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. nso09

    Finding the ratio of thicknesses of films (destructive)

    Homework Statement I need help on figuring out part C which is determining the ratio between ##t_1## and ##t_2## in order to get constructive interference. I'm given the index of refractions ##n_1=1.5## and ##n_2=2## and that I know that wave 1 and 2 have half cycle shift and wave 3 does not...
  2. C

    Specific heat ratio of gas mixture

    I am doing some multi-fluid hydrodynamic modelling and I have a quick question. I think I know the answer, but I am not convinced. One of the things that I need to know is the specific heat ratio, ##\gamma##, for the gas and my question is, how does one calculate this from the values of each...
  3. 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...
  4. karush

    MHB Ratio Test for Sum $\tiny{206.10.5.84}$

    $\tiny{206.10.5.84}$ \begin{align*} \displaystyle S_{84}&=\sum_{k=1}^{\infty} \frac{(4x)^k}{5k}\\ \end{align*} $\textsf{ ratio test}$ $$\frac{a_{n+1}}{a_n} =\frac{ \frac{(4x)^{k+1}}{5(k+1)}}{ \frac{(4x)^k}{5k}} =\frac{4xk}{k+1} $$ $\textsf{W|A says this converges at $4|x|<1 $ so how??}$
  5. moenste

    Ratio of the rate of decay of R to that of S after 2 hours

    Homework Statement At a certain time, two radioactive sources R and S contain the same number of radioactive nuclei. The half-life is 2 hours for R and 1 hour for S. Calculate: (a) the ratio of the rate of decay of R to that of S at this time. (b) the ratio of the rate of decay of R to that of...
  6. toforfiltum

    Find ratio between dimensions of can w/ largest capacity

    Homework Statement A cylindrical metal can is to be manufactured from a fixed amount of sheet metal. Use the method of Lagrange multipliers to determine the ratio between the dimensions of the can with the largest capacity. Homework EquationsThe Attempt at a Solution $$V(r,h)=\pi r^2h$$ $$2...
  7. S

    Solving Gearbox Ratio for 12" Wheel Travel @ 2mph

    I need to figure out a gearbox ratio to get a 12 inch wheel to travel at 2mph. If I remember right the equation should be 1foot * 3.14*gearbox output rpm*60 then all divided by 5280 to get the final mph. Am I on the right path? Then I need a gearbox output around 58rpm. Thanks to all of...
  8. karush

    MHB Supposed to use the root and ratio test

    $\tiny{206.b.46}$ \begin{align*} \displaystyle S_{46}&=\sum_{k=1}^{\infty} \frac{2^k}{e^{k}-1 }\approx3.32569\\ % e^7 &=1+7+\frac{7^2}{2!} %+\frac{7^3}{3!}+\frac{7^4}{4!}+\cdots \\ %e^7 &=1+7+\frac{49}{2}+\frac{343}{6}+\frac{2401}{24}+\cdots \end{align*} $\textsf{root test}$...
  9. S

    Ratio of cosmic and cosmogenic radiation

    Air stops most cosmic radiation. Yet some particles do reach sea level. The cosmic radiation at sea level is estimated at around 300 microsieverts per year. Cosmic radiation also causes nuclear reactions in air that stops it. Many isotopes created by cosmic radiation are stable, or short lived...
  10. Monoxdifly

    MHB How many people need to be added to complete the project in 5 days?

    A project can be done in 35 days by 12 people. However, after 25 days the project paused for 5 days. How many people need to be added? I guess it's 12. Am I right?
  11. Monoxdifly

    MHB Ratio of Boys & Girls in Class: 24 Boys & 16 Girls?

    In a class, the mean of boys' mark is 7.1 while the mean of girls' mark is 8.1. Their overall mean is 7.5. If there are 40 students in the class, determine: a. The ratio of boys and girls b. The number of boys and girls I got this question from someone I tutored. I got the number of boys as 24...
  12. jhan

    Constant Ratio of Drag coefficient and terminal velocity

    Guys,, please check my own way to get Drag coefficient and Terminal Velocity by given Drag force,.. okay,, lets for example: we know drag force is Fd= Cd*pf*v^2*A/2,, ill give little example (Cd=.02)*(pf=1027kg/m^3)*(v^2=.0025m/s)*(A=24m)/2 =( Fd .6162N) so drag force is .6162N,, okay..according...
  13. S

    Rocket Launch: Achieving Escape Velocity w/ Fuel-Mass Ratio of 300

    Homework Statement Rockets are propelled by the momentum of the exhaust gases expelled from the tail. Since these gases arise from the reaction of the fuels carried in the rocket, the mass of the rocket is not constant, but decreases as the fuel is expended. Show that for a Rocket starting...
  14. M

    MHB Ratio of the area of triangle in terms of another triangle

    :D I have trouble in determining the ratio of the area of $\triangle PST$ in terms of $\triangle PQR$ In the triangle PQR $QT=TR$, $PS=1 cm$ , $SQ=2 cm$ , How should I be writing the area of $\triangle PST$ in terms of $\triangle PQR $ What is known by me : Since...
  15. Gurfin321

    Automotive What Gear Ratio Is Needed for a 30-40 km/h Electric Longboard?

