1. Equivalent ratios

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 $\frac{1}{2}$.

 

  

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 $\frac{1\times 3}{2\times 3}=\frac{3}{6}$.

 

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