Ratio Definition and 1000 Threads

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. K

    MHB Solve Ratio Word Problem: Find Value of x

    hi , this is one simple math but i am not getting the answer. the work done by (x-3) men in (2x+1) days and the work done by (2x+1)men in (x+4) days are in the ratio of 3:10.find the value of 'x'.
  2. K

    MHB Solving Ratio and Proportion Problem: (a+b+c)^2/(a^2+b^2+c^2)

    hi , i am stuck with a problem . the problem is if a , b , c are in continued proportion ,then prove that (a+b+c)^2/(a^2 +b^2 +c^2) =(a+b+c)/(a-b+c) i have tried solving the problem in different way like breaking the formula of (a+b+c)^2 =a^2 +b^2 +c^2 + 2ab +2bc+2ca , then used...
  3. J

    MHB Proportions and Equations: Can You Prove a Ratio with this Equation?

    if x/(b+c-a)=y/(c+a-b)=z/(a+b-c) prove that.. x(by+cz-ax)=y(cz+ax-by)=z(ax+by-cz)
  4. A

    Why is C-14 Radioactive Despite Low N/P Ratio?

    Why c - 14 is radio active though n/p ratio is less than 1.5?
  5. H

    Transformers Turn ratio versus Impedence ratio

    Hello, This is my first post, so I hope this is in the right section and format. I've looked all over the web, but I can't find anything that addresses my question clearly. I know that for an ideal transformer to not lose any power, the turn ratio has to be the square root of the...
  6. L

    Help Poisson's Ratio Calculation Problem

    Hi. I can't seem to see where I am going wrong or if i have gone wrong as the answer I got for Poissons Ratio looks incorrect. Can anyone help or point me in the right direction? Thanks. An axial load of 28.5kN is applied to a bar of length280mm, width 38mm and thickness 21mm. After the load...
  7. R

    Stoichiometric ratio calculation

    Dear all, I am trying to synthesis a compound as given the paper below. Can someone help me of how to calculate the stoichiometric ratio and amount of each compound (i.e. Nd pieces, As, Fe, Fe2O3, FeF3 powders) required to prepare the same compound as in that paper. Especially I don’t know...
  8. J

    Obtaining yield stress knowing only Poisson's ratio and UTS?

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  9. B

    Poissons ratio close-packed spheres

    Hello, See question 7.4 from the link. http://books.google.com/books?id=0N0...ow&w=685&w=800 "Assuming that atoms are hard elastic spheres, show that Poisson's ratio for a close-packed array of spheres is 1/3" I am having trouble explaining the proof for this. I know the that the...
  10. B

    Poissons ratio close-packed spheres

    Hello, See question 7.4 from the link. http://books.google.com/books?id=0N06swAJI0AC&pg=PA338&img=1&zoom=3&hl=en&sig=ACfU3U1qlbfJCRXsRow1xzu7hxEWOjYCow&w=685&w=800 "Assuming that atoms are hard elastic spheres, show that Poisson's ratio for a close-packed array of spheres is 1/3" I...
  11. B

    Time above ground question involving ratio

    In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat the athlete as a particle and let ymax be his maximum height above the floor. To explain why he seems...
  12. V

    Ratio of velocities between proton and electron?

    Homework Statement An electron and a proton are separately placed at rest midway between two oppositely charged metal plates. A) Which way will the electron accelerate? B) Which way will the proton accelerate? C) Which particle, if either, will acquire more kinetic energy just before striking...
  13. C

    MHB Sum series- Prove the equality of ratio and root.

    I found this on the internet, but did not find the proof. Curious to me is that the the ratio and root test have the same conditions. How can i basically prove this equality? \frac{a_{n+1}}{a_{n}} = \sqrt[n]{a_{n}} Thank you!
  14. D

    What is the terminology for this geometry ratio?

