The ratio describes the "relationship" between two or more things.

The ratio connects the given terms and describes how many times greater or smaller a certain magnitude is than another.

Let's see an example from everyday life:

When asked in a class, what is the ratio between boys and girls, it refers to how many girls there are in relation to a certain number of boys.

Or, for example, if in a certain vase there are red and white balls, the ratio between them can describe how many red balls there are in relation to a certain number of white balls or vice versa.

We know that the ratio between apples and oranges in a basket is $2:3$. The total amount of fruit in the basket is $25$. We are asked to calculate the number of apples and oranges in the basket. We can deduce that the $2$ represents the number of apples and the $3$ represents the number of oranges. We will denote both fruits with a variable $X$.

Now let's draw a simple equation:

$2X+3X=25$

$5X=25$

$X=5$

From here we can infer that the number of apples is $10 (2X)$ and the number of oranges is $15 (3X)$. We can always go back and check our result by verifying that the total number of apples and oranges is $25$, as shown in the first piece of data we received.

Example 2

In the dishware cabinet, there is a total of $30$ utensils that include plates and bowls. The ratio between plates and bowls is $7:3$.

We are asked to determine how many plates and bowls are in the cabinet.

According to what we have learned, we can deduce that the $7$ represents the number of plates and the $3$ the number of bowls.

Let's denote both with a variable $X$.

Now let's set up a simple equation:

$7X+3X=30$

$10X=30$

$X=3$

From here we can infer that the number of plates is $21 (7X)$ and the number of bowls is $9 (3X)$.

We can always go back and check our result by verifying that the total number of utensils in the cabinet is $30$, as seen in the first given data.

Examples and exercises with solutions of Ratio

Exercise #1

Given the rectangle ABCD

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