Ratios Definition and 224 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.

View More On Wikipedia.org
Recent contents Top users
  1. A

    What can we conclude about the phenotypic ratios in these genetic crosses?

    Phenotypic ratios help... Hello all, I am trying to do some revision on basic genetics for a biology exam coming up; there is one practice question I cannot understand, I was hoping if someone could verify how the answer came to be ^^. The question is below: Color of lentils is determines...
  2. W

    Dark Fringe Ratios: Which Slit is Widest and What is the Ratio?

    Homework Statement Two different single slits are used in an experiment involving one source of monochromatic light. With slit 1 in place, the first dark fringe is observed at an angle of 45 degrees. With slit 2, the first dark fringe is observed at an angle of 55 degrees. a) Which slit is...
  3. M

    Effective Area Ratio for Sky Diver's Terminal Speeds?

    The terminal speed of a sky diver is 170 km/h in the spread eagle position and is 305 km/h in the nose dive position. a) Assuming the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross section area in the slower position to that in...
  4. H

    Why do cosine and secant have the same sign in all quadrants?

    Identifying the signs of ratio in four quadrants. It turns out that -ive trignometric identity will be negative but not for cos and sec. But why?
  5. S

    Masses and ratios of steller objects

    Homework Statement The question is really long, so I am going to summarize the information that I have for the problem. I have two stars with their radial velocities Star1= 5.4 and Star2 = 22.4. The time period between first contact and minimum light is .58 days, the length of primary minimum...
  6. Loren Booda

    Infinite product of consecutive odd/even, even/odd ratios

    ?=\prod_{n=1}^\infty(n/(n+1))
  7. D

    Finding Mole Ratios of 3 Substances

    How can you find mole ratios for 3 substance ex 2.94 X 10 to the 5 of NH3 1.56 X 10 to the 5 O2 9.61 X 10 to the 3 CH4
  8. B

    Solving Force & Mass Ratios: Find m1/m2 & Acceleration

    Homework Statement A force F applied to a mass m1 produces an acceleration of 3.0 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.0 m/s2. a. Find the value of the ratio m1 / m2. b. If m1and m2 are combined, what will be the acceleration of...
  9. O

    Simple Ratios problem from old SAT book

    Homework Statement Aggregate # of nickels and dimes = 20 coins. If the ratio between nickels and dimes is 2:3, what is cent value of 20-coin set? Homework Equations 2x = 3y The Attempt at a Solution 20 = nickels(x)+dimes(y); ratio = 2x:3y; 2x = 3y; y = 2x/3 20 = x + 2x/3; x...
  10. H

    Gear Ratios and Progressive slowing?

    I would like to take a line of rope and slow it down to a stop in a relative short period of time using a gear mechanism that would activate when touched to the reel wheel. Any suggestions on something that may already be out there or perhaps the easiest way to go about doing this? Thank you for...
  11. F

    Explaining Bicycle Gear Ratios to Non-Physicists

    I am a cyclist and am starting to think about gear ratios. I have counted teeth on my bike gears (touring) and calculated ratios and the results do not make sense to me. I am left with the beliefe that ratio is not all at work here. It seems that it also has to do with the diameter of the gear...
  12. I

    A quick question about gear ratios and how to find them

    I was not sure where to put this since it is both engineering and math so feel free to move it but to the point I have a few small engines I am going to use on a project and I need to convert the rpm to mph though to do that I need to know the Gear ratio and do not know what that is without...
  13. D

    What is the proof for sin(45+x).sin(45-x) = \frac{1}{2}cos2x?

    Homework Statement Prove that sin(45+x).sin(45-x) = \frac{1}{2}cos2x Homework Equations double angle formulae reduction formulae special angles identities The Attempt at a Solution (sin45.cosx+cos45.sinx)(sin45.cosx-cos45.sinx) =(sin45.cosx-cos45.sinx)2...
  14. M

    Simple Pulley Ratios: Find T1, T2, T3, T4, T5, F

    Homework Statement The 14.0 kg block in Figure P8.34 is held in place by the massless rope passing over two massless, frictionless pulleys. Find the following values. http://img26.imageshack.us/img26/4025/p834.gif Find tension T1, tension T2, tension T3, tension T4, tension T5 and the...
  15. A

    What Is the Stoichiometric Air-Fuel Ratio for a Dual Fuel IC Engine?

