B C Ratio Meaning

[Geri Cutcher]

Thenumbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.

Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers.

A more specific definition adopted in physical sciences (especially in metrology) for ratio is the dimensionless quotient between two physical quantities measured with the same unit.[4] A quotient of two quantities that are measured with different units may be called a rate.[5]

For a (rather dry) mixture of 4/1 parts in volume of cement to water, it could be said that the ratio of cement to water is 4:1, that there is 4 times as much cement as water, or that there is a quarter (1/4) as much water as cement.

The meaning of such a proportion of ratios with more than two terms is that the ratio of any two terms on the left-hand side is equal to the ratio of the corresponding two terms on the right-hand side.

Euclid collected the results appearing in the Elements from earlier sources. The Pythagoreans developed a theory of ratio and proportion as applied to numbers.[16] The Pythagoreans' conception of number included only what would today be called rational numbers, casting doubt on the validity of the theory in geometry where, as the Pythagoreans also discovered, incommensurable ratios (corresponding to irrational numbers) exist. The discovery of a theory of ratios that does not assume commensurability is probably due to Eudoxus of Cnidus. The exposition of the theory of proportions that appears in Book VII of The Elements reflects the earlier theory of ratios of commensurables.[17]

The existence of multiple theories seems unnecessarily complex since ratios are, to a large extent, identified with quotients and their prospective values. However, this is a comparatively recent development, as can be seen from the fact that modern geometry textbooks still use distinct terminology and notation for ratios and quotients. The reasons for this are twofold: first, there was the previously mentioned reluctance to accept irrational numbers as true numbers, and second, the lack of a widely used symbolism to replace the already established terminology of ratios delayed the full acceptance of fractions as alternative until the 16th century.[18]

Euclid does not define the term "measure" as used here, However, one may infer that if a quantity is taken as a unit of measurement, and a second quantity is given as an integral number of these units, then the first quantity measures the second. These definitions are repeated, nearly word for word, as definitions 3 and 5 in book VII.

Definition 3 describes what a ratio is in a general way. It is not rigorous in a mathematical sense and some have ascribed it to Euclid's editors rather than Euclid himself.[20] Euclid defines a ratio as between two quantities of the same type, so by this definition the ratios of two lengths or of two areas are defined, but not the ratio of a length and an area. Definition 4 makes this more rigorous. It states that a ratio of two quantities exists, when there is a multiple of each that exceeds the other. In modern notation, a ratio exists between quantities p and q, if there exist integers m and n such that mp>q and nq>p. This condition is known as the Archimedes property.

If there are 2 oranges and 3 apples, the ratio of oranges to apples is 2:3, and the ratio of oranges to the total number of pieces of fruit is 2:5. These ratios can also be expressed in fraction form: there are 2/3 as many oranges as apples, and 2/5 of the pieces of fruit are oranges. If orange juice concentrate is to be diluted with water in the ratio 1:4, then one part of concentrate is mixed with four parts of water, giving five parts total; the amount of orange juice concentrate is 1/4 the amount of water, while the amount of orange juice concentrate is 1/5 of the total liquid. In both ratios and fractions, it is important to be clear what is being compared to what, and beginners often make mistakes for this reason.

Fractions can also be inferred from ratios with more than two entities; however, a ratio with more than two entities cannot be completely converted into a single fraction, because a fraction can only compare two quantities. A separate fraction can be used to compare the quantities of any two of the entities covered by the ratio: for example, from a ratio of 2:3:7 we can infer that the quantity of the second entity is 3 7 \displaystyle \tfrac 37 that of the third entity.

If we multiply all quantities involved in a ratio by the same number, the ratio remains valid. For example, a ratio of 3:2 is the same as 12:8. It is usual either to reduce terms to the lowest common denominator, or to express them in parts per hundred (percent).