    So if we imagine a rectangle. The aspect ratio is width/height. What if you want the ratio of the parallel sides? Is there a terminnology for that ratio?
  15. A

    Ratio of charges in thomson expt

    Homework Statement three particles having charges 1:2:3 produce the same point on the photographic film in the thomson experiment. The masses are in the ratio of a) 1:2:3 b)3:2:1 c) 2:3:1 d) 1:3:2 Homework Equations a = F/m = Eq/m The Attempt at a Solution Since all the...
  16. M

    How Much Farther Would a Car Skid on Wet Concrete?

    "A driver makes and emergency stop and locks up the brakes of the car, which skids to a stop on dry concrete. Consider the effect of rain on this scenario. If the coefficients of kinetic friction for rubber on dry and wet concrete are μk (dry)=0.80 and μk(wet)=0.50, how much farther would the...
  17. K

    Need some tips in designing a deep ratio helical gear pair

    Hi, For a final drive of a light commercial truck, I have to design a final drive helical gear pair. The expected ratio is 8.2. The centre distance is 134 mm. The input max. torque is 120 Nm. I have sized few combinations. I have a feeling that this ratio is too deep. Pl. share me your...
  18. J

    Chemistry What is the mole ratio of NaOH to C8H8O3 in this reaction?

    Homework Statement We are given the fact that 0.12 mol NaOH reacts with 0.015 mol methyl salicylate (C8H8O3) to form disodium salicylate (C7H4Na2O3). We're asked to calculate the mole ratio of NaOH to C8H8O3, identify the limiting reagents, and find the theoretical yield. Homework Equations...
  19. R

    Solving the Train Length Ratio Puzzle

    Homework Statement Two trains, A and B, are moving towards each other with relative speed 0.8c. The passing of the two trains (from when their fronts align to when their backs align) takes 20% longer as observed from train A as is does as observed from train B. What is the ratio of the length...
  20. maistral

    Ergun Equation reulting to zero pressure ratio

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  21. R

    The ratio of the gravitational force between electron and proton

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  22. C

    MHB Quit Ratio - Function Question

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  23. B

    Calculating Moles Ratio of Reactants for Yield f in K Equilibrium

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  24. R

    Symbols used to represent surface area Ratio in Refrigeration

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  25. Fernando Revilla

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  26. R

    Refrigeration Heat Exchanger Area Ratio Optimization

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  27. siddharth23

    Maximum transmission ratio of a spur gear pair

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  28. H

    Why does high contact ratio in gear result in inefficiency?

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  29. L

    Help to find force given a diameter reduction (Poissons Ratio)

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  30. J

    Reply to an old thread on the ratio of parabolas

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  31. C

    Estimating the damping ratio from the waveform graph

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  32. E

    When triangles are similar, ratio of corresponding sides is equal.

    "When triangles are similar, ratio of corresponding sides is equal." "When triangles are similar, ratio of corresponding sides is equal." I was wondering if there is any theoretical proof for this statement or is it only experimental?
  33. P

    What Is the Ratio of Baryonic to Dark Matter in the CMB?

    What is the observed DM ratio in CMB ? Is there observational evidence for the DM ratio in the CMB? Other then the info-graph from Wikipedia which I was explained is based on the assumption of DM being the same total amount back then but the mass of relativistic particles was higher. Would...
  34. paulmdrdo1

    MHB Converting a repeating decimal to ratio of integers

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  35. A

    Polarization: ratio of transmitted to incident intensity

    Homework Statement A beam of unpolarized light is incident on a series of three polarizers as shown. The angle of the transmission axis of each polarizer is indicated by the dashed line, with q1 = 110, q2 =230, and q3 = 370 (all defined relative to vertical). What is the ratio of the...
  36. U

    Find Ratio of Integrals: $\lim_{n \to\infty} I_n/I_{n-2}$

    Homework Statement If I_n = \displaystyle \int^1_0 x^n. \sqrt{1-x^2} dx then \lim_{n \to \infty} \dfrac{I_n}{I_{n-2}} is equal to Homework Equations The Attempt at a Solution Integrating by parts x^n \displaystyle \int \sqrt{1-x^2}dx - \int nx^{n-1} \int \sqrt{1-x^2} dx But...
  37. V

    Has the Proton:Electron Mass Ratio Been Solved Yet?

