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. JoeMarsh2017

    Finding Turns Ratio and Average Current in the Primary Winding

    Homework Statement A half wave rectifier circuit has a transformer inserted between the source and the remainder of the circuit. The source is 240Vrms and 60 Hz, and the load resistance is 20ohms. 1) Determine the required Turns Ratio of the transformer such that the average load current is...
  2. V

    Determine the ratio of the charge to the mass

    Homework Statement A beam of electrons passes undeflected through two mutually perpendicular electric and magnetic fields. If the electric field is cut off and the same magnetic field maintained, the electrons move in the magnetic field in a circular path of radius 1.14 cm. Determine the ratio...
  3. engnrshyckh

    I want to calculate mark space ratio: f=25000Hz,T=4us

    <Moderator's note: Moved from a technical forum and therefore no template, which would have helped a lot in this case ...> i know that mark time is duration in which a pulse is present and space time is a duration is which pulse is not present. my attempt to ques is: f= 25000Hz...>...
  4. A

    Find the ratio of two line segments in a triangle

    1. The problem statement, all variables, and given/known data Triangle ABC has a point D on the line segment AB which cuts the segment in ratio AD : DB = 2 : 1. Another point E is on the line segment BC, cutting it in ratio BE : EC = 1 : 4. Point F is the intersection of the line segments AE and...
  5. M

    EGR ratio from exhaust gas composition

    Homework Statement given:-fuel and air mass flow, measured mole ratios of exhaust composition y_i. Let's assume stoichiometric combustion so we have only CO2, H20 and N2 as products. Homework Equations Can EGR ratio be calculated from available data? The Attempt at a Solution I get result...
  6. SonnetsAndMath

    I Effective Mass-to-Charge Ratio of Electroweak or QED Vacuum

    Apologies if my question is confused, because I'm beginner in field theory: adding up all corrections, can we talk about an effective (at least approximate) overall mass-to-charge ratio for the electroweak or QED vacuums? Suppose we want to talk about the relative strength of...
  7. ORF

    Biochemist -- Is isotope ratio unique for each trophic level?

    Hello As far as I know, the reaction velocity depends on the isotope ("kinetic isotope effect"). So, is the isotope ratio (for example, for Nitrogen or Carbon isotopes) dependent on the trophic level? Thank you for your time. Regards, Alvaro.
  8. Hiero

    B Poisson's ratio, steel rod for example

    Steel has a "Poisson ratio" μ of 0.29 (in my book of problems at least). Am I understanding the meaning of this ratio correctly: if a steel cylinder is stretched along its symmetry axis by a factor p (something like 1.01 or 0.99) then the radius will change by a factor 1-μ(p-1)? [So then the...
  9. F

    Find the gear ratio for maximum angular acceleration

    Homework Statement A constant torque is applied to a pinion which has a moment of inertia of I_m. The pinion(A) drives two gears, one (B) which is connected to a mass which has a moment of inertia = I_m and the other(C) is connected to a mass which has a moment of inertia = 2I_m. The gear...
  10. A

    How mass flow and pressure ratio is related in case of a Gas Turbine

    Hi, As per my observation and experience, when we use evaporative cooler to cool the inlet air to the gas turbine, the compressor discharge pressure (i.e PCD or P3) rises. As, the temp. of the inlet air drops and the mass flow increases due to the increase in density, I believe the discharge...
  11. A

    Dimensionless mass-to-charge ratio of the electron

    In SI units, the mass-to-charge ratio of the electron is $$\frac{m_{e}}{|q_{e}|} = \frac{9.11 \times 10^{-31} \text{kg}}{1.6 \times 10^{-19} \text{C}} = 5.7 \times 10^{-12} \text{kg/C}.$$ In which system of units do we have the dimensionless mass-to-charge ratio $$\frac{m_{e}}{|q_{e}|} \simeq...
  12. S

