# What is Ratio: Definition and 1000 Discussions

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
The numbers 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.
A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient a/b. Equal quotients correspond to equal ratios.
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. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.

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1. ### Ratio Test vs AST

Hi, I'm having difficulty understanding why the interval of convergence is (0, 18]. When I tested x=18, I got the following conclusion using the ratio test. When I attempt using AST, the function still diverges as the lim (n -> inf) = 2^n / n ≠ 0. What am I missing? Thanks!
2. ### Ratio of frequency between heavier and lighter part of composite cord

Is the answer 1? Because the cord is connected to vibrating source and it vibrates with a frequency of 100 Hz so section A and B have the same frequency Thanks
3. ### Is a Distribution Function a Ratio of Differentials?

I read on a post here titled 'Understanding Fourier Transform for Wavefunction Representation in K Space' that if one represents the squared-amplitude as a ratio of differentials, the solution is given. Letting the squared-amplitude be ##\phi##. $$\frac{d\phi}{dp}=\frac{d\phi}{dk}\frac{dk}{dp}$$...
4. ### Use Saha-Boltzmann statistics to get the relative number densities

When I am using the Saha equation, how i am suppose to know the electron pressure? Which are required to calculate the ration? Since: P_e = n_ekT (electron pressure and n_e is related to each other, but n_e is also unknown based on my understanding).

35. ### I Gearbox Gear ratio: How to get 60 rpm to 3500rpm? help please

Hello I am trying to achieve 3500 rpm from 60rpm. The gear ratio I have worked out is 58:1. To minimize the size I have divided into 4 levels with the gear ratio of 2:1, 3.1, 3.1, 3,1, which rounds me up to 54:1 ratio is also ideal for me can anyone please help mw find the appropriate solution...
36. ### Understanding the Ratio Test for Series and Its Applications

So I am having some difficulty expressing this series explicitly. I just tried finding some terms ##b_{0} = 5## I am assuming I am allowed to use that for ##b_{1}## for the series, even if the series begins at ##n=1##? With that assumption, I have ##b_{1} = -\frac {5}{4}## ##b_{2} = -...
37. ### Age Word Problem Involving Ratio

The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them. I never saw an age problem involving a ratio but let's see. Abraham to Adam = 5 : 7 Let x = present age of Abraham and Adam. Age of Abraham = 5x...
38. ### Pulley system for cardboard pulp shredder/mixer

Hi everybody, first message on this forum ! I am building a machine for a friend who works with cardboard pulp, he is also a performance artist and would like a machine where 2 or 3 performers can activate the machine by hand with pulleys and wheels, and shred the pieces of cardboard that are...
39. ### How do I calculate the ratio of forces between two conducting spheres?

Here are the answer choices: a) F1 = 2F2 b) F1 = 8F2 c) 2F1 = F2 d) F1 = 4F2 e) F1 = F2 I figured that Coulomb's law would tell us the magnitude of the forces are identical, so I answered E, but that was incorrect. (Screenshot of question attached)
40. ### How to Find the "Net Change Ring Area Ratio" for the Zeeman Effect

To find ##\delta## for the 1st order, all I need to do is to square the diameter of the 2nd ring and subtract it to the square of the diameter of the first ring. $$\delta_{1st \; order} = {d^2}_{2nd \; ring} - {d^2}_{1st \; ring}$$ To find ##\Delta##, I can use the below equation...
41. ### Engineering What is a low slenderness ratio for a column?

What counts as a low slendernous ratio. i was look at column slenderness ratios and stress, it was talking about a column with slenderness ratio of 80-90 and stress of 300MPA. Is 300MPA low or high stress. Wanted to know so i can say wheather the low ratio says that it will fail at high or...
42. ### What's the deal with plasma physicists setting heat cap. ratio to 3?

This has persistently bugged me in my intro plasma course. They keep using ##\gamma = 3## aka ##N_d = 1## (where ##N_d## is the number of degrees of freedom in the molecule) as an approximation. See for example, the Bohm-Gross dispersion curve. I can tell you from deriving this that the factor...
43. ### Calculate the charge to mass ratio in this mass spectrometer problem

2(7.28E+08) / (0.038^2) R^2 i don't know how to get r
44. ### A Calculate variance on the ratio of 2 angular power spectra

In the context of Survey of Dark energy stage IV, I need to evaluate the error on a new observable called "O" which is equal to : O=\left(\frac{C_{\ell, \mathrm{gal}, \mathrm{sp}}^{\prime}}{C_{\ell, \mathrm{gal}, \mathrm{ph}}^{\prime}}\right)=\left(\frac{b_{s p}}{b_{p...
45. ### Can I series buck converters to get higher stepdown ratio?

I have two capacitors in series across my bus. I have a some series resistors across the capacitors for voltage balancing. I would like to power some low voltage low voltage components tapping off of the voltage divider using that as the voltage supply. The bus voltage will be approximately 2...
46. ### Finding I3: Resistance Ratio Calculation

Should it be I3 = \frac{(R2+R4)}{(R2+R4) +R3} I or I3 = \frac{R2}{R2 +R3} I
47. ### Propeller with bell lift distribution has best thrust/power ratio?

This source http://sustainableaviation.org/sas2017/session/prandtl-wing-maximum-efficiency/index.html claims : "Bell lift distribution can be applied to propulsion systems (no more “minimum induced loss”). We believe this results in a gain of 15.4% thrust for the same input torque/power." Bell...
48. ### Propeller blade lift distribution for best thrust/power ratio?

What is ideal lift distribution for propeller blade to get best thrust/power ratio? To do this blade must has minimum drag, because drag releted to torque,and torque x RPM= power..
49. ### MHB Demonstration of a formula for the ratio between the hypotenuses of two triangles

Hello, everybody: I am a philologist who is fond of mathematics, but who unfortunately has just an elementary high school knowledge of them. I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of...
50. ### Finding the ratio of the fluxion of x using Newton's method

I was asked to find the ratio of the fluxion of x to the fluxion of 1/x using Newton's synthetic method of fluxions. I do not understand how to do this.