    I would like to know what gear ratio i would need for my electric longboard. The goal is to run the longboard at 30 - 40 km/h at max power. Me and the longboards weight is approximately 65 kg. The brushless motor i am running has an rpm of approximately 18000 rpm (as it is an airplane engine)...
  16. M

    MHB Ratio of the area of triangles

    In the figure , the area of triangle $ABC$ is twice that of triangle $BCD$.USing the given information , find the ration of the area of the triangle $CFG$ to the area of triangle $BEG$ Hint- Use the midpoint theorem. (Wave) Stuck in this problem & currently I have no workings to show.
  17. D

    Ratio of the periods of a damped and undamped oscillator

    Homework Statement Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by \frac {T_d} {T_0} = \sqrt {1+ \frac {1}...
  18. K

    Charge to Mass Ratio Calculation for Object

    Homework Statement A small object with mass m, charge q, and initial speed v0 = 6.00×10^3 m/s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm(Figure 1) . The electric field between the plates is directed downward and has magnitude E = 600 N/C ...
  19. S

    Determine the maximum ratio h/b

    Determine the maximum ratio $$h/b$$ for which the homogenous block will slide without toppling under the action of force F.The coefficient of static friction between the block and the incline is $$\mu_s$$. I have a doubt.About which point should the rotational equilibrium be applied?Should it...
  20. T

    MHB Ratio test with an integer power of an in numerator

    I have $$\sum_{n = 1}^{\infty} \frac{2^n}{n^{100}}$$ and I need to find whether it converges or diverges. I can use the ratio test to get: $$\lim_{{n}\to{\infty}} \frac{2^{n + 1}\cdot n^{100}}{2^n \cdot (n + 1)^{100}}$$ But I'm not sure how to get the limit from this. I know the limit of...
  21. C

    Help me derive the Doppler effect ratio

    Homework Statement I'm watching this lecture and wanted to attempt to derive the expression for ΔTo/ΔTs Homework Equations ΔTo = ΔTs + VΔTo / U The Attempt at a Solution I have worked out that ΔTs = 1-V / U, however I'm stuck trying to get ΔTs / ΔTo because of the ΔTo on both sides of the...
  22. I

    A What are the bounds of a ratio with a given set of numbers and variables?

    Sorry in advance if I've posted in the wrong section. given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}## where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##How would you go about finding the bounds of something like this, or determining if it even has any? ##( \...
  23. Z

    Ratio Question with 3 quantities

    Homework Statement If 15 workers can pave 18 driveways in 24 days, how many days would it take 40 workers to pave 22 driveways Homework Equations Actually i don't know which equation should be used for 3 quantities. I know the eq for two quantities. Because we increasing labours so we would...
  24. T

    AC vs evaporative cooler: ratio of (BTUs/hr)/electric watts

    Hi Air conditioner vs evaporative cooler: ratio of (BTUs/hr) / electrical watts I know evaporative coolers do not state BTUs/hr. I do not know why. Did anyone try them and record time taken to cool. I found this example, but I do not know if it is practically relevant...
  25. D

    B Ratio of circumference to diameter for infinitely large circ

    If you divided the circumference of an infinitely large circle by its diameter, would the result be pi?
  26. R

    I Propagating Error in both numerator and denominator of ratio

    Hello, I have a set of N samples, each of which yields the measurable variables A and B. I am interested in computing the mean and standard error of the ratio A/B within the group. The catch is that I need to do background subtraction on both A and B, and the two different background values BGA...
  27. Joseph Richard

    Continuous Ratio Conditions: Product of 1296, Last Term 1/6 of Sum of Means

    Homework Statement Determine the conditions of a continuous ratio knowing that the product of the four terms is 1296 and the last term is equal to 1/6 of the sum of means. Original question (in Portuguese): Determinar as condições de uma proporção contínua sabendo que o produto dos quatro...
  28. R