    Homework Statement a mixture of 0.64 x 100 percent iso-octane and {1-0.64} x 100 percent methanol, based on volume, is mixed with air and combusted. Calculate the stoichiometric air fuel ratio. Note: please not this is mixing on a molar basis, not mass basis. It is necessary to perform a...
  16. P

    Regarding Fluids and hydrostatic force ratios

    http://img255.imageshack.us/img255/7909/hrw71431.gif http://g.imageshack.us/img255/hrw71431.gif/1/ An open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm^2 is fixed to the top of a cylindrical barrel of diameter D= 1.2m and height H=1.8 m The barrel and the tube are filled with...
  17. S

    What gear ratios are best for optimum torque transfer with a given motor?

    Hey guys, I am trying to determine which gear ratio is best to use for my project. We have 2 cars attached by rope, and whichever pulls the other one on its side, that car wins. We are given a motor with the following specs: rpm@torque=3500 rpm stall torque=0.61Nm So I was wondering...
  18. F

    Calculating Hydrogen-Oxygen Ratios at the Space Center

    I went to visit the space center in my new home of Huntsville AL the other day. I figured i'd do a quick calculation from tank capacity as read from the plaque for the second and third liquid hytrogen stages. Assuming an ideal reaction, there should be a mass ratio of oxyogen to hydrogen of...
  19. Shackleford

    Understanding Inverted Images: Calculating M and f Ratios

    How do I know the image is inverted? Reporter photographs an actress. The ratio of the actual height of the actress to the height of the image on the film is M = hi/ho = .00471 f = .220
  20. D

    Calculating gear teeth & ratios.

    1. This is a question that I've asked a few people and have not been able to get a solid explanation to: The crankshaft gear (A) has 14 teeth. It drives gear (B) with 21 teeth which is on a shaft & on the other end of the shaft is gear (C) with 9 teeth. The distributor is driven off gear (C)...
  21. K

    Divide by one thousand and equate the ratios

    Substitute each of the letters A, B, C, D, E, F, G and H by a different decimal digit from 0 to 9 to satisfy this crytarithmetic equation: (ABC)/(DEFC) = (GHA)/1000 Note: None of A, D and G can be zero.
  22. N

    Finding Ratios of Forces in a Two-Force System | Homework Question

    Homework Statement Here's the question: Two forces, Fa and Fb, are applied to an object. The larger force is Fa. When both forces point due east, the object's acceleration has a magnitude of 0.50 m/s^2. However, when Fa points due east, and Fb points due west, the acceleration has a...
  23. J

    Definition of short- and long-distance effects in branching ratios

    Would somebody be kind enough to explain what exactly is meant when discussing short- or long-distance contributions/effects to branching ratio calculations?
  24. L

    Ratios of integrals and its derivatives

    Hi guys, I've been trying to figure out if this ratio is less than 1, can anyone help me? it involves the ratio of an integral over its derivative, times the ratio of a function over its cumulative function. So I get something like f(t)/F(t) * Int{from 0 to t} f(x)dx/F(t). are there any rules...
  25. B

    Resistivity Ratios: Germanium Homework Statement

    Homework Statement (a) A sample of n-type Germanium contains 1023 ionized donors per cubic meter. Estimate the ratio at room temperature (300K) of the resistivity of this material to that of high purity intrinsic Germanium. The Electron hole product for Germanium is 1038m-6 and it can be...
  26. Holocene

    The physics behind air/fuel ratios in 4-stroke engines.

