### Theory:

When two ratios are in proportion $$a:b::c:d$$, then the product of the extremes is equal to the product of the means. This is called the proportionality law.

Here '$$a$$' and '$$d$$' are the extreme values and '$$b$$' and '$$c$$' are the mean values.

Also, if two ratios are equal, then they can be related as follows.

$\begin{array}{l}\frac{a}{b}=\frac{c}{d}\\ \\ \mathit{ad}\phantom{\rule{0.147em}{0ex}}=\mathit{bc}\end{array}$

It is called the cross product of proportion.
Example:
Let us check the ratios $$7:2$$ and $$21:6$$ are in proportion.

We can use the proportionality law to check the condition.
It says that 'When two ratios are in proportion $$a:b::c:d$$, then the product of the extremes is equal to the product of the means'.
$\begin{array}{l}\frac{a}{b}=\frac{c}{d}\\ \\ \mathit{ad}\phantom{\rule{0.147em}{0ex}}=\mathit{bc}\end{array}$

Here $$a = 7$$, $$b = 2$$, $$c = 21$$ and $$d = 6$$.

Apply the values in $$ad = bc$$.

$$7×6 = 2×21$$

$$42 = 42$$.

As the proportionality law satisfies, the given ratios are in proportion.