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.