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. L

    I Modern vs Euclid's definition of equivalent ratios

    Euclid defines equivalent ratios as the following : "Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former...
  2. paulb203

    B Sharing Ratio -- A shop sells a mix of small chocolate bars and large chocolate bars

    A shop sells small chocolate bars and large chocolate bars The small bars are sold in packs of 4 The large bars are sold in packs of 9 On one day; packs of small sold ; packs of large sold = 5:2 A total of 95 bars were sold How many small bars were sold? * My question; Is this an example...
  3. S

    B How do equivalent ratios work in practical terms?

    my doubt is that let's say we have a ratio 5:10 now the equivalent ratio for this would be 1:2 but what I am not able to understand is - let's say we have a situation in which it is given that the ratio of girls to boys is 5:10 which means for every 5 girls we have 10 boys but if we see the...
  4. RChristenk

    Prove that these three ratios are equivalent

    I have the solution: ## \dfrac{2x-3y}{3z+y} = \dfrac{z-y}{z-x} = \dfrac {x+3z}{2y-3x} ## (1) ## \dfrac{2x-3y}{3z+y} = \dfrac{3(z-y)}{3(z-x)} = \dfrac {x+3z}{2y-3x} ## (2) ##= \dfrac{(2x-3y)-3(z-y)+x+3z}{(3z+y)-3(z-x)+(2y-3x)} ## (3) ##=\dfrac{x}{y}## My question is how is it possible to go...
  5. rudransh verma

    Trigonometric ratios of angles above 90 degrees

    I have been doing the resolutions of vectors on x and y-axis with making triangles and reference angles in all quadrants. But I want to calculate now how to find something like ##\sin 235## without the help of reference angles. I know we don’t need to. Calculator and Taylor theorem is handy here...
  6. S

    MHB Can you solve this problem using bar models and ratios?

    I need help with how to use bar models with these kinda stuff. Thanks
  7. sciencebum

    Maximizing Boat Speed: Exploring Human Power Ratios

    In competitive rowing, the more people in a boat, the faster it goes, but what is the ratio of additional human to speed, and what is the theoretical limit? If I could fabricate a boat where each additional person added 100kilos, 100watts of power, and 1 meter of length to the wetted surface...
  8. JD_PM

    A Branching ratios | Higgs phenomenology

    Hi everyone! I am studying Higgs phenomenology, in particular its BRs My line of reasoning is this: I first had a look at the decays where the Higgs particle couples directly (i.e. without intermediate particles) to the products; those are ##H^0 \to b \bar b, \ H^0 \to \tau \bar \tau##...
  9. A

    Poisson ratios for Orthotropic materials (composites)

    I'm new to composite materials. I've studied mechanical engineering but I am actually usually involved in hydrodynamics (in which I've done my masters). However for a project we do fluid structure interaction with composites, and as these things go, you cannot get away with the 'black box'...
  10. D

    Is Anthropogenic Climate Change Still Debated on Science Forums?

    I'm wondering if anthropogenic climate change (C13: C14 and C14:C12 ratios) is still contentious on these forums. Counting the amount of fossil emissions in the last 100 years isn't particularly difficult, and matching the curve with NOAA measurements seems trivial, so I'm wondering what kind of...
  11. J

    Exploring Tension Ratios: 3 vs. 9

    I was thinking it would 3 or 9 times the tension rather than 1/3 or 1/9 but that is just a guess. an explanation would help very much!
  12. AndreasC

    Confidence intervals for ratios of variances and other confusing stats

    Now I don't really know much about the subject, I'm primarily just peaking into my textbook to see how to solve this or that exercise. I believe I can figure out how to solve the third question. However I couldn't find how to solve the first two. I know how to find a 95% confidence interval for...
  13. I

    Gear ratios for this motorcycle

    Hello guys I have a motorcycle engine in which I know the ratios of the transmission. and given the diagram of Power and rpm I made a function of P(ω) which is a polynomial of 6 order. Then I said that F(friction)*u=P(ω) then I substitute ω=u*r/v v(ratio) and have F(u).Next knowing the Pmax...
  14. A

    Calculating Energy Ratios: Moving Mass to and from Earth's Core

    a) In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength (force per unit mass) inside the Earth at a distance r from the center is gr/R, where R is the radius of the Earth. (In actual fact, the outer layers of rock have...
  15. Kaushik

    Maths: Question on Ratios, proportions, and percentages

    Amal, Geoffrey, and Julia each have some fireworks. If Amal gives half of his fireworks to Geoffrey, then Amal and Geoffrey will have in a 2:3 ratio. If Julia has 1/5th as many as Geoffrey (after Amal gives half his fireworks to Geoffrey), then what is the ratio of the number of fireworks Amal...
  16. G

    Pump with intake and compression using different pressure ratios

    Lets say we got a larger cylinder-piston combo and a smaller one. First we move the larger cylinder, filling in with vacuum. Then we pump in air, using the smaller cylinder, isothermally, with variable expansion ratio. Here, we clearly have exp ratio > P_atm/P_final We then compress the larger...
  17. T

    Why is the gear ratio reversed in a planetary gear system?

