### 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 $\frac{1}{2}$.

**$\frac{2}{4}$**

*It can be noted that the second fraction***$\frac{1}{2}$**

*is the result of the product of the first fraction**$\frac{1\times 2}{2\times 2}=\frac{2}{4}$*

**and****the number**\(2\)**in both numerator and denominator. That is***.*

**$\frac{3}{6}$**

*The third fraction***$\frac{1}{2}$**

*is the result of the product of the first fraction**$\frac{1\times 3}{2\times 3}=\frac{3}{6}$*

**and****number**\(3\)**in both numerator and denominator**.**That is***.*

*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.