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).


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