## What is a reason?

Let's consider a race car with **4m** in length and a kart with **2 m** of lenght. To compare the measurements of cars, just divide the length of one by the other. Like this:

(The size of the race car is twice the size of the go-kart).

We can also say that the kart has half the length of the race car.

The comparison between two rational numbers, through a division, is called **reason**.

The reason it can also be represented by 1: 2 and means that each meter of the kart corresponds to 2m of the race car.

We call it**reason**between two numbers

*The*and

*B*(

*B*non-zero)

the quotient or

*a: b*.

The word **reason**, comes from Latin *ratio*, and means "division". As in the previous example, there are several situations in which we use the concept of reason. Examples:

Of the 1200 entered in a competition, 240 candidates passed.

Reason for successful candidates:

(out of 5 applicants registered, 1 was approved).

For every 100 guests, 75 were women.

Ratio between number of women and number of guests:

(out of every 4 guests, 3 were women).

Comments:

1) The ratio between two rational numbers can be presented in three ways. Example:

Ratio between 1 and 4: 1: 4 or or 0.25.

2) The ratio between two rational numbers may be expressed with a negative sign, provided that their terms have opposite signs. Examples:

The ratio between 1 and -8 is .

The reason between é .

Next: Terms of a Reason