If the two or more ratio quantities encompass all of the quantities in a particular situation, it is said that "the whole" contains the sum of the parts: for example, a fruit basket containing two apples and three oranges and no other fruit is made up of two parts apples and three parts oranges. In this case, 2 5 \displaystyle \tfrac 25 , or 40% of the whole is apples and 3 5 \displaystyle \tfrac 35 , or 60% of the whole is oranges. This comparison of a specific quantity to "the whole" is called a proportion.

If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4:3 aspect ratio, which means that the width is 4/3 of the height (this can also be expressed as 1.33:1 or just 1.33 rounded to two decimal places). More recent widescreen TVs have a 16:9 aspect ratio, or 1.78 rounded to two decimal places. One of the popular widescreen movie formats is 2.35:1 or simply 2.35. Representing ratios as decimal fractions simplifies their comparison. When comparing 1.33, 1.78 and 2.35, it is obvious which format offers wider image. Such a comparison works only when values being compared are consistent, like always expressing width in relation to height.

Ratios can be reduced (as fractions are) by dividing each quantity by the common factors of all the quantities. As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers.

Odds (as in gambling) are expressed as a ratio. For example, odds of "7 to 3 against" (7:3) mean that there are seven chances that the event will not happen to every three chances that it will happen. The probability of success is 30%. In every ten trials, there are expected to be three wins and seven losses.

Ratios may be unitless, as in the case they relate quantities in units of the same dimension, even if their units of measurement are initially different.For example, the ratio one minute : 40 seconds can be reduced by changing the first value to 60 seconds, so the ratio becomes 60 seconds : 40 seconds. Once the units are the same, they can be omitted, and the ratio can be reduced to 3:2.

On the other hand, there are non-dimensionless quotients, also known as rates (sometimes also as ratios).[23][24]In chemistry, mass concentration ratios are usually expressed as weight/volume fractions.For example, a concentration of 3% w/v usually means 3 g of substance in every 100 mL of solution. This cannot be converted to a dimensionless ratio, as in weight/weight or volume/volume fractions.

Since all information is expressed in terms of ratios (the individual numbers denoted by α, β, γ, x, y, and z have no meaning by themselves), a triangle analysis using barycentric or trilinear coordinates applies regardless of the size of the triangle.

Moreover, a cursory glance at ancient history shows clearly how in different parts of the world, with their different cultures, there arise at the same time the fundamental questions which pervade human life: Who am I? Where have I come from and where am I going? Why is there evil? What is there after this life? These are the questions which we find in the sacred writings of Israel, as also in the Veda and the Avesta; we find them in the writings of Confucius and Lao-Tze, and in the preaching of Tirthankara and Buddha; they appear in the poetry of Homer and in the tragedies of Euripides and Sophocles, as they do in the philosophical writings of Plato and Aristotle. They are questions which have their common source in the quest for meaning which has always compelled the human heart. In fact, the answer given to these questions decides the direction which people seek to give to their lives.

Philosophy's powerful influence on the formation and development of the cultures of the West should not obscure the influence it has also had upon the ways of understanding existence found in the East. Every people has its own native and seminal wisdom which, as a true cultural treasure, tends to find voice and develop in forms which are genuinely philosophical. One example of this is the basic form of philosophical knowledge which is evident to this day in the postulates which inspire national and international legal systems in regulating the life of society.

4. Nonetheless, it is true that a single term conceals a variety of meanings. Hence the need for a preliminary clarification. Driven by the desire to discover the ultimate truth of existence, human beings seek to acquire those universal elements of knowledge which enable them to understand themselves better and to advance in their own self-realization. These fundamental elements of knowledge spring from the wonder awakened in them by the contemplation of creation: human beings are astonished to discover themselves as part of the world, in a relationship with others like them, all sharing a common destiny. Here begins, then, the journey which will lead them to discover ever new frontiers of knowledge. Without wonder, men and women would lapse into deadening routine and little by little would become incapable of a life which is genuinely personal.

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