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.

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  1. K

    Proportional ratios with exponents - Need Help

    proportional ratios with exponents - Need Help! A walker's speed, v, is proportional to the ratio of his leg length, L, and the period of the repeating motion of his legs, T, that is, v ∝ L/T. If the period is measured to be proportional to Lp, where p = 4/5, what power of L must the speed be...
  2. L

    Determining Aspect Ratios for a model glider

    Hello, First I’m not an engineer! I have a son who is in the eighth grade and is taking soaring lessons. I'm asking these questions because my motive on soaring lessons is to try and introduce practical applications of math (I'm an account and out of my depth here) with the hope that it sparks...
  3. S

    Can there be ratios using different sizes of infinities?

    Pretend that some god has every real number in its head, and it is thinking of only one of them randomly. There seems to be a better chance of it being a real number, minus the naturals, rather than just a natural number. If this example is even allowed to be conceived, what does the ratio...
  4. V

    Is there a general method to aproximate functions with ratios of polynomies?

    Is there a general method to aproximate functions with ratios of polynomies?? Hi All, There is a variety of methods to approximate functions (Taylor expansions, Fourier series, Splines, Interpolation, ... ) yet, when it comes to approximate some statistical distributions none of these...
  5. E

    Question about a matrix of vector element ratios

    if I have square matrix A whose decimal elements a_{i,j} = \frac{v_i}{v_j} how do I find (or approximate) the vector that would produce the matrix elements. what's a good way to do that? i guess you can scale the vector however you want and it'll still produce the same matrix.. thanks.
  6. P

    Why aren't mixed ratios allowed in Euclid's Elements ?

    Why aren't mixed ratios allowed in Euclid's "Elements"? Why did Euclid forbid the comparing of different kinds of magnitudes? And was it the same for numbers? Or were ratios specifically meant for magnitudes (lines, planes, solids) What are the consequences of comparing 2 different kinds of...
  7. A

    Converting Trigonometric Ratios to Degree

    Hi! I'm just a beginner i don't know much about trigonometry... can you tell me how to convert the trigonometric ratios to degree.. for example: o.3333 how did it become 19.47degree ? i saw it in the book... can you tell me how? I know this is simple for you all! i want to solve it without using...
  8. F

    Bicycle gear ratios vs force required

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  9. B

    Possible Ratios for Integers Between 20 and 70

    Hi Folks, I need to calculate the number of possible ratios for the following R=1- (P1*S2/P2*S1) where P1,P2,S1,S2 are integers between 20 and 70? Some one came up with a figure of 51*51*51*51 possible ratios but I don't know how this was determined. What branch of Math does this...
  10. U

    Compound gear train ratios and how to assemble gears?

    Homework Statement Hello fellow Physics Forumers My first post and , hopefully not my last. I've been lurking for a long while and the tempo has increased since I started my 1st year engineering course last semester. So I decided to register today as I have a bit of a puzzle. We have a...
  11. A

    For what angles can the exact value of all trigonometrig ratios be found?

    I have learned a lot of formulas for converting trigonometric values, but when I looked up sin(pi/10) I got the exact answer (1/4)(√5 +1). I tried to arive at this using formulas, but I couldn't. How is this found? What other angles can be found exactly. Ps. I already know about how taylor...
  12. S

    Barometric formula and height ratios

    Homework Statement Starting from the barometric formula for a thin, isothermal atmosphere, show that the ratio of the pressure P(z2) at height z2 to the pressure P(z1) at height z1 is given by P(z2)/P(z1) = e(-(z2-z1)/y) where y is the scale height Homework Equations Barometric formula: P(z)...
  13. N

    Physics puzzle ratios of two times which it take an object to fall down.

    Homework Statement What is the ratio between times for the aliens to hit the floor. you have two spheres of equal density throughout. One has a radius R and the other 1/2R. An alien falls down one and takes time T, the other it falls down in time t. In the second on, time t, half of the mass...
  14. S

    Thrust to Power Ratios for Modern Propulsion Systems

    Does anybody know some ballpark figures for thrust to power, Newtons per watt, ratios for modern propulsion systems, mechanical drive train ie cars trucks, propeller driven craft, boats planes, and rockets. I've found one reference that states the F/P ratio for a DC-9 jet engine is 0.016 N /...
  15. I

