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In mathematics, the ratio is a binary relationship between magnitudes (that is, objects, people, students, tablespoons, SI units, etc.), generally expressed as "a to b" or a:b. In the case of numbers, every reason can be expressed as a fraction and eventually as a decimal. For example, if the ratio of the height of two trees is 3:5, it means that if the height of the first tree is 3 meters, the height of the second will be 5 meters. Or if the height of the first is 9 meters, then the second will be 15 meters. According to the analysis, the change in the ratio of the old partner with the entry of a new partner is called a ratio.
Sometimes arithmetic ratio and geometric ratio are discussed in the context of arithmetic progressions and geometric progressions, respectively. In both cases, the ratio is understood as the relationship between two consecutive terms of the sequence, called antecedent and consequent, this relationship being the difference in the case of arithmetic progressions and the quotient in the case of geometric progressions. Traditionally, the number resulting from this difference or quotient has been called the exponent or exponent of the ratio. In general, reason is understood as the dimensionless quotient between two numbers, and it is in this sense that we talk about aspect ratio in an image or teacher-student ratio in an educational center.
The ratio between numbers A and B can be expressed as:
The numbers A and B are sometimes called terms, with A being the antecedent and B the consequent. Represented by a fraction, the numerator is the antecedent term and the denominator is the consequent term.
The ratio of two or more quantities of the same species is the quotient of the numbers that express their measures, considered in the same unit. Quantities are characteristics of objects that can be compared and whose measures can be added, subtracted or divided by one another.
Thus, the concept of reason allows us to make comparisons of magnitude between two numbers. For example, to find out how many times the number 100 is greater than the number 2 (or in other words, the ratio between 100 and 2), we proceed as follows:
100 : 2 = 50
Therefore, the number 100 is 50 times greater than the number 2.
The ratio is the relationship between two quantities that are already related, it is a division between two values, an example is the ratio between a perimeter and the measurement of one side of a triangle, the ratio would be the perimeter divided by the measurement of the side.
The quantities being compared for a reason can be physical quantities such as speed, or they can refer simply to the number of objects in particular. A common example of the latter case is the ratio of the volume of water to that of cement used in concrete, which is usually 1:4. This means that the amount of cement used is four times greater than that of water. The reason gives no indication of the total amount of water and cement used, nor how much concrete is being made. Equivalently, it could be said that the ratio of cement to water is 4:1, or that the amount of water is a quarter (1/4) of that of cement.
The older models of televisions have screens (screens) in which the ratio between width and height is 4 to 3, that is, whose height is equivalent to three quarters of the width. Modern widescreen TVs have a 16:9 aspect ratio.