ratio

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ratio.

The ratio of two quantities expressed in terms of the same unit is the fraction that has the first quantity as numerator and the second as denominator. For example, if in a group of 100 people 5 die, the ratio of deaths to the total number in the group is 5/100=1/20=.05. Ratios are indicated also by writing the two values with a colon between them, e.g., the ratio of 4 to 8 can be expressed by 4:8 as well as by 4/8.

Ratio

A relationship in magnitude, quantity, or degree between two or more similar things.

Ratio

 

The ratio of two numbers is the quotient from the division of the first number, by the second. The ratio of two homogeneous magnitudes is the number obtained by measuring the first magnitude when the second is chosen as the unit of measurement. If two magnitudes are measured in the same unit of measurement, their ratio is equal to that of the numbers that measure them.

The ratio of the lengths of two segments may be expressed by a rational or irrational number. In the former case the segments are said to be commensurable, and in the latter incommensurable. Mathematicians of the ancient world had no knowledge of irrational numbers. For them the concept of the ratio of two segments did not reduce to the concept of number. In their conception the geometrical theory of the ratios of magnitudes was not connected with the concept of number and played an independent role. In a sense, it substituted for a theory of real numbers. Indeed, according to Euclid the four segments, a, b, a’, and b’ form the proportion a: b = a’:b’ if for any natural numbers m and n one of the relations ma = nb, ma > nb, ma < nb is satisfied simultaneously with the corresponding relation ma’ = nb’, ma’> nb’, or ma’ < nb’. It follows that when a and b are incommensurable the subdivision of the rational numbers (x = m/n) into two classes according to whether a > xb or a < xb coincides with the subdivision according to whether a’ > xb’ or a’ < xb’ —this is the idea behind the modern theory of Dedekind cuts.

ratio

[′rā·shō]
(mathematics)
A ratio of two quantities or mathematical objects A and B is their quotient or fraction A / B.

ratio

Maths a quotient of two numbers or quantities
References in classic literature ?
Thus the progress of the Hawiians and Tahitians to utter extinction is accelerated in a sort of compound ratio.
Perfection of loveliness, they say, is in the direct ratio of the extent of this lump.
George's mind, as he paced the pier, was divided between the beauties of Nature and the forthcoming crisis in his affairs in the ratio of one-eighth to the former and seven-eighths to the latter.
In dirty upper casements, here and there, hazy little patches of candlelight reveal where some wise draughtsman and conveyancer yet toils for the entanglement of real estate in meshes of sheep-skin, in the average ratio of about a dozen of sheep to an acre of land.
I could understand the reason for this, as with the narrowing expanse of Omean as the waters rose toward the apex of its dome, the rapidity of its rise would increase in inverse ratio to the ever-lessening space to be filled.
Personal rights, universally the same, demand a government framed on the ratio of the census; property demands a government framed on the ratio of owners and of owning.
Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.
It was altogether repulsive to him, and he never entered into any calculation of the ratio between the Vicar's income and his more or less necessary expenditure.
And in the same ratio had it made any other life distasteful to him.
That swing of the shoulders that had frozen the timid when he was but a lad had increased with his growth and education at the ratio of ten to one.
You may have observed that the indisposition to write a merely social letter is in the ratio of the square of the distance between you and your correspondent.
The estimation in which these gentlemen were held, according to one of the most scientific exponents of the Gun Club, was "proportional to the masses of their guns, and in the direct ratio of the square of the distances attained by their projectiles.