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. M

    MHB Proving Boundedness of Seq. $(a_n)$ Given Bound Seq. $(\frac{a_{n+1}}{a_n})$

    Hey! :giggle: Show for each sequence $(a_n)\subset (0, \infty)$ for which the sequence $\left (\frac{a_{n+1}}{a_n}\right )$ is bounded, that $\sqrt[n]{a_n}$ is also bounded and that $$\lim \sup \sqrt[n]{a_n}\leq \lim \sup \frac{a_{n+1}}{a_n}$$ I have done teh following: The sequence $\left...
  2. H

    Calculating the Ratio of A:B with K=2.3 & 70% Product

    Summary:: Direction of reaction A = 2B and we know that there is 70% of products and K = 2.3 Question is: What is the direction of reaction A = 2B and we know that there is 70% of products. K = 2.3 K = B^2 / A B:A = sqrt (K.A) / A I have came here but what should I do now? Because when I...
  3. Rongeet Banerjee

    Medical What is the significance of Nuclear-Cytoplasmic Ratio in cell aging and cancer?

    From Wikipedia I have found out that as a cell ages, it's Nucleus shrinks and thus the intial N/C decreases from 4:1 for most cells to 2:1. I also have a rough idea that Cell machinery becomes unorganised and inefficient.Also high N/C is a characteristic of Cancerous cell.But I do not know the...
  4. N

    I UV mercury lamps: Changing the 185nm vs 253.7nm ratio

    According to Wikipedia, (citation needed) https://en.wikipedia.org/wiki/Ultraviolet What would alter this proportion of emitted radiation to favor more 185nm radiation? Preferably not with a filter that filters out 253.7nm (mathematically would also increase the ratio of radiance of...
  5. S

    Mathematica Ratio of functions -- automatically apply l'Hospital rule when needed

    I want to plot the ratio f1(x) / f2(x), where they have some common zeros. Does Mathematica have a feature that will do this, switching automatically to f1'(x) / f2'(x) when appropriate, avoiding F.P. errors and optimizing numerical precision? If not, is there a good way to implement this?
  6. Faris ARSLAN

    Approximate energy loss ratio in mechanical springs

    Hi!.. As known, a certain amount of energy is applied for compressing a mechanical spring. Thus mechanical spring is charged with energy and it stores it as elastic-potential energy. But whole energy, applied for compressing spring, can not be converted into potential energy. The reason is...
  7. C

    Find the ratio of the energy of the La characteristic x-ray to the Ka

    I found my energies for Potassium. I have 3.3 KeV for the k alpha nd 254.6 ev for L alpha, using z=19 and n=3. Are these values correct? Edit: I found the ratio to be .077
  8. B

    Poisson Ratio -- Finding a corresponding analytical solution for the strain

    Hi, I ran into problems using the poisson ratio. For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge. Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir. The material parameters are E = 100, and v...
  9. M

    A Claimed derivation of Weinberg angle, Higgs/W mass ratio

    https://arxiv.org/abs/2010.15621 Superselection of the weak hypercharge and the algebra of the Standard Model Ivan Todorov [Submitted on 29 Oct 2020] I haven't had time to study this paper yet. But a few curiosities: It talks about Clifford algebras. But in fact it builds on work due to...
  10. WMDhamnekar

    MHB Computation of the ratio of barometric pressure

    Hi, The Homestake gold mine near Lead,South Dakota is excavated to 8000 feet below the surface. Lead is nearly a mile high; the bottom of the Homestake is about 900 m below sea level. Nearby custer peak is about 2100 m above sea level. What is the ratio of barometric pressure on the top of the...
  11. greg_rack

    Change in volume given the ratio of the heights

    The question is: how do I know the increase in the minor and greater radius, given just the ratio of the heights?
  12. L

    Optimizing Exposure Time for Different Magnitude Stars

    Summary:: An image was taken with a ##60## second exposure time of a 6th magnitude star and the signal to noise ratio was detected to be ##S/N = 20##. a. What should the exposure time be if you wanted a ##S/N = 100##? b. Now calculate the ##S/N## if it were a 2nd magnitude star for a ##10##...
  13. B

    I Tau Decay: More Pions, Less Ratio?

