Density of Numbers Math Example 1

Solution

1. 1
   Method 1 (mediant / averaging): Average of $\dfrac{2}{5}$ and $\dfrac{3}{5}$: $\dfrac{1}{2}\left(\dfrac{2}{5}+\dfrac{3}{5}\right) = \dfrac{1}{2} = 0.5$. First number: $\dfrac{1}{2}$.
2. 2
   Average of $\dfrac{2}{5}$ and $\dfrac{1}{2}$: $\dfrac{1}{2}\left(\dfrac{4}{10}+\dfrac{5}{10}\right) = \dfrac{9}{20}$. Second number: $\dfrac{9}{20}$.
3. 3
   Average of $\dfrac{1}{2}$ and $\dfrac{3}{5}$: $\dfrac{1}{2}\left(\dfrac{5}{10}+\dfrac{6}{10}\right) = \dfrac{11}{20}$. Third number: $\dfrac{11}{20}$.
4. 4
   Check order: $\dfrac{2}{5} = \dfrac{8}{20} < \dfrac{9}{20} < \dfrac{10}{20} < \dfrac{11}{20} < \dfrac{12}{20} = \dfrac{3}{5}$. ✓