In the world of Physics as well as the world in general both rate and ratio are very important tools that are used to understand various quantifiable quantities that are present in nature. It is with the help of these mathematical tools that we are able to understand how various things happen and how they operate around us.

The terms rate and ratio are mainly used in the fields of physics, mathematics, finance, business, etc. Both of these terms are very simple to understand, but since they used the same mathematical function, that is division, to be calculated, hence it is understandable that there might be some confusion between these two terms.

**Rate vs Ratio**

The difference between rate and ratio is that rate can have more than one type of quantity while ratio has only a single type of quantity, and hence it is dimensionless.

Rate is the amount by which a single quantity changes with respect to one or more other quantities. One is usually familiar with the term rate of change of a quantity with respect to another quantity.

Ratio tells us about the relationship of how quantity varies when another quantity varies at the same time. However, it is important to note that both the quantities used in a ratio belong to the same unit.

**Comparison Table between Rate and Ratio**

Parâmetros de comparação | Taxa | Razão |

Definição | Rate defines the amount of change of one quantity with respect to another quantity. | Ratio tells us about the relationship between two quantities. |

Dimensão | Rate has a dimension of one or more. | Ratio is dimensionless. |

Dependência | Usually, the numerator is dependent on the denominator. | Usually, both are mutually dependent. |

Usar | Rate is mostly used in science and finance. | Ratio is mostly used in science and mathematics. |

Variation | The numerator usually varies while the denominator has a unit value. | Both the numerator and the denominator change if either of them alters the value. |

**What is Rate?**

Rate is the amount by which a single quantity changes with respect to one or more other quantities. One is usually familiar with the term rate of change of a quantity with respect to another quantity. So basically read tells us how often or how frequently does the value of a single quantity change while the other quantities stay fixed at a certain value. Usually, the quantity of the denominator is equal to one so that any change which occurs in the numerator can be easily analyzed or calculated.

The most common forms of rate which we use in our day to day life include that of speed, acceleration, price of vegetables, etc. When we say that a car is moving at a hundred kilometers per hour (100 km/hour) we mean to say that the car covers a distance of hundred kilometers every single hour. This is an example of a rate, which shows the change of distance with respect to time.

Another such example is the price of vegetables. Suppose we say that a dozen bananas cost 30 rupees. This is an example of a rate because for every dozen bananas the price is 30 rupees.

One very important feature to note about rate is that rate will always have one or more dimensions. This is because the units in the numerator and denominator denote different quantities hence and division they do not cancel each other out, which is why the final quantity which is created by the date has some kind of dimension.

**What is Ratio?**

Ratio tells us about the relationship of how quantity varies when another quantity varies at the same time. However, it is important to note that both the quantities used in a ratio belong to the same unit. While studying in school people are most familiar with the term ratio used in the subject of mathematics, and the definition of this term remain the same across all subjects.

Ratios are used in various subjects for various purposes, whether it is in mathematics to calculate the circumference of a circle, or whether it is in science to calculate the molarity of a solution, or anywhere else.

It is important to note that, in a ratio, the numerator or the denominator need not necessarily be a unit quantity. However, both the numerator and denominator should be reduced as much as possible. This means that there should be no common factor between the denominator and numerator.

Ratio was also useful to analyse demographics. One of the most common ratios used as a demographic tool is the sex ratio of a country. The sex ratio tells us about the number of women in a country per thousand men. In special cases like these where either the numerator the denominator is specified one need not reduce these terms to the lowest possible value.

The values in a ratio follow a proportion, and if one increases the other increases proportionately. Similarly if one decreases the other decreases proportionately too.

**Main Differences Between Rate and Ratio**

- The main difference between rate and ratio is that rate shows the amount of change undergone by a quantity with respect to another quantity, while ratio tells us how two quantities are related quantitatively.
- Rate has a dimension of one or more than one, while ratio is dimensionless.
- In rate often the numerator depends on the denominator, while in ratio both, the numerator and the denominator are mutually dependent.
- Rate is mostly used for science and finance, while ratio is mostly used for science and mathematics.
- In rate the numerator usually varies while the denominator has a unit value, while in ratio both of these values vary at the same time.

**Conclusão**

Tools such as rate and ratio are important in understanding the physical world around us. They are also important for analysis purposes like that in finance, business, surveys, etc.

One very convenient thing about them is that they have a simple mathematical formula and easily calculated. Understanding and interpreting rate and ratio can help simplify things such as a presentation and become more informative and interesting.

**Referências**

- https://link.springer.com/article/10.1023/A:1022318321416
- https://journals.sagepub.com/doi/abs/10.1177/0956797615617799

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