    Hello! Tau decay has a branching ratio to a charged pion + neutral pion + tau neutrino much bigger than to a charged pion and a tau neutrino. Based on consideration of available phase space, I would imagine that adding an extra pion would decrease the branching ratio. Why is this happening...
  14. S

    Compression ratio and volume reduction of CO2

    The question is: If the compression ratio of car engines is increased by 10% (from 10 to 11), estimate the volume reduction in annual CO2 emission. Assume there are 30 million cars each consuming one cubic meter of fuel annually. The question is looking for a rough estimate for an answer. I...
  15. G

    To find the ratio of forces around a right triangle

    Could I please ask for help with the following: ABC is a right-angled triangle in which AB = 4a; BC = 3a. Forces of magnitudes P, Q and R act along the directed sides AB, BC and CA respectively. Find the ratios P:Q:R if their resultant is a couple. Book answer is 4 : 3 : 5 Here's my diagram...
  16. Y

    How to select a stepper motor and gear ratio?

    Hello, I could use some help learning how to properly size stepper motor. Suppose that I want to use a stepper motor to move a load against the force of gravity. It must be able to start, stop, and hold it's position against the static load. I know the maximum torque of the load. In addition, I...
  17. nomadreid

    I Ratio of a real value to the max theoretical value: what term to use?

    If the Summary is not clear, the following is an example translated from: https://telecombloger.ru/7335 '... air conditioning systems. For example, the efficiency of a compressor is about 85%. The remaining 15% is spent on friction, oil movement, overflows, heating, etc. The efficiency of the...
  18. E

    Young's Modulus and the Poisson Ratio of Aluminium

    Hi. I've been given these sets of value. How do I calculate Young's modulus and Poisson Ratio from these set of value. I tried to create a stress vs strain graph but the graph does not look like a common stress vs strain graph but instead more of a y=x graph. The diameter of the rod is 10mm and...
  19. F

    B What is the entire gear reduction ratio of a vehicle?

    As I was looking in the caracteristics of an old tank, I found a number that I could not get anything of on the web. It is called "entire reduction ratio" and was presented just under the gearbox caracteristics. His value is 1:13.4. My question is : is it useful? Does this value have relation...
  20. M

    Engineering Common Mode Rejection Ratio: Instrumentation Amplifier Calculation

    Hi, I have a question regarding a practical CMRR calculation. Main information: - Signal input: 10 mV rms - Interference input: 1.5 V rms - In an earlier part of the question, we found that for the second stage of the instrumentation amplifier (the summation amplifier) that: $$...
  21. karush

    MHB -ratio to ratio club membership

    60% of the members of our club are men and the rest were women. When 45 new members joined the club, the number of a female members increased by 50% and the number of men was 1 1/2 times as many as before. how many club members were there initially? ok from the $ \dfrac{60\%}{40\%}$ ration we...
  22. S

    MHB What amout of percentage should be added to the ratio?

    Sam wants to convert a mixture of acid and water in the ratio 16 : 19 to 19 : 16. What is the amount of acid as a percentage of initial solution that should be added to achieve the required ratio?
  23. S

    Ratio of acceleration of two solid cylinders released on two inclined planes

    I am not sure about my free body diagram. I assume the cylinder rolls without slipping so the forces acting on the cylinder are: Weight directed vertically downwards Normal force directed perpendicular to the plane friction directed upwards, parallel to the plane Am I correct till this point...
  24. B

    Engineering Velocity Ratio, mechanical advantage, Efficiency of a screw jack

    Hello, I have completed the question below. I am just unsure on whether i am correct or not. I am unsure on Mechanical Advantage. As i have seen a few different equations. Question: Answer: a) Velocity Ratio = $$\frac{\text{Distance Moved By Effort}}{\text{Distance Moved By Load}}$$...
  25. C

    I Akaike Information Criterion Vs Likelihood Ratio Test

    Hello, I want to understand the difference between both goodness-of-fit tests, I would be glad if you could help me: Akaike Information criterion is defined as: ## AIC_i = - 2log( L_i ) + 2K_i ## Where ##L_i## is the likelihood function defined for distribution model ##i## . ##K_i## is the...
  26. S

    Bicycle gear system's Input-Output ratio?

