominators 5 and 4 of both the fractions is 20 .

We can write:

$\frac{3}{5}=\frac{3 \times 4}{5 \times 4}=\frac{12}{20}$

$\frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}$

Since the integers between the numerators 12 and 15 are not sufficient, we will multiply both the fractions by 5 .

$\frac{12}{20}=\frac{12 \times 5}{20 \times 5}=\frac{60}{100}$

$\frac{15}{20}=\frac{15 \times 5}{20 \times 5}=\frac{75}{100}$

There are 14 integers between 60 and $75 .$ They are $61,62,63 \ldots \ldots 73$ and $74 .$

Therefore $, \frac{60}{100}, \frac{61}{100}, \frac{62}{100} \ldots \ldots \ldots \frac{73}{100}$ and $\frac{74}{100}$ are the 14 fractions.

We can take any 10 of these.

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