    Help Easy Physics - Resistivity Ratios

    The resistivity of Aluminium is twice that of copper. However, the density of Aluminium is one-third that of Copper. a) For equal length and resistance, calculate the ratio: mass of aluminium/mass of copperI'm thinking, the density ratio (Al:Cu) is 1:3 ...and the resistivity ratio is 2:1 ...so...
  16. O

    Comparing mass ratios and 'proving the law of multiple proportions holds true'

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  17. J

    Object visibility and size-to-distance ratios

    Kind of just a random question I thought of that I thought was a physics question - I apologize in advance if it is not a physics question. Here goes: What is the relationship between the size of an object and the distance from your eye at which the object becomes non-visible? Obviously...
  18. F

    Calculating Elastic Potential Energy with Varying Masses

    Homework Statement A 2.6-kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of the spring/mass system is 1.3 J. What is the elastic potential energy of the system when the 2.6-kg block is replaced by a 4.8-kg block...
  19. O

    Value of 3 reciprocal trigonometric ratios

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  20. R

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    Homework Statement Hi, I am having a problem with calculating the proper sizes for a pulley.The pulleys are turning threaded bars and I want them to turn at different speeds. They are connected via a Belt. There are three pulleys arranged in a triangle. One is the driver pulley(Ø31mm) which I...
  21. A

    Transformers for Maximum Power Transfer

    Determine the turns ratios a1 and 12 for maximum power transfer to the 20 ohm load resistor. a=n2/n1; Rs=RL for maximum power transfer, i.e. Zsource = the complex conjugate of the load.i have try to use Z1=a1^2*Zs and Z2=a2^2*Z1 and i know Z1=-j/(2*pi*f*c)
  22. Femme_physics

    Finding out pressure in a container if you know temp' and state-of-matter ratios

    Let's say you have a container with water in it. Let's say that you know that the temperature inside the container is 150 Celsius. Let's say that you have the ability to see inside the container and see the ratio of gas to liquid. So, if you know the ratio and know the temperature, can you find...
  23. S

    Law of Ratios? derving a differential Fick Equation

    Hello, I'm trying to make sense how a mathematical derivation (equation 4) from equations 2 and 3. Basically it defies any algebraic law I know. The paper is cited below and the the equations are attached as picture. Do you think this is a correct derivation? Is there such a thing as...
  24. M

    Understanding the Pythagorean Theorem's Ratios

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  25. M

    Unpacking Trig Ratios: Understanding Sine, Cosine, Tan, and More

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  26. H

    Calculating Gear Ratios for a Bicycle

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  27. M

    Are There Limitations to Using Ratios in Measuring Investment Returns?

    Hi, Consider a hypothetical. An investor short* sells Stock A for $100 and uses that money to buy Stock B for $100. After one month, stock A drops in value by 5% to 95 and stock B rises 10% to 110. The investor closes his investment ( sells stock B for $110, uses $95 of that to buy a stock A...
  28. S

    Abundance of isotopes based on ratios

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  29. Loren Booda

    Golden ratios in quantum mechanics?

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  30. Darth Frodo

    2nd Level Vectors question. Tan ratios.

    If I am only ginen the following how can I solve the whole Tan ratio part? If vector U is 10 units "Alpha Symbol" = Tan -1 (Tan inverse) 3/4 find U Vectors V = 13 units "Beta" = Tan -1 (Tan inverse) 3/4 find V I tried to multiply the 2 Tan ratios together but no luck. I imagine you...
  31. N

    How Do You Calculate Kinetic Energy Changes in Rotational Motion?

    Homework Statement [PLAIN]http://img576.imageshack.us/img576/6328/physics2.jpg Homework Equations KE(final)/Ke(initial) The Attempt at a Solution 1/2mv2/1/2mv2 v(final)2/v(initial)2 v= wr r(initial)=? and r(final)=? I originally thought the r's would cancel, but...
  32. T

    Finding Trig Ratios of Any Angle: A General & Easy Way

    Is there any general and hopefully 'easy' way to find the trigonometric ratios of any angle? That is without using the sin, cos etc tables? If not any angle ... atleast whole number angles?
  33. N

    Products and ratios Bessel functions -> any known approximations?