    A person weighing 60 kg exerts 30 kg of thrust on a pedal (crank) x 2 pedals = 60 kg of force per Revolution. Let's say @ 30 RPM. What is the output kg of force per RPM on the back wheel where it meets the tar. I have all the sizes and forces, yet the correct formula eludes me. The ratio per 1...
  27. A

    I The Ratio of Total Derivatives

    If we have two functions C(y(t), r(t)) and I(y(t), r(t)) can we write $$\frac{\frac{dC}{dt}}{\frac{dI}{dt}}=\frac{dC}{dI}$$?
  28. P

    Can Mixed Units in Ratios Be Converted and Used Accurately in Calculations?

    I have the solution, but my question is that in my first attempt, I simply calculated a_c = 60^2/150 ignoring the fact that the units for 60 are km/hr and the units for 150 are meters. Is this ever salvageable? Is there any way to retain the 'mixed' units of km with meters in the ratio and...
  29. G

    How to expand this ratio of polynomials?

    I could simplify the expressions in the numerator and denominator to (1+x^n)/(1+x) as they are in geometric series and I used the geometric sum formula to reduce it. Now for what value of n will it be a polynomial? I do get the idea for some value of n the simplified numerator will contain the...
  30. Vicga

    A W+/W- bosons ratio in proton-proton collision

    Hi guys, I'm studying my first-year physics in college, and I'm having to write a report of some proton-proton collisions that were registered in the LHC of CERN years ago. The main goal is to identify different bosons (W and Z) that are decaying into other elemental particles. I've been asked...
  31. P

    Chemistry Solving for electron activity given pH and ratio of redox elements

    I've written out the half reaction 8e- + 9H+ + SO42- = HS- + 4H2O and I know the logK = 4.25 (that's the constant mentioned in the prompt) I've written out the equilibrium statement of 10^4.25 = ([x^1/8]*[H2O^1/2])/([10x^1/8]*[e-]*[(10^-8.2)^9/8] However, from there, it seems like I have two...
  32. P

    Ratio of the Earth's core radius to total radius via seismic turning point

    I've attached a figure I've made; I know I'm to assume the Earth is a perfect sphere in this case. Assuming the 103 degrees is measured as latitude, I've calculated the distance in kilometers (Xp in the second equation above) to be 1.1453e4 km. I know I need u = p at the turning point, but not...
  33. M

    Engineering Two Stage Epicyclic Gear-box - Finding the Gear ratio

    Hi, Just have a question about the method in attempting this two-stage epicyclic gear-box. We are given the following information about the number of teeth: S1 = 48, P1 = 28, S2 = 96, and P2 = 48 My attempt: 1. Work out the number of teeth for the two ring/annulus gears From geometry, we can...
  34. engnrshyckh

    Engineering Control system damping ratio

    I don't know how to calclute error in derivative for daming ratio of 0.5
  35. Cheesycheese213

    What is the meaning of polarization ratio?

    I was trying to research about polarizing lasers for an experiment, and there were some things that were confusing? A website said, I was wondering if the polarization ratio was the same as the extinction ratio? Also, I was curious because I thought 100:1 would be a lot, and not much light...
  36. A

    Conceptual thermodynamics question regarding specific heat ratio

    The solution can be found at https://study.com/academy/answer/an-insulated-rigi... After using the two equations I can't see why (h2-h1)/(u2) should equal (T2)/(T1). Can someone explain why specific heat ratio is equal to temperature ratio?
  37. K

    I Simple explanation for cross section ratio

    Hello! Is there any simple (i.e. using some physics arguments, without actually doing the math) explanation for why $$\sigma(pp \to \pi^+d)/\sigma(np\to\pi^0d)=2$$ where d is the deuteron? Thank you!
  38. E

    Energy ratio of two systems with charged planes

    Honestly no idea how to get an answer. I found the electric field between the planes and out of it in those two cases but this didn't take me very far. The final answer is E(B)/E(A)=2. Can someone please explain why?
  39. D