    Correct me if I'm wrong, but the hottest combustion temperatures will result when the air/fuel ratio is ideal, or stoichiometric, no? I ask, because there seems to be this mentality that a lean mixture will result in even hotter temperatures, and could cause engine damage. This has not...
  27. R

    Solve Trigonometric Ratios: 2ab/(b^2 - a^2)

    Homework Statement Given: sin x + sin y= a cos x + cos y=b find tan(x+y) Prove it to be equal to" \frac{2ab}{b^{2}-a^{2}} The Attempt at a Solution I get stuck after this: 2ab= 2 sin (x+y)+sin 2x+sin 2y b^{2}-a^{2}= cos 2x + cos 2y + 2 cos (x+y) Division of the two never...
  28. Y

    Gravity Ratios using pronumerals

    Homework Statement There are two planets called Alpha and Beta. mass of alpha=M mass of beta=0.01M They are distance R apart. At what distance, expressed in terms of R, from the planet Alpha, along a straight line joining the centres of Alpha and Beta, will the ratio of [force alpha ...
  29. G

    Estimating K$^+$ Decay Ratios Without Mass Dependence

    Homework Statement Give a simple estimate of the ratio of decay rates for K^+ \rightarrow e^+ \nu_e / K^+ \rightarrow \mu^+ \nu_\mu. Homework Equations Fermi's Golden Rule for decay width \Gamma = \hbar W = 2\pi (dn/dE_f)|M_{if}|^2. For comparison, from the PDG, \Gamma / \Gamma_i are 1.55...
  30. S

    Exploring Higgs Branching Ratios: Surprising Results for WW and ZZ Production

    Hi there :) I'm currently looking at Higgs Branching ratios. The fermions are all behaving as expected from the Yukawa terms and producing results proportional to mass. I'm a bit confused however that my WW (and WW*) BRs are higher than ZZ (and ZZ*), I was expecting tem to be the other way...
  31. C

    Angle Ratios: Solving for θ between 0 and 360°

    Hi, Homework Statement Find every angle θ between 0 and 360° for which the ratio of sin θ to cos θ is -3.00. (Round your answer to the nearest degree.) Homework Equations The Attempt at a Solution I used the unit circle and took the x value divided by the y value and none of...
  32. S

    Solving Problems Using Ratios: Tips & Tricks

    Hello, I'm currently in my 2nd year of physics and one thing I've noticed is how often problems can be solved using ratios, for example I had a problem in my thermodynamics class that involved finding a temperature after knowing its pressure and using the triple-point of water and its...
  33. P

    High voltage electromachinery - the key to absurdly high power to weight ratios?

    I've recently become very interested in designing efficient motors and alternators for use in a gas turbine hybrid electric vehicle. I feel that these designs may be able to achieve uniquely high power to weight ratios compared to the components in commercially available hybrid electric...
  34. B

    How Do You Find Molar Ratios for a Test?

    I'm new to this site so I'm not sure how this really works or if anyone will really answer at all. I have a huge test coming up and I need to learn how to find mole ratios. If someone could help me out I would really appreciate it. Here are a couple of example problems maybe you could...
  35. J

    Ratios of Initial to Final Energy/Momentum/Velocity

    Homework Statement A rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the star after collapse is 4.00 10-4 times the radius before collapse. There is no change in mass. In both cases the mass of the star is uniformly distributed in a...
  36. R

    How Does Distance from Earth Affect Gravitational Weight?

    Homework Statement For this problem, use ratios only to obtain the weight of a person at the following distances. Assume the person weighs 980N on the surface of Earth. a) 128 000km above the surface of Earth b) 4.5 times the distance from the centre of Earth c) 745 400km from Earths...
  37. R

    Universal law of gravity involving ratios

    Homework Statement For this problem, use ratios only to obtain the weight of a person at the following distances. Assume the person weighs 980N on the surface of Earth. a) 128 000km above the surface of Earth b) 4.5 times the distance from the centre of Earth c) 745 400km from Earths...
  38. K

    Solving Mass Ratios from Acceleration: The 3-Body Experiment

    Consider three bodies with mass m0 m1 and m2 at rest on a frictionless surface. When we insert a compressed spring between bodies 0 and 1 and release the spring we notice that the magnitudes of their accelerations are related by: a1=4a0. When we do the same experiment with bodies 0 and 2 we...
  39. cepheid

    How can I play a movie on my TV from my laptop without black bars?

