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

There are 18 balls in a box, $\frac{2}{3}$ of which are white.

How many white balls are there in the box?

Video Solution

Answer

12

Exercise #2

In a box there are 28 balls, $\frac{1}{4}$ of which are orange.

How many orange balls are there in the box?

Video Solution

Answer

7

Exercise #3

There are two circles.

One circle has a radius of 4 cm, while the other circle has a radius of 10 cm.

How many times greater is the area of the second circle than the area of the first circle?

Video Solution

Answer

$6\frac{1}{4}$

Exercise #4

There are two circles.

The length of the radius of circle 1 is 6 cm.

The length of the diameter of circle 2 is 12 cm.

How many times greater is the area of circle 2 than the area of circle 1?

Video Solution

Answer

They are equal.

Exercise #5

There are two circles.

The length of the diameter of circle 1 is 4 cm.

The length of the diameter of circle 2 is 10 cm.

How many times larger is the area of circle 2 than the area of circle 1?

Video Solution

Answer

$6\frac{1}{4}$

Do you know what the answer is?

Question 1

There are two circles.

The length of the diameter of circle 1 is 4 cm.

The length of the diameter of circle 2 is 10 cm.

How many times larger is the area of circle 2 than the area of circle 1?