    Checking the convergence of this numerical series using the ratio test

    ## \sum_{n=0}^\infty \frac {(2n)!}{(n!)^2} ## ##\lim_{n \rightarrow +\infty} {\frac {a_{n+1}} {a_n}}## that becomes ##\lim_{n \rightarrow +\infty} {\frac { \frac {(2(n+1))!}{((n+1)!)^2}} { \frac {(2n)!}{(n!)^2}}}## ##\lim_{n \rightarrow +\infty} \frac {(2(n+1))!(n!)^2}{((n+1)!)^2(2n)!}##...
  40. Z

    On/Off Ratio Limits: Practical Lower Limit for Logic Functionality

    When does an on/off ratio become impractical? I've read that typical CMOS devices have an on/off ratio of 10^6-10^10. Is there a lower limit that prevents logic devices from functioning appropriately? As in, what is a practical lower limit for the on/off ratio but still enable logic functionality?
  41. G

    Understanding Poisson's Ratio and Its Effects

    Hi everybody, Poisson's ratio determine that when applying force in one direction (let say z direction) it would cause a relative major strain at that direction, and also two additional strains at the two other directions (x & y). My question is, what is the explanation for the change in the...
  42. F

    Infinite Series (The Ratio Test)

    I found that ρn = √(2n+1)/(n+1). Then, I found ρ = lim when n→∞ |(1/n) (√(2n+1))/((1/n) (n+1))| = 0 Based on this result I concluded the series converges; however, the book answer says it diverges. What am I doing wrong?
  43. kolleamm

    Higher gear ratio but less torque?

    There's a micro motor with a gear ratio of 298:1 and there's a servo with a ratio of 188:1. The first runs at 12v and the other at 7.4v. How is it that the motor with the bigger gear ratio has only a 70 oz-in torque, while the second motor has a 560 oz-in torque? First motor ...
  44. S

    How to Find the Ratio of Areas in a Scalene Triangle?

    I do not know where to start. I draw scalene triangle and assign each coordinates to the vertices. Tried writing something but none working. Please give me a hint to start. Thanks
  45. pkress

    Engineering Minimum Critical Power Ratio (nuclear engineering applications)

    Im having a really tough time with this problem, I am assuming that in order for q'(z) to be a maximum, e^(-az/L)sin (pi(z)/L) must be a maximum. I believe this occurs when the derivative with respect to with respect to z/L is zero, which gives me z = 0.322L, but I am not sure if this is correct...
  46. karush

    MHB Ratio Test Determines Divergence: 11.6.1

    Determine Convergence or divergence and test used $\displaystyle\sum_{n=1}^{\infty} \dfrac{1+4^n}{1+3^n}$ W|A says diverges using ratio test so $\therefore L=\lim_{n \to \infty}\left|\dfrac{a_n+1}{a_n}\right|>1$ Steps $\displaystyle L=\lim_{n \to \infty}\left|...
  47. caters

    What is the ratio after 1 month given certain conditions?

    So this question is a math question having to do with me calculating the rate of population growth starting from a population of 100,000. I have already gotten the first 3 steps done (sex ratio, ratio of cycle time, and pregnancy ratio) after a week among those in the fertile timeframe...
  48. karush

    MHB 11.6.8 determine convergent or divergence by Ratio Test

    Use the Ratio Test to determine whether the series is convergent or divergent $$\sum_{n=1}^{\infty}\dfrac{(-2)^n}{n^2}$$ If $\displaystyle\lim_{n \to \infty} \left|\dfrac{a_{n+1}}{a_n}\right|=L>1 \textit{ or } \left|\dfrac{a_{n+1}}{a_n}\right|=\infty...
  49. Boltzman Oscillation

    Engineering Help finding the damping ratio formula for this circuit

    The circuit to be analyzed is shown below: Since initial conditions are zero (from the instructions) I will use laplace transforms for the cirucit and I will use the MAME method to solve this circuit. The laplace transforms that are required will give me: $$E_g(s) = \frac{10}{s}$$ $$ L_3 =...
  50. J

    Engineering What is Poisson's ratio and how does it relate to stress and strain?

    I'm working through the equations and I have a lot of information missing. I have calculated the longitudinal strain to be 0.4mm (4/90) is the lateral strain directly proportional to the longitudinal strain? As I need to work out poisson's ratio in order to calculate Bulk modulus, then youngs...
Back
Top