Question

Find ten rational numbers between\[\frac{- 2}{5} \text{and} \frac{1}{2} .\]

Answer 1

\[\text{L . C . M of the denominators (2 and 5) is 10 .} \]
\[\text{We can write:} \]
\[ \frac{- 2}{5} = \frac{- 2 \times 2}{5 \times 2} = \frac{- 4}{10} \]
\[\text{and} \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}\]
\[\text{Since the integers between the numerators ( - 4 and 5 ) of both the fractions are not sufficient, we will multiply the fractions by 2 .} \]
\[ \therefore \frac{- 4}{10} = \frac{- 4 \times 2}{10 \times 2} = \frac{- 8}{20}\]
\[\frac{5}{10} = \frac{5 \times 2}{10 \times 2} = \frac{10}{20}\]
\[\text{There are 17 integers between - 8 and 10, which are - 7, - 6, - 5, - 4 . . . . . . . . . . . . . . . . . . . 8, 9 .} \]
\[\text{These can be written as:} \]
\[\frac{- 7}{20}, \frac{- 6}{20}, \frac{- 5}{20}, \frac{- 4}{20}, \frac{- 3}{20}, . . . . . . . . . . . . . . . . . . . \frac{8}{20} and \frac{9}{20}\]
\[\text{We can take any 10 of these .} \]