# Reason - Examples, Exercises and Solutions

## What is direct proportion?

Direct proportionality indicates a situation in which, when one term is multiplied by a certain amount, the same exact thing happens to the second term.

In the same way, when one term is divided by a certain amount, the same exact thing happens to the second term.

The ratio between both magnitudes remains constant.

Let's observe an example that illustrates this concept.

## Practice Reason

### 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?

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?

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

$6\frac{1}{4}$

### 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?

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

$6\frac{1}{4}$

### Exercise #1

How many times longer is the radius of the red circle than the radius of the blue circle?

5

### Exercise #2

How many times longer is the radius of the red circle, which has a diameter of 24, than the radius of the blue circle, which has a diameter of 12?

2

### Exercise #3

How many times longer is the radius of the red circle than the radius of the blue circle?

### Video Solution

$2$

### Exercise #4

How many times longer is the radius of the red circle than the radius of the blue circle?

### Video Solution

$2\frac{1}{2}$

### Exercise #5

How many times longer is the radius of the red circle (14 cm) than the radius of the blue circle, which has a diameter of 7?

4

### Exercise #1

ABCD is a deltoid with an area of 58 cm².

DB = 4

AE = 3

What is the ratio between the circles that have diameters formed by AE and and EC?

3:26

### Exercise #2

Given the rectangle ABCD

AB=X

The ratio between AB and BC is $\sqrt{\frac{x}{2}}$

We mark the length of the diagonal A the rectangle in m

Check the correct argument:

$m^2+1=(x+1)^2$

### Exercise #3

Given the rectangle ABCD

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

We mark the length of the diagonal $A$ with $m$

Check the correct argument:

$x^2+2x=m^2$