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.

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

    Determining Damping Ratio for Spring-Damper System

    Hi, my question is about determining the damping ratio for the upper spring-damper part of the system given in the link. Is it still r2/(2*sqrt(k2*m2)) or something equivalent should be determined? http://img217.imageshack.us/img217/3148/sprdampmass.png Thank you!
  2. C

    Ratio of gravitational/repulsive electrostatic force

    Homework Statement Calculate the ratio of the magnitude of the attractive gravitational force to the repulsive electrostatic force between two protons. Homework Equations Mass of proton = M = m = 1.672e-27 kg g = 9.80665m/s2 Q = q = 1.60219e−19 C k = 8.9875e9...
  3. E

    Temperature given a ratio of power out/power in

    Homework Statement Statement: If Jupiter emitted just as much energy per second (as infared radiation) as it receives from the Sun, the average temperature of the planet’s cloud tops would be about 107 K. Given that Jupiter actually emits approximately twice this much energy per second...
  4. X

    Chemistry Moles Ratio: Calculate Heat Generated by N2 & H2

    Homework Statement Given: (1/2) mol N2 + (3/2) mol H2 -> NH3 change in H = -46.11 kJ/mol If the number of moles of N2 are changed to 10 and the number of moles of H2 to 35, how much heat is generated if only 10% of the Nitrogen reacts? The Attempt at a Solution After setting...
  5. E

    Temperature given ratio of power out/power in

    Statement: If Jupiter emitted just as much energy per second (as infared radiation) as it receives from the Sun, the average temperature of the planet’s cloud tops would be about107 K. Given that Jupiter actually emits approximately twice this much energy per second, calculate what the average...
  6. A

    Relationship between velocity ratio and dynamic displacement in sinusoidual vibration

    Homework Statement I am asked to provide an anti vibrational support mount for equipment mounted on turbo-prop aircraft. The equipment has a mass of 40kg. the vibrational response of the equipment to the environmental disturbances will need ot satisfy a safety limit prescribed by the...
  7. D

    Ratio of masses of merry-go-round and the boy

    Homework Statement A boy of mass mboy stands at the edge of a merry-go-round of radius R = 3.4 m and mass mmgr, and both are initially at rest. The boy then walks along the edge of the merry-go-round. After walking a distance of 25 m relative to the merry-go-round, the boy finds that the...
  8. J

    Did I Use the Ratio Test Correctly?

    Homework Statement Hi I want to see if you guys could check my work an tell me if i did it correct and also explain me how to cancel "look at the graph" Homework Equations The Attempt at a Solution
  9. D

    How Does a Bug Affect the Spin of a CD?

    Homework Statement A CD (radius 6.0 cm) is spinning freely with an angular velocity of 420 rpm when a bug drops onto the CD a distance 4.4 cm from the center. If the CD slows to 280 rpm, what is the ratio of the bug's mass to the mass of the CD? (Ignore the effect of the hole in the center of...
  10. B

    Ratio of the velocities of two atoms, based on kinetic energy

    Homework Statement An oxygen atom is four times as massive as a helium atom. In an experiment, a helium atom and an oxygen atom have the same kinetic energy. What is the ratio vHe /vO of their speeds? Homework Equations K=.5mv2 The Attempt at a Solution...
  11. J

    Cal 2 ratio test where is my mistake

    cal 2 ratio test "where is my mistake" Homework Statement I attached a pic I solved the problem but i get 4^1 and the book says 4^2 I don't know why? Homework Equations http://img690.imageshack.us/img690/1518/problem15.jpg The Attempt at a Solution
  12. S

    Ratio of molar mass 2 component ideal solution

    Homework Statement Component 1 and 2 form an ideal solution. The vapor pressure of pure component 1 is 13.3kPa at 298K, and the corresponding vapor pressure of component 2 is approximately zero. If the addition of 1.00 g of component 2 to 10.0g of component 1 reduces the total vapor pressure...
  13. W

    Find Ratio ||v||/||u|| for u and v

    Homework Statement For u = (−1, 2, 1) and v = (3, 3, 6) find the ratio ||v|| / ||u|| Homework Equations || u || = (u^2 + u2^2 + ...un^2)^.5 The Attempt at a Solution I found the || u || to be 6^(1/2) and || v || to be 54^(1/2) Therefore the ratio should be 54^(1/2) divided by...
  14. N

    Rate of change of volume and poisson's ratio

    Homework Statement Consider a rectangular block of isotropic material of dimensions a, b and c, with c >> a or b. It is characterised by its elastic constants: Young's modulus E, shear modulus G and Poisson's ratio . The block of material is subjected to axial deformation along the c...
  15. Y

    Ratio of Kinetic Energy lost in a collision.

    For collisions wouldn't the distance traveled during the collision be the same? The energy lost is from heat, sound, deformation, etc. but wouldn't the work done on each car be the same since during the duration of contact they have to move the same distance (as soon as they move different...
  16. D

    How Do Velocities Affect the Mass Ratio of Skaters?

    Homework Statement Two objects are moving along the x-axis with velocities of 37 m/s (object 1) and -19 m/s (object 2). (b) What is the ratio of their masses Homework Equations The Attempt at a SolutionNo idea
  17. L

    Solve Ratio Word Problem: Add 1.6667 lbs Barley to Mixture

    Homework Statement A 5 pound mixture of barley and oats is 4/5 oats by weight. How much barley in pounds must be added to the mixture to make it 3/5 oats by weight?Homework Equations - The Attempt at a Solution I honestly cannot figure this problem out. The book gives the answer and...
  18. V

    Turbofan Engines: Bypass Ratio Selection Criteria

    What Basis Bypass Ratio Has Chosen For Turbofan Engine
  19. S

    Gilbert Damping Ratio in Ferromagnets

    Does anyone know the highest alpha (Gilbert damping ratio) you could get on ferromagnets? People for various reasons aim for the lowest alpha and it is around 0.008 these days (dimensionless). But I need to know whether higher values are possible or not. A brief reminder on what alpha is: It...
  20. X

    Solving Ratio & Proportion | Nitrogen, Phosphorus, Potassium Removal

    If 100 bu of corn per acre remove 90lb of nitrogen, phosphorus, and potassium (N, P, and K, respectively), how many pounds of N, P, and K are removed by the yield of 135u per acre? I try to figure out how to starting to solve this problem but don't know how some help please
  21. L

    Binary star system ratio of force

    Homework Statement 2 stars rotating around the common centre of mass have masses m and 3m. What is the ratio of the force due to each star at the common centre of mass. Homework Equations None The Attempt at a Solution I tried to find the centre of mass and applied Newtons law of...
  22. J

    Degrees of freedom affect on heat capacity ratio

    Homework Statement Why would vibrational and rotational degrees of freedom affect the heat capacity ratio more for N2 and CO2 than He or Ar? Would this occur at room temperatures? Homework Equations d.o.f.: 3N vibrational d.o.f., linear molecule: 3N - 5 nonlinear: 3N - 6 The...
  23. A

    Find the Ratio: Solving Recoil Speed in Homework Equations

    Homework Statement A person is standing on a sheet of ice so slippery that friction may be ignored. This individual fires a gun parallel to the ground. When a standard cartridge is used , a 13-g bullet is shot forward with a speed of 290 m/s, and the person recoils with a speed of vc. When a...
  24. J

    Unknown Charge Ratio Calculation

    Homework Statement You are given two unknown point charges, Q_1 and Q_2 . At a point on the line joining them, one-third of the way from Q_1 to Q_2 , the electric field is zero (see figure). The charges are separated by length, L. What is the ratio of the charges Q1/Q2? Homework Equations...
  25. S

    Calculating Cross Sectional Dimensions of Steel Bar Under Compression

    A steel bar of rectangular cross section 120mm x 60mm is compressed along its longitudinal direction by a force of 1500kN. Do the cross sectional dimensions increase or decrease ? Calculate and write down the resulting dimensions for both sides for both sides of the cross section. Youngs modulus...
  26. J

    Find Poisson's Ratio of Aluminum from Torsion and Tensile Tests

    1. Torsion test showed aluminum to have shear modulus of 4.60x10^6psi. Under a tensile test, the same specimen showed a modulus of elasticity of 12.2x10^6psi. Find Poisson's Ratio. 2. Poisson's Ratio=lateral strain/axial strain 3. The ratio is a function of both strains. The...
  27. N

    Can Ratio and Root Tests Determine the Convergence of Complex Series?

    1. \sum_{n=1}^{\infty}ntan\frac{1}{n} dont know where to start here 2. \frac{1*3*5*****(2n-1)}{n!} \frac{2n-1}{n!} \frac{2(n+1)-1}{(n+1)!}*\frac{n!}{2n-1} \frac{2n+1}{(n+1)(2n-1)} ->0 my book is showing divergence
  28. H

    How does the mass ratio M_W/M_Z evolve with energy?

    The masses of the elementary particles are renormalized somewhat, when the energy (the momentum) increases. Assuming that the standard model of particle physics is correct to all energies, is there any data on how the ratio M_W/M_Z between the two vector boson masses changes with energy? Does...
  29. K

    Solve the Repaid-Diaper-RA-RE Puzzle

    Substitute each of the letters by a different digit from 0 to 9 to satisfy this equation. None of the four numbers can contain any leading zero. (REPAID)/(DIAPER) = (RA)/(RE) Note: Each of the four numbers represent the concatenation of the digits, and does not denote the product of the...
  30. M

    Improve SNR Microphone Amplifier: Opamp Tips

    What are some ways to improve signal to noise ratio for a microphone amplifier, beyond getting low noise components. My amplifier is a single opamp.
  31. K

    Application of specific heat capacity ratio of air

    simple application please..o:)
  32. D

    Uncovering the On/Off Ratio of Silicon Transistors

    Research-related question: What is the typical on/off ratio of a silicon transistor? This seems like basic information, but I can't find it anywhere. Also, how high does the on/off ration need to be in order for transistors (say, in a logic circuit) to function correctly? Thanks!
  33. Helios

    Intermediate Ratio: Proof & Name

    Given positive integers a, b, c, d and for fractions a/b and c/d, it seems that ( a + c )/( b + d ) is between a/b and c/d. There's likely an easy proof of this. I'd like to know if there's a formal name for ( a + c )/( b + d ) or the operation that brings it about.
  34. M

    Pendulum gravity on X planet ratio

    Homework Statement Now you take off to an unknown planet with the same pendulum as in part (a). You measure the period of the pendulum on that planet and you find it to be twice as much compared to the one of the pendulum while on Earth. What is the ratio of ge on Earth to the gx of the...
  35. A

    Highest income to working-hour ratio

    Highest "income to working-hour" ratio Which careers have the best income to working hour ratio?
  36. G

    Expansion ratio of burned Fuel

    When a fuel/air mixture burns it expands. How much does it expand? Is there a formula or known volume increase? After a fuel burns it contracts. How much does it contract? Is there a formula or known volume that it contracts? Gasoline/Air mixture ratio is 15 to 1 for jet engines. A...
  37. A

    Optimizing the ratio of two integrals

    Frequently, I have encountered optimization problems which involve finding the optimal function to maximize the ratio of two integrals (bounds from 0 to infinity). e.g: Maximize \frac{\int_0^\infty (g(x))^3 g'(x) dx}{\int_0^\infty (g(x))^3(1-g(x)) dx} I am aware that variational calculus...
  38. M

    Relationship of Critical Damping Ratio in Elastomers

    Hi guys, working a project where I need to guess the damping ratio (used for a numerical analysis) based on other properties of a material. We're looking to use an RTV as a vibration damper (we don't need a lot) but I can't seem to get any vibrational properties (called Honeywell, Dupond...
  39. G

    Mixture Ratio for oxygen/propane in a rocket engine?

    What is the Air/Propane mixture Ratio? The Fuel Air Ratio of a Jet Engine is 15 to 1. This is for JP4. What is the Fuel Air Ratio for Propane Gas? I have learned the only difference between a rocket engine and pulse jet engine is the pulse jet runs on the oxygen that is in the air (30%...
  40. K

    Exploring the Ratio of Gravity to Curvature of the Earth

    If I dig 2 holes a little space apart, and then they intersect straight down, because of the curvature of the earth, then there is more than one up direction from the center. The closer 2 points at an equal distance down from the surface in separate holes get to the center, the less distance...
  41. Y

    Why Does Transformer Coil Ratio Halve Current Despite Doubling Voltage?

    If a transformer with coil ratios 2:1 creates a voltage twice that of the primary in the secondary coil why is the current halved? I realize that this is a consequence of the conservation of energy, but there must be a physical reason behind this. What is causing the additional impedance that...
  42. P

    Ratio of Sun's Diameter to the Moon's

    Homework Statement During a total solar eclipse, your view of the Sun is almost exactly replaced by your view of the moon. Assuming that the distance from you to the sun is about 400 times the distance from you to the moon. Find the ratio of the Sun's diameter to moon's diameter.Homework...
  43. I

    Trig Ratio Values Using Bow-Tie Diagram: sin 45, cos 60, tan 30, tan 45

    Use the "bow-tie" diagram to state the value of each trigonometric ratio. a) sin 45 b) cos 60 c) tan 30 d) tan 45 My Answer: a) 1 / \sqrt{2} b) 1 / 2 c) 1 / \sqrt{3} d) 1 Once again with this text the wording has thrown me off. It asks for the ratios but throws in that you should...
  44. M

    Transformer: Excitation Frequency and Turns Ratio

    Another transformer question: if I have an oil-filled transformer coil and I calculate the turns ratio with voltage in / voltage out at 60 Hz, why, when I increase the frequency to 23 kHz would the turns ratio appear to change? Is it because of the inductance of the primary coil? My boss'...
  45. L

    Calculate Charge to Mass Ratio from J.J. Thomson's Experiment

    Homework Statement In an experiment similar to J. J. Thomson's, charged particles are observed to travel through a magnetic field of 0.040 T with a radius of curvature of 0.20 m. The path of these particles is made straight again when an electric field is introduced by two parallel plates...
  46. T

    Calculating Energy Ratio of EM-Radiation

    Homework Statement Hi! I'm trying to calculate the energy ratio of EM-radiation in the visible spectrum and EM-radiation in the entire spectrum, of a body with known temperature. Homework Equations Planck's law: http://feps.as.arizona.edu/outreach/images/Blackbody_gr_3.gif.[/URL]...
  47. L

    Ratio and proportion - HEEEEELLLLPP

    Hi! I don't have ANY IDEA on how to do ANY kind of math problem coz i am not a math student but i have to do some QA questions for my entrance exams so I need a little bit of help here! so...here's the question:- The monthly incomes of A and B are in the ratio 8:7 and those of B and C are...
  48. U

    Understanding the Confusing Concept of Ratio: A Beginner's Guide

    Dumb Question on "ratio" I have some text that implies the following (which makes abolutely no sense to me). The ratio of 1/12, 5/12, 7/12, 11/12 is 4/11 Can anyone think of any context or meaing of "ratio" here for which this statement would make any sense?
  49. G

    Calculating Tension Ratio in Inelastic Collision of Hanging Clay Balls

    Homework Statement A clay ball of mass m hangs from a string with length L. When a second clay ball with mass 2m approaches it with a speed of sqrt(2gL) on the same plane. The collision is completely intelastic so that the balls stick together after the collision. Let T1 be ethe tension in the...
  50. B

    Pressure Ratio of He to N2 at Equal Density

    Homework Statement Calculate the pressure ratio of He to N2 at which helium would have the same density as nitrogen if their temperatures were the same. Homework Equations I used D = m/v The Attempt at a Solution DHe = mHe/v DN2 = mN2/v Both gases occupy the same volume, so...
Back
Top