    Hi there, Bear with me, this will take a bit of background explanation. I have a 19" LCD TV. I have a laptop computer (more specifically a brand new Apple MacBook -- I've been a PC user up to now and recently switched). I wanted to connect the computer to the TV for the purpose of playing...
  40. M

    Is My Formula Accurate for Calculating Vehicle Transmission Ratios?

    I think I have devised a formula to depict the correlation between engine speed and tire speed. Can anyone confirm or correct this? [ 1 mile / ( diameter of rim + profile thickness of tire ) * pi ] * ( x / 60 ) * ( gear ratio ) * ( final gear ) I used this in a function to graph the 5...
  41. B

    Ratios of Line Segments in Parallelogram ABCD: Divide BC & AE

    Homework Statement in the parallelogram ABCD, DC is extended to E so that DE:EC= 3:2. The line AE meets BC at F. Determine the ratios in which F divides BC and F divides AEThe Attempt at a Solution so i figured i could use the division-point theorem OP=[b/(a+b)]*OA +[a/(a+b)]OB but i don't...
  42. R

    Understanding the Circle of Fifths and Its Diatonic Ratios

    The circle of fifths operates around relative diatonic scales- FCGDAEB The reasoning is because it sounds good to the human ear at a ration of 3:2. How do you go about this?
  43. D

    Sequence of ratios of primes and integers

    I am fairly certain that \frac{n}{p_n} is not monotone for any n, but I can't give a proof of it without assuming something at least as strong as the twin prime conjecture. I was wondering if anyone has some advice to prove this using known methods?
  44. D

    How does octane number affect EGT readings in a 2-stroke engine?

    I am doing a project and was researching some information and found this site and read some information as to what I am doing but it didn't have all the answers needed. I'm doing a project on egt readings and twin cylinder 2 stroke snowmobile engines. For example what effects higher or lower...
  45. A

    Question about ratios, proportions and percents

    Does it matter what order you put ratios and proportions in? For example: The weight of the tea in a box of 100 identical tea bags is 8 ounces. What is the weight, in ounces, of the tea in 3 tea bags? Here is the provided solution to the problem: x/8=3/100 100x=24 x=.24 Here is...
  46. C

    Find Ratio of Segments in Triangle XYZ

    Homework Statement For triangle XYZ, point P divides XZ in the ratio 3:1 and Q is the midpoint of XY. If R is the point of intersection of PY and QZ, find the ratio into which R divides PY. Homework Equations This is the only equation that may pertain to this that I can think of...
  47. A

    Poisson distribution, likelihood ratios

    Homework Statement An independent, identically distributed sample, x = (x1, ... , xn) of size n, is drawn from a Poisson distribution, parameter A. We want to test the null hypothesis H0 : A = A1 against the alternative hypothesis H1 : A = A2 where A1 < A2. Write down the likelihood ratio...
  48. S

    Specific heat ratios of water, air, and related questions

    I've been working on a research project and I'm having difficulty with finding heat capacity values/heat capacity ratios. I have been getting 1.33 for the gamma value of steam, and 1.4 for air (at 300K). I was hoping someone could confirm these values. also, I have a question...let's say we...
  49. V

    Calculate Distance Above Earth's Surface: 1.4x Radius

    At a certain distance above the surface of the Earth, the graviational force on an object is reduced to 18% of its value at Earth's surface. Determine this distance and express it as a multiple of Earth's radius. FYI the Earth's mass is 5.98x10^24 kg and the Earth's radius is 6.38x10^6 m...
  50. T

    Calculating Length Ratio for Pendulum Period Increase by 50s

    a pendulum with the length (1) = 100 cm has a period of T(1). What length (2) is needed to increase the period by 50 s? i found out that T(1) = 2.0063s then for T(2),length(2) = 162.071m i use T = 2pi sqrt(length / gravity) i think there is smtg wrong with my calculation can smby...
Back
Top