    Hello, I am confused about something. I will take the time to work it out, but right now, I am using it to remember. And I am now confused. Go here: https://www.smlease.com/entries/mechanism/gear-train-gear-ratio-torque-and-speed-calculation/ Scroll down to the section on...
  18. H

    Did I find the correct ratio in this magnetic field question?

    I used the two equations i listed by using B1=B2 and by doing that i ended up finding that N1/N2=λ. However i am not sure if that's the correct answer as λ is just a variable and not an actual number. Do you think it has to be an actual number or is it not really necessary?
  19. Sourav Guha

    A Solve for x using trigonometric ratios

    I have a mathematical term of the form tan(A.x)/tan(B.x)=C.How do I find out the value of x?
  20. S

    MHB Using ratios to calculate weights in a weighted average (or not)

    As a 'non-mathematician' (somebody who sucks at maths) I've been enjoying reading up on a lot of the stuff that flew over my head in maths class many years ago. I've encountered some examples of weighted averages and I've been puzzling over how one might derive the weights in the following...
  21. D

    What is the branching ratio for alpha decay to Pu-237?

    I understand that In general, the branching ratio for a particular decay mode is defined as the ratio of the number of atoms decaying by that decay mode to the number decaying in total. But I can’t get this specific branching ratio.
  22. Thathrooban

    I How to select gear/sprocket ratios for vehicle?

    The mass of vehicle with driver is 150kg. The specification of motor are 12kw, 27Nm torque, using 110/80 R17 wheels . 1. what is the general consideration to do transmission calculations of bikes 2.How to select gear ratios and sprocket ratio?
  23. S

    B Are trigonometric ratios physical quantities?

    I already know the fact that angles are physical quantities, but sin, cos of some angles are quantities? Quantities are those things, which can be quantified, are sin, cos, tan be quantified through measurement, if yes then other mathematical functions should also be categorised as physical...
  24. Auto-Didact

    Naturalness: dimensionless ratios

    The concept of naturalness as dimensionless ratios of parameters of order unity has recently come under criticism, most obviously because Sabine Hossenfelder wrote a book (Lost In Math) criticizing it. Very recently however, Peter Shor and Lee Smolin had a discussion about this over at Peter...
  25. Krushnaraj Pandya

    Relation between vector length and direction ratios

    Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1...(2) The...
  26. B

    MHB Find the ratios of the areas of the four regions

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  27. Physiona

    Angles involving trigonometric Ratios Worded Problem

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  28. Photonino

    I Why do systematic uncertainties disappear using ratios?

    Hello, I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty". I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...
  29. D

    Calculating pump to cylinder pressure ratios

    This may not be the proper forum but i need to find a way to calculate how much effort it will take to move a cylinder using a manual helm pump. The hydraulic cylinder i intend on using is a 32mm bore with a 16mm diameter. Stroke of 178mm. Volume of 107 cc The helm pump (attaches to a steering...
  30. M

    Question about calculation of planetary gear ratios

    So I've found the following formula for calculating the gear ratio of a planetary gear. Tr Turns of the ring gear Ts Turns of the sun gear Ty Turns of the planetary gear carrier R Ring gear teeth S Sun gear teeth P Planet gear teeth ( R + S ) ×Ty = R × Tr + Ts × S The example I saw on the same...
  31. D

    I Find Variance of Ratios in Lab Experiments (No Maths Background)

    This is from labwork experiments. I have no background in mathematics. We have an experimental setup that measures the levels of two targets: The Reference (R) and the target of Interest (I). We are interested in the ratio I/R. For healthy individuals we know this ratio to be precisely 1. For...
  32. C

    B How Does Detector Placement Affect Ratios in the Double Slit Experiment?

    Here is a setup that only uses fixed detectors. Will the ratio between the number of detections at D0 and the sum of the numbers detected on D1 and D2 be close to 1? For this question instead of the coincidence counter, 3 simple counters are needed. Also the detectors D1 and D2 need some lenses...
  33. J

    Enthelpy of water / ethanol at different ratios -- trend?

