Division in a given ratio means splitting a total quantity into parts that maintain a specific proportional relationship, based on the ratio provided. In a division according to a given ratio, we will have a defined quantity that we must divide according to said ratio. The process ensures that the ratio between the parts stays consistent, regardless of the total amount being divided. This concept is frequently used in various scenarios, such as dividing an inheritance, sharing resources, or solving problems in geometry.

Let's use an Example:

We want to divide $100$ Dollars in a $2:3$ ratio. So, the quantity is $100$, and the ratio provided is $2:3$.

In order to do so, let's follow there simple steps:

Add the parts of the ratio. In our case: $2 + 3 = 5$. Now we know that we need to divide the quantity to $5$.

Divide the total amount by $5$. In our case: $100:5=20$ So we get $20$ Dollars per part.

Multiply each of the ratio side by the part. So: $20\cdot2=40$, $3\cdot20=60$.

And so the $100$ Dollars is divided into $40$ Dollars and $60$ Dollars , maintaining the $2:3$ ratio.

From here it follows that the number of refrigerators is $75 (3X)$, and the number of air conditioners is $X=25$.

We can always go back and check our result by verifying that the total number of appliances in the store is $100$, as stated in the first piece of data given.

Examples and exercises with solutions for division according to a given ratio

Exercise #1

Given the rectangle ABCD

AB=X the ratio between AB and BC is equal to$\sqrt{\frac{x}{2}}$