Question

Find ten rational numbers between\[\frac{3}{5} \text{and} \frac{3}{4} .\]

Answer 1

\[\text{The L . C . M of the denominators 5 and 4 of both the fractions is 20 .} \]
\[\text{We can write:} \]
\[\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}\]
\[\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\]
\[\text{Since the integers between the numerators 12 and 15 are not sufficient, we will multiply both the fractions by 5 .} \]
\[\frac{12}{20} = \frac{12 \times 5}{20 \times 5} = \frac{60}{100}\]
\[\frac{15}{20} = \frac{15 \times 5}{20 \times 5} = \frac{75}{100}\]
\[\text{There are 14 integers between 60 and 75 . They are 61, 62, 63 . . . . . . . 73 and 74 .} \]
\[\text{Therefore,} \frac{60}{100}, \frac{61}{100}, \frac{62}{100} . . . . . . . . . . \frac{73}{100} and\frac{74}{100} \text{are the 14 fractions .} \]
\[\text{We can take any 10 of these .}\]