Answer: The number that best completes the given two equations is [tex]\dfrac{20}9}.[/tex]
Step-by-step explanation: We are given to find the numbers that best completes the following two equations :
[tex]\dfrac{2}{3}\div\dfrac{3}{10}=?\\\\\\?\times\dfrac{3}{10}=\dfrac{2}{3}.[/tex]
Let x and y be the numbers that completes the first and second equation respectively.
So, we get
[tex]x=\dfrac{2}{3}\div\dfrac{3}{10}=\dfrac{2}{3}\times\dfrac{10}{3}=\dfrac{20}{9}[/tex]
and
[tex]y\times\dfrac{3}{10}=\dfrac{2}{3}\\\\\\\Rightarrow y=\dfrac{\frac{2}{3}}{\frac{3}{10}}\\\\\\\Rightarrow y=\dfrac{2}{3}\times\dfrac{10}{3}\\\\\\\Rightarrow y=\dfrac{20}{9}.[/tex]
Thus, the number that best completes the given two equations is [tex]\dfrac{20}9}.[/tex]