    MHB Solve Ratio Problem: Jackson's Votes in Mayor Election Explained

    Here's the question: Last year there were three candidates who ran for mayor, Morris, Jackson, and Victor. Out of a total of 12,320 votes, Jackson received 30% of the votes. If for ever 3 votes for Morris there were 5 votes for Victor, how many votes for Jackson were there for every 7 votes for...
  13. David K

    Ideal Windsheld Cleaner + Simple Green Ratio

    We are wondering if there is an ideal ratio of simple green + glass cleaner to get the bugs off & keep it streak-free. Thought there might be a chemist with the ideal ratio. We will experiment and let you know what happens.
  14. 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...
  15. B

    Ratio of Potential: Calculating ##\phi_0/\phi_1##

    Homework Statement Consider a charge distribution which has the constant density ##\rho## everywhere inside a cube of edge ##b## and is zero everywhere outside. Let ##\phi## zero at infinity, ##\phi_0## at the centre of cube and ##\phi_1## at one corner of the sphere. Determine the ratio...
  16. G

    What's the aspect ratio of human vision?

    What's the average aspect ratio of human vision as we perceive it?
  17. K

    Ratio of rotational inertias for belt-connected wheels

    Homework Statement Wheels A and B as shown in the figure are connected by a massless belt that does not slip. The radius of A is R and the radius of B is r. What is the ratio of rotational inertias ##\frac{I_a}{I_b}## if the two wheels had the same angular momentum about their central axes...
  18. Albert1

    MHB Calculating Ratio of $\overline{BP}$ to $\overline {PN}$ in Hexagon $ABCDEF$

    Regular hexagon $ABCDEF$,points $M$ and $N$ are midpoints of $\overline{CD}$ and $\overline {DE}$ respectively, point $P$ is the intersection of $\overline {AM}$ and $\overline{BN}$ Find $\dfrac {\overline{BP}}{\overline {PN}}$
  19. E

    MHB Scaling : ratio and proportion

    Hey guys. Last question I have is A scale on a drawing is 1/8" = 3'. Determine the length of a rafter if it measures 1 3/8" on the blueprint. Thanks
  20. parshyaa

    I What does negative ratio mean in mathematics?

    Whats the difference between (4/3) and -(4/3) Why ratio in external division is negative? I have answer for how it is negative but not why? X = (mx2+nx1)/(m+n) ⇒ (mx2+nx1) = X(m+n) ⇒m(x2-X) = n(X-x1) ⇒(m/n) = (X-x1)/(x2-X) From the above equation we can conclude that when division is...
  21. A

    How to estimate a spring-mass-damper system's damping ratio?

    I have constructed a torsional balance, which basically consists of a torsional spring, and a damper. I model this as a spring mass damper system. And it is used to measure thrust of some propulsion system. This is how the system looks like. I am just very eager to find out, how to model the...
  22. E

    MHB What is the formula for calculating pulley diameters and rates of revolution?

    I got a couple of questions to ask. And if you can just tell me how you would solve these like how would you setup the equation: 1. A bronze casting is made up of six parts copper, five parts tin, and one part antimony. The casting has a mass of 60KG. Find the mass of each component in Kg. 2...
  23. EthanVandals

    Moment of Inertia Ratio for Disk and Ring with Point Mass

    Homework Statement What is the ratio of inertia of a 5 meter radius disk to that of a 5 meter radius ring? How would this ratio change if the ring were replaced with a since point mass a distance 5 meters from a pivot point? Homework Equations I = mr2 The Attempt at a Solution The wording in...
  24. D

    How to calculate the gear ratio of this moonphase watch

    I would like to calculate the gear ratio of this moonphase watch, however i cannot calculate the exact day of its mentioned. What's wrong with my calculation? https://www.ochsundjunior.swiss/watches/moon-phase/tech-specs/ my calculation is 1/(2/12*14/18*14/109)/2=30.03 which is different from...
  25. E

    MHB Solving Ratios & Proportions Questions - Get Help Here!

