Question
Fill in the missing numbers: $\frac{14}{21}=\frac{\square}{3}=\frac{6}{\square}$

Answer

In order to get the first missing number, we consider the fact that $21 = 3$ $\times$ $7$. i.e.
 when we divide $21$ by $7$ we get $3$.
This indicates that to get the missing number of second ratio, $14$ must also be divided by $7$.
When we divide, we have, $14$ $\div$ $7 = 2$
Hence, the second ratio is $\frac{2}{3}$
Similarly, to get third ratio we multiply both terms of second ratio by $3.$
Hence, the third ratio is $\frac{6}{9}$
Therefore, $\frac{{14}}{{21}} = \frac{{\boxed2}}{3} = \frac{6}{{\boxed9}}$

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