    Reading my old copy (3rd edition) of H&R's Fundamentals of Physics and it states that no theory can predict the value of the proton:electron mass ratio to date, and that it's a "sure-fire" Nobel Prize problem. Has this been resolved yet? Can't find anything on the web. Thanks in advance.
  38. J

    Limit Ratio Test: Solving $$\sum_{n=1}^{\infty}\frac{1}{2^n}$$

    Homework Statement $$ \sum_{n=1} ^\infty\frac{1} {2^n} $$ Homework Equations The Attempt at a Solution I know just by looking at it that it converges no problem. You do the ratio test and you get something of the form \displaystyle\lim_{n\rightarrow \infty}...
  39. H

    What is the angle of an incline with a ratio of 1:25?

    Hey, I need to calculate the angle of an incline, But they only give me the ratio of 1:25, The only thing i can think of what to do is, 1 / 25 = 0.04 then 100% x 0.04 = 4 degrees, Im i right in asuming this?
  40. Fernando Revilla

    MHB  Use the Ratio Test for Convergence/Divergence

    I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.
  41. A

    Kinetic energy of two different masses (ratio)

    Homework Statement Two masses, one of 20kg and the other of 40kg, are pushed using the same force on the same distance. What is the ratio of the kinetic energy? (Kinetic energy of 20kg/kinetic energy of 40kg) Homework Equations Ek=mv^2 F=ma v=at The Attempt at a Solution So, I...
  42. D

    Ratio test for math convergence

    Homework Statement show ## \sum \frac{x^{2}}{(1+x^{2})^{n}} ## converges uniformly on R Homework Equations The Attempt at a Solution I know by ratio test it is absolutely convergent for all x in R. I am guessing you use m-test. However I do not really understand how...
  43. C

    Quantum Harmonic oscillator, <T>/<V> ratio

    Homework Statement Consider an electron confined by a 1 dimensional harmonic potential given by ## V(x) = \dfrac{1}{2} m \omega^2 x^2##. At time t=0 the electron is prepared in the state \Psi (x,0) = \dfrac{1}{\sqrt{2}} \psi_0 (x) + \dfrac{1}{\sqrt{2}} \psi_4 (x) with ## \psi_n (x) = \left(...
  44. S

    Propeller Driven Aircraft with Thrust to Weight Ratio Greater than One

    Hello all, this is my first post. I was wondering if any of you could point me in the direction of a source with details on propeller aircraft able to produce a T / W Ratio greater than one. Thank You!
  45. V

    Likelihood Ratio Statistic & P-value

    Homework Statement Homework Equations So far I have only worked on question 1, as I was not able to solve it. The likelihood ratio test statistic is defined as follows: λ = 2 Log(L(theta-hat)/L(theta-hat_0)) Where L is the likelihood function, the product of all the pdfs/pmfs, and theta-hat is...
  46. P

    The ratio between temporal lengths is frame-invariant

    Hi, I am a researcher in (analytical) philosophy. I am writing a paper on the conventionalism vs. objectvism about temporal metric, which is focused on a problem that arises before any relativistic consideration. However, in a note, I just wrote the following "the ratio between temporal lengths...
  47. R

    What is the air-fuel ratio for liquid petrol

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  48. F

    Ratio test (convergent or divergent?)

    Homework Statement ∞ Ʃ n / 2^n n=1 Homework Equations ratio test lim |a(n+1) / a(n)| n->∞ The Attempt at a Solution I have the answer and the steps its just there's one part I am confused on, first I just apply n+1 to all my n terms, which gives me, ∞ Ʃ...
  49. D

    Signal to Noise ratio calculation

    A 200mv peak to peak sinusoidal signal is applied to an ideal 12 bit A/D converter, for which Vref(v p-p full scale) is 5v. Find signal to noise ratio. This is a problem worked out by one of my lecturer and the answer seems to be 46dB. But I am confused on his method. Is there anyone who...
  50. D

    Ratio of product to difference - terminology?

    Is there a specific mathematical term, which refers to this expression? A * B ------ A - B
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