    Hi. I'm doing some questions about ratio and proportions. I'm just having difficulty with some of the questions and i hope you guys can help. So question 1: A length of chain 15'-3" long weighs 78lbs. How long would a similar chain be if it weighs 102lbs. (Answer to nearest inch) Length...
  26. MaxKang

    Aspect ratio used in induced drag and lift calculations

    Hello everyone, I am working on a 3.2 meter wing span electric aircraft with another group of 30 engineering students. In calculating the induced drag and lift for preliminary calcs I am a little confused as to whether I need to include the width of the fuselage in the wing span(b) for induced...
  27. T

    Goodness of fit: How to decide which ratio to deal with?

    The problem statement, all variables and given/known data with attempts While solving problems of Goodness of fit, I'm faced with an issue, how to decide which ratio to consider to find the test statistic from given set of observations. E.g. 1 A supplied sample contains four types of seeds and...
  28. D

    MHB Confusion about greater variance in the numerator for F ratio

    Hi, I am studying about F ratio and how, as a random variable, it follows F Distribution. So let me explain what confuses me. This is what the theory says -- We draw two random samples $sample_x$ and $sample_y$ from two different Normally distributed populations with equal variance...
  29. G

    Algebra problem involving work using specific heat ratio

    NO TEMPLATE BECAUSE SUBMITTED TO NON-HOMEWORK FORUM I'm stuck on substituting the following (where gamma is the specific heat ratio): W=(P1v1 - P2v2) / (gamma-1) P1v1^gamma = P2v2^gamma substituting for v2... <= this is where I get stuck... W = [(P1v1) / (gamma-1)] * [(P2 /...
  30. asseya

    Ratio of specific heats of 52NiO-YSZ and YSZ

    Hi everyone! In a simulation using COMSOL, the ratio of specific heats of both 52NiO-YSZ and YSZ are required as these materials are not included in the software's bibliography. So, I would like to know the ratio of specific heats (gamma) of 52NiO-YSZ and YSZ. Thank you.
  31. B

    I Is dy/dx Truly Not a Ratio Even When Defined via Limits?

    I read people saying that dy/dx is not a ratio because it is a limit or standard part of a ratio. $${dy\over dx} = \lim_{h \to 0} {f(x +h) - f(x) \over h}, \ \ \ {dy\over dx} = st\left( {f(x +h) - f(x) \over h}\right)$$ what I get is ##{f(x +h) - f(x) \over h}## is a ratio but putting a limit...
  32. 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...
  33. jlmccart03

    Find ratio of diameter of two Cylindrical Resistors?

    Homework Statement Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one(A) dissipates twice as much power as the other(B). Find ratio of dA/dB. Homework Equations P = VI = V2/R = I2R Area of cylinder = 2πrh + 2πr2 The...
  34. W

    I Exact expression for the tensor-to-scalar ratio

    Based on the vast cosmology texts, I have seen that the expression for the tensor-to-scalar ratio ##r## in cold inflation is, ##r=16\epsilon_H = -16\frac{\dot H}{H^2}\qquad## where, ##~~~\epsilon_H = -\frac{\dot H}{H^2}## ##H## is the Hubble parameter, and ##\epsilon_H## is the Hubble slow...
  35. S

    Automotive Air fuel ratio effects in diesel vs. petrol engines

    I'm a mechanic who is currently doing a study automotive engineering. Being someone who worked on both diesel and petrol cars I know what a higher or lower air fuel ratio (AFR) will do for both engines. However I don't fully understand how the following is possible. "Adding fuel in a diesel...
  36. K

    MHB Ratio Of Area To Perimeter

    The length of a rug is eight times greater then the width. if the width of the rug is (w+5), what is the ratio of the area of the rug to the perimeter of the rug in simplest form?
  37. I

    I Experimental Shear Modulus and Poisson Ratio

    I'm designing a 'thing' for my masters project, which has to be 3D printed. I've designed this in Inventor, but it doesn't have PLA (Polylactic Acid), so I've been using Inventor's PMMA (Perspex) thus far. I want to get more accurate figures, so I've had a 1 cm3 block printed to get an exact...
  38. W

    Doppler effect with frequency ratio

    Homework Statement An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the...
  39. Arman777

