To easily solve ratio problems and to gain a better understanding of the topic in general, it is convenient to know about equivalent ratios.

Equivalent ratios are, in fact, ratios that seem different, are not expressed in the same way but, by simplifying or expanding them, you arrive at exactly the same relationship.

José and Dani have notebooks and pencils. José has $4$ notebooks and $8$ pencils.

The ratio between the notebooks and pencils that Dani has is the same as José's. Dani has $6$ notebooks. We are asked to calculate how many pencils Dani has.

We see that the number of pencils José has is double the number of notebooks he has. Since we already know that the ratio between notebooks and pencils that José and Dani have is identical, we can deduce that Dani has $12$ pencils ($6$ times $2$, so that the number of pencils is double the number of notebooks).

Examples and exercises with solutions of Equivalent Ratios

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?