    Confused - Materials question regarding c/a ratio

    Hi everyone, first time poster here, I'm studying for a Materials exam, one of my weakest subjects and this question is causing me a lot of pain: Beryllium (Be) is a HCP metal with an atomic weight of 9 g mol-1 , an atomic radius of 0.112nm and a density of 1850 kg m-3 . Calculate its c/a ratio...
  29. M

    Stoichiometric air/fuel ratio of gasoline vapor

    Hello, Can someone tell me the optimum stoichiometric air/fuel ratio of gasoline VAPOR? I know that with liquid gasoline the optimum stoichiometric air/fuel ratio is 14.7 parts ambient air to 1 part gasoline. Thank you in advance for your help.
  30. Pattonias

    Aspect Ratio of Continuous Cast Rolled Steel

    We have a requirement that if our pipe is going to be fabricated from plate, then it must have a larger than 6-to-1 reduction from the original conventionally cast ingot or continuously cast slab. It is not specified whether this would be hot/cold rolling, but we figured that .5 inch plate...
  31. M

    MHB Find the ratio of lines in a circle

    I have no idea how to solve this problem. ABCD is just an irregular Quadrilateral so nothing too special with that figure. We are looking for the ratio BC:CD and we only have that two angles. I know that the answer is 1:√2, but I have no idea how to find it.
  32. mertcan

    I Is there a proof for the precision of convergence or divergence at x=+,-(1/L)?

    hi, If you look at my attachment you can see that the book express that for the situation of x=+,-(1/L) we need further investigation. It means being converged or diverged is not precise. I would like to ask: Is there remarkable proof that if x=+,-(1/L) convergence or divergence is not...
  33. alijan kk

    How Do Kinetic Energies Compare When Two Bodies Have Equal Momentum?

    Homework Statement 4. Two bodies of mass m1 and m2 have equal momentum their kinetic energies E1 and E2 are in the ratio. ans. m2 : m1[/B]Homework Equations E1=E2 P= mv The Attempt at a Solution E1=E2 1/2M1v^2=1/2M2v^2 (Mv^2)/2=(M2v^2)/2 multiply both side by 2 mv^2=2(m2v^2)/2 mv^2= m2v^2...
  34. W

    Ratio of size of prototype and model

    Homework Statement a gemoetrical similar open chanel model is constructed with 10: 1 , if the model discharged 7m^3 /s , what is the corresponding discharge in prototype? Homework EquationsThe Attempt at a Solution Q = (L^3) / T , [ (Lp^3)/ (Tp) ] / [ (Lm^3) / Tm ] = (Lr^3) / Tr [/B] but...
  35. T

    Find TX turns ratio and 'class' questions?

    Hi, Just made a small thought experiment on the train, haven't really thought about it in depth. I was just wondering, if I created the above scenario (open circuit secondary and a voltmeter), would I get a voltage (assuming there is a difference in turns for primary and secondary)? Neglecting...
  36. Firasf1dream

    Effective Compression Ratio Definition?

    hello everyone, i would like please to know what is Effective Compression Ratio for an RC 2stroke Engine that i have ? the value in the info is 9.7, so i need to know the meaning and what values are the best ? what is the range ?
  37. U

    Ratio for the dimples in a golf ball

    I'm conducting an experiment in order to find the effectiveness of dimples in a golf ball when flying through the air. As part of the experiment, I'm planning on testing the different dimple patterns of various golf balls. However, I'm having trouble coming up with a numerical ratio that can...
  38. prashant singh

    I Section formula, external ratio

    I want to know how mathematician got the idea of external division , how they can say that a point can divide a line externally, what's the reason behind this discovery . Why they discovered it.
  39. RoboNerd

    Finding ratio of masses of two blocks

    Homework Statement Two crates are stacked on top of each other on a horizontal floor. The coefficient of static friction between Box A and Box B is 0.6. The coefficient of static friction between Box A and the floor is 0.2. A force of 100 N is applied parallel to the floor on Box B. The boxes...
  40. RoboNerd

    Ratio of angular speed with conservation of energy

    Homework Statement A ball rolls down an incline plane without slipping. What is the ratio of its angular velocity at h/3 to its angular velocity at 2h/3? 1) 1:2 2) 1:sqrt(2) 3) 1:1 4) sqrt(2):1 5) 2:1 Homework Equations Conservation of energy with provisions for rotational and...
  41. S

    Calculate motor/gear ratio on single axis

    Firstly, let me explain that I am mostly inept at mathematics. Piecing together the required information is becoming a real challenge because of that. I am motorizing a dobsonian telescope. I have read many accounts of success and the steps involved. The places where detail is commonly left out...
  42. P

    Why Does Poisson's Ratio Differ for Different Materials?

    For any rod Poisson's ratio should be same i.e