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