**The proportions** . Equality between two ratios is called proportion. The theory of proportions was developed by the great Greek mathematician Eudoxio_de_Cnidos . His original work on the theory of proportions did not arrive until the present time, but thanks to one of his successors, Euclid of Alexandria , this theory was known, since he collected it in his book V of the Elements .

## Summary

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- 1 Ratios and proportions
- 1 Reason
- 2 Proportion

- 2 Proportionality
- 1 Direct proportionality
- 2 Inverse proportionality

- 3 Source
- 4 See also

## Ratios and proportions

### Reason

The ratio is the relationship between two numbers , defined as the ratio of one number to the other. So:

The ratio between two numbers a and b is the fraction and read **a** is a **b** . This ratio can also be written **to: b** .

To find the ratio of two numbers, form the quotient between them and simplify them as much as possible.

For example, the ratio between 10 and 2 is 5, since 10/2 = 5

### Proportion

Given two reasons and we will say that they are in proportion if =

The terms **a** and **d** are called extremes while **b** and **c** are the means.

In every proportion the product of the extremes is equal to the product of the means

= ** ****⇒**** a · d = b · c**

## Proportionality

Many times in practice we are presented with situations in which the value or quantity of one quantity depends on the value of the other.

For example, if a meter of fabric is priced at $ 10, the cost of a fabric cut depends on how many meters the length is. The greater the number of meters of fabric, the higher the cost.

### Direct proportionality

When two magnitudes are related so that the values of one of them are obtained by multiplying the corresponding values in the other by the same number, they are said to be **directly proportional**

In the fabric meter example, the cost of fabric cutting is obtained by multiplying the length of the cut by the price of one meter which is $ 10. We can then say that the cost of a fabric is directly proportional to the length of the cut . The number by which it is multiplied is called **the proportionality factor. **In this case 10 is that factor.

In direct proportionality, any two quantities of a magnitude and their corresponding quantities in the other form a proportion.

### Inverse proportionality

There are other forms of relations between magnitudes in which the behavior is different from that of the examples given of direct proportionality, in these cases, if the values of one increase, the corresponding values in the other decrease.

For example, if a car travels with a certain speed and increases it, the time it takes to reach its destination decreases.

When two magnitudes are related so that the values of one of them are obtained by multiplying by the same number the reciprocals of the corresponding values of the other magnitude, they are said to be **inversely proportional**