    Hi, I work in a computational neuroscience lab, where we study human perception using Bayesian models. In our models we often have to compute products and ratios of Bessel functions (specifically, zeroth-order modified Bessel functions of the first kind). Our computations could speedup...
  34. F

    Trigonometric Ratios for 14π: Solving for sin, cos, and tan

    Homework Statement Find the trigonometric ratios sin\theta, cos\theta, tan\theta for the angle \theta = 14\pi. If a ratio does not exist or is undefined, write "DNE". The Attempt at a Solution I know that the other equivalent angle for 15pi is just pi. But I do not know how to write the...
  35. Z

    Ratios and Proportions: Finding a,b,c from s-a : s-b : s-c

    Homework Statement Let s-a : s-b : s-c :: 1:2:3 then how do we find a:b:c from this? Homework Equations The Attempt at a Solution
  36. U

    2 equations, 3 unknowns - finding 2 ratios of unknowns

    Homework Statement I have two equations with three unknowns. Obviously, this is indeterminate and not all three variables can be independently solved. However, I only need (want) to solve for two ratios of the three unknowns. I am writing greatly simplified versions of the equations below...
  37. M

    Converting Ratios to Decibels for Data Analysis

    I am analyzing sets of data in ratio form (0 to 1). My interest at the moment is the differences between 2 sets of data, let's say set A and set B. Initially I thought I wanted to analyze the data all in the form of ratios so all my means and SDs are calculated based on those ratios. Again, my...
  38. O

    Problem involving ratios to find the length of a shadow

    Homework Statement The shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios? I already...
  39. M

    Help understanding trig ratios

    Hi there need help understanding trig ratios thanks a lot vati
  40. B

    Bicycle gear ratios for maximum efficiency

    We all know that there are several options of front sprocket/rear sprocket combinations that achieve the same gear ratio. i.e. A large front sprocket with medium rear or medium front with larger rear will produce the exact cadence at a given speed. What I've always wondered, is there any...
  41. D

    What motor and gearbox combination is needed for pulling a sled over 3 days?

    Hi All, I have a project which involves pulling a sled (wheeled, on rails - low friction) weighing approximately 15kgs over a set distance and time. The distance is approx 60cms and the duration is 3 days. To minimise cost I intend to anchor a motor(ac or dc)/gearbox combination and use a...
  42. T

    Musical Frequencies Overtones, ratios

    Homework Statement Two strings on a musical instrument are tuned to play at 262 Hz (C) and 294 Hz (D). Questions: 1. If the two strings have the same length and are under the same tension, what must be the ratio of their masses (MC/MD)? 2. If the strings, instead, have the same mass...
  43. B

    Fresnel equations and energy ratios

    I'm having trouble understanding the reflectivity and transmissivity (the ratios of energy reflected and transmitted through a boundary separating different media). Since energy is proportional to the square of the field, if you have a superposition of two fields at a point, to obtain the...
  44. S

    What Are the Largest Gear Ratios Possible for a Steam Turbine System?

    Hi, I'm new to the site so I hope I'm in the right place, I have a question regarding gears for a project that I am working on at uni. I'm designing a building which has a steam driven turbine at the base, what I want to have is levels above which are attached to the same axle as the turbine...
  45. F

    Minimize Cost of Norman Window: Area Ratio of h/r

    Homework Statement A Norman window has the shape of a rectangle with a semicircular top. Assume that the semicircular portion of the peripmeter is three times as costly to build per metre as the straight edges. For a given area, what ratio of heigh to radius would minimize the cost. Homework...
  46. M

    Human Sex Ratios: 50/50 Chance of Offspring?

    If there is a 50/50 percent chance that offspring could be either a male or a female (at least that's what my bio teacher tells me) then what are the chances that the male/female human population is (for the most part) split 50/50?
  47. W

    How are branching ratios determined? by experiment only?

    Greetings, when I look up how nuclear reactions take place, I often see branching ratios listed as percentages. So I'm wondering: are those ratios determined only by experiment or is there some fundamental theory that can predict what those percentages will be? many thanks, Mark
  48. B

    Understanding Torque Consumption in a Multi-Pulley System

    I would like to ask if anyone could explain how torque is consumed through a reduction ratio - in this case pulleys on a common shaft. I have a three shaft system, joined by belts. The motor pulley is 25.4mm, turning at 100 rpm, with an available 1.4Nm torque. This is connected to the second...
  49. B

    Line segments problem with ratios.

    Homework Statement The line AB meets the line 3x+2y-21=0 at M. Find the coordinates of M and show that M divides AB in the ratio 2:1 Equation of AB is y=(2/3)x+4 Homework Equations Given solution of M is (3,6). The Attempt at a Solution First solve for y such that...
  50. T

    General Angle Ratios: Help & Explanation

    can someone please help with the General Angle ratios,i don't understand the division into 4 quadrants,I would like someone to expain in detail
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