### Theory:

Equivalent ratios can be found by multiplying or dividing the numerator and denominator by a common factor.
Example:
Let us see the situation which involves equivalent ratios. Here we have $$1$$ red diamond and $$2$$ yellow diamonds in the first rectangle, $$2$$ red diamonds and $$4$$ yellow diamonds in the second rectangle, and $$3$$ red diamonds and $$6$$ yellow diamonds in the third rectangle.

The ratio of red diamond to yellow diamonds are $$1:2$$, $$2:4$$ and $$3:6$$.

The fraction form of the number of diamonds red to yellow in each case can be written as $\frac{1}{2}$, $\frac{2}{4}$, and $\frac{3}{6}$.

On simplifying the fractions, all the values will lead to $\frac{1}{2}$, $\frac{1}{2}$, and $\frac{1}{2}$.

It can be noted that the second fraction $\frac{2}{4}$ is the result of the product of the first fraction $\frac{1}{2}$ and the number $$2$$ in both numerator and denominator. That is $\frac{1×2}{2×2}=\frac{2}{4}$.

The third fraction $\frac{3}{6}$ is the result of the product of the first fraction $\frac{1}{2}$ and number $$3$$ in both numerator and denominator. That is $\frac{1×3}{2×3}=\frac{3}{6}$.

Note that the reduced form of all the fractions will be the same.

As the common factor here is $$2$$ and $$3$$, the ratios $$1:2$$, $$2:4$$, and $$3:6$$ are equivalent ratios.