    Drag Force Ratio: Jet vs Transport at 1200 km/h, 15 km Altitude

    Homework Statement Calculate the ratio of the drag force on a jet flying at ##1200 km/h## at an atttude of ##15 km## to the drag force on a prop-driven transport flying at half that speed and altitude.The density of air is ##0.38(\frac {kg} {m^3})## at ##10 km## and ##0.67(\frac {kg}...
  40. Biker

    Exploring the Ratio of Melting Ice Cubes

    Homework Statement The following chart shows the temperature before and after Melting Ice. (A, B) have the same amount of water. If the heat required to fuse both cube are equal. The ratio between the two cubes mass: Cup Before After A 25 21 B 25 23...
  41. A

    MHB Can the Sum of Two Unknown Variables be Determined with Limited Information?

    Hi there, I need help with the following situation. Apologies if I'm not using the correct arithmetic terms! Variables: d,e,f e + f = g d / g = j j x e = K j x f = L K + L = M d = M the above situation is a simplified problem, which is easily solvable. Here's where I run into trouble...
  42. H

    B Phi Ratio in Physics | G Factor Calculation

    Hello it's me again, I looked into connections between Pure Mathematics and Physics again and came across this interesting Web Page that proposes time in Quantum Physics may be related to Phi << Dubious Link Deleted by Mentors >> it's not a lot to read and I was wandering what you people think...
  43. G

    I Ratio between spontaneous/stimulated emission

    Hi. In thermodynamic equilibrium, the ratio between spontaneous and stimulated emission is $$\frac{A_{21}\cdot N_2}{B_{21}\cdot N_2\cdot u(f)}=e^{\frac{hf}{k_B T}}-1$$ where ##A_{21}## and ##B_{21}## are Einstein coefficients. This means, that there's always much more spontaneous than...
  44. saybrook1

    Don't understand this limit change in a ratio test

    Homework Statement I would like to understand how the limit was changed in the ratio test from step 1 to step 2 in the image that I've posted. I thought that the denominator would look like (2/n+2)(2/n+1) in step 2 since it looks like we are just turning the n's into reciprocals. Any help here...
  45. Aleph_null

    Find the minimum and maximum of a ratio for equilibrium

    Homework Statement Consider the rod as shown in the figure. The coefficient of static friction at A and B is \mu_s. I'm trying to find how big and how small the ratio l/d can be for the rod to still be in equilibrium. I have calculated how big all forces are acting upon the rod in the case...
  46. DaTario

    I 360 degrees and the Golden Ratio

    Hi All, I have just found in the internet an identity showing that the Golden Ratio can be expressed as a function of the cosine of the angle of 36 degrees. It seemed to me as an important fact related to this specific angle. Had this fact, historically, any relevance to the choice of the 360...
  47. T

    A Improving intuition on applying the likelihood ratio test

    I am trying to better understand likelihood ratio test and have found a few helpful resources that explicitly solve problems, but was just curious if you have any more to recommend. Links that perhaps work out full problems and also nicely explain the theory. Similar links you have found...
  48. H

    Momentum question asking ratio of final 2 velocities

    Homework Statement A cart mass of M moving at 3V (right) collides with a stationary mass of M, Determine the ratio of the two final velocities if the collision is elastic Homework Equations p=mv ek=(mv^2/2) The Attempt at a Solution m1v1=m1v1'+m2v2' Since the masses are all equal and v1 is...
  49. TheSodesa

    A gyromagentic ratio for a cylinder

    Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...
  50. Albert1

    MHB Finding the Ratio of x,y,z in $R^+$

    $x,y,z\in R^+$ $x=\sqrt{{y^2}-\dfrac{1}{25}}+\sqrt{{z^2}-\dfrac{1}{25}}$ $y=\sqrt{{z^2}-\dfrac{1}{36}}+\sqrt{{x^2}-\dfrac{1}{36}}$ $z=\sqrt{{x^2}-\dfrac{1}{49}}+\sqrt{{y^2}-\dfrac{1}{49}}$ $find \,\,\,\, x:y:z$
Back
Top