Question

Find ten rational numbers between \[\frac{1}{4} \text{and} \frac{1}{2} .\]

Answer 1

\[\text{The L . C . M of the denominators (2 and 4) is 4 .} \]
\[\text{So, we can write} \frac{1}{4} \text{as it is .} \]
\[\text{Also,} \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}\]
\[\text{As the integers between the numerators 1 and 2 of both the fractions are not sufficient, we will multiply the fractions by 20 .} \]
\[ \therefore \frac{1}{4} = \frac{1 \times 20}{4 \times 20} = \frac{20}{80}\]
\[\frac{2}{4} = \frac{2 \times 20}{4 \times 20} = \frac{40}{80}\]
\[\text{Between 20 and 40, there are 19 integers . They are 21, 22, 23, 24, 25, 26, 27 . . . . 39, 40 . }\]
\[\text{Thus,} \frac{21}{40}, \frac{22}{40}, \frac{23}{40}, \frac{24}{40}, \frac{25}{40}, . . . . . . . . . . . . . . . . . . . \frac{38}{40} and \frac{39}{40} are the fractions . \]
\[\text{We can take any 10 of these .} \]