    Hello, I was doing some research on enthalpy of water-ethanol mixtures at different ratios, and when looking at all the information graphed, I don't understand why it produces the trend line it does. Why doesn't it produce a 'quadratic' trend line? Shouldn't having a 10:90 water-ethanol exert...
  34. E

    A Hadrons with significant branching ratios to muons

    Hi, I'm undergraduate researcher and my professor is interested in the answer to this question. He's kind of left me in the dark on why this is important to us, but that is another matter. We want hadrons that are produced at LHC conditions and decay before reaching the detector. So far all...
  35. S

    I Neutrino Production by Sun: Heep's Intensity & Branching Ratios

    Sun produces neutrinos by sundry reactions: p+p→d+e++νe - called "pp" p+p+e→d+νe - called "pep" 3He+p→α+e++νe - called "hep" 3He+p+e→α+νe - never mentioned. What should it be called? "Heep"? Now, heep neutrinos should form a sharp line at a quite high energy. What is the intensity of heep line...
  36. Joe Wolf

    I Brachistochrone for Specific Ratios

    It is commonly known that the solution to the brachistochrone problem is a cycloid. However, in order for a solution curve to be a cycloid, the ratio between points A on the y-axis and B on the x-axis has to be r/pi*r, since that is the ratio between the "height" of the cycloid and half of its...
  37. J

    Should I avoid using high ratio spur gears?

    So I have been looking into efficiency, My system is high radius with the motor located outside. This motor is small, and thus the gear being driven by the motor, is also small for space requirements. I have wanted to use a ratio of about 22:1 to make this system, and everything seems to work...
  38. E

    MHB Ratios and proportion: Scaling

    Hi guys. We're on a new topic in math now which has to do with ratios and proportions but with scaling. A few questions I have are How can I express the following scales in ratio? 1/2" = 1" 1/8" = 1'0" Also we're doing a Job and Drawing scale A dimension on a job is 24 in. Using scale...
  39. W

    Calculating gear ratios for a drivetrain

    I'm trying to calculate the required gear sizes for the system shown below: The driven wheel is connected to a 600mm diameter bicycle wheel and the driver wheel connected to a 580 mm long lever arm which has a forward driving force of 40 N. I want to calculate the most efficient sizing of...
  40. I

    MHB Election Outcome Hinges on Vote Ratios: Can You Solve It?

    In a recent election, the ratio of the number of voters for the Purple Party to the number of voters for the Pink Party was 15:16 and the Pink Party won the election. Had 300 more people voted for the Purple Party and 200 fewer people voted for the Pink Party, the ratio would have been 11:10 and...
  41. caters

    All other ratios from just a small set

    Homework Statement A person has come to a world full of pets. He notices right away that dogs are the most prevalent of all pets. But that's not all. He notices these 8 ratios: Dog:Cat = 5:1 Dog:Rodent = 1:5 Dog:Lizard = 1:3 Dog:Snake = 2:1 Dog:Turtle = 1:3 Dog:Alligator = 3:1 Dog:Crocodile =...
  42. M

    Magnetisation ratio in human body using gyromagnetic ratios

    Homework Statement The number density of 1H nuclei in the body is roughly 600 times greater than that of 13C nuclei. By what factor is the magnetisation M0 of 1H greater than 13C in the same external magnetic field? Homework Equations 3. The Attempt at a Solution [/B] Surely it can't be as...
  43. V

    Why Are My Trig Ratios csc and sec Incorrect for (7π)/4?

    Homework Statement The question states to find the primary trig ratios for (7π)/4 Homework EquationsThe Attempt at a Solution I got sin= (-√2)/2 cos=(√2)/2 tan= -1 csc= 2/(-√2) sec= 2/(√2) cot= -1 I got all of them correct except for csc and sec, and I am unsure why the solutions are telling...
  44. E

    Calculating Inertia Ratios of Carts on a Low-Friction Track

    Homework Statement The vx(t) curves for two carts, A and B, that collide on a low-friction track are shown below: What is the ratio of their inertias? Homework Equations the ratio i am looking for is mB/mA The Attempt at a Solution I believed that the ration was 1/2 however that is not...
  45. Liam C

    What is 2nd Sine? Solving a Triangle with 13.5 Hypotenuse

    Homework Statement A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P. Angle p is on the same line as the 90 degree angle and I found out that it must be sine. Homework Equations sine = opposite/hypotenuse The Attempt at a Solution sin p = 11.8/13.5 sin p =...
  46. F

    Calculating focal length from a number of focal ratios

    Homework Statement A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam...
  47. E

    Stress and Strain ratios in sheet metal?

    Hello! I'm having some trouble understanding stress and strain rations in sheet metal forming. I understand that they're constants, but how do you calculate them? Or are they usually given? Thank you!
  48. F

    What is the justification for the branching ratios of tau lepton decay?

    Homework Statement Branching ratios of tau lepton decay: hadrons 66% muon 17% electron 17% Use your knowledge of the decay of W bosons to justify these rates. Homework EquationsThe Attempt at a Solution [/B] The W+ boson can decay to any combination of quarks with +1 charge, but the CKM...
  49. prashant singh

    I Why trigonometric ratios were defined for a unit circle

    To make it useful for any angles. I need a good explanation for this.
  50. 9

    Automotive Understanding Gear Ratios: Inputs vs Reality

    The gear ratio is the ratio of angular displacement, angular velocity, angular acceleration, torque etc of the input with respect to output. However, I would like to know that which of these variables will be scaled exactly to the gear ratio in reality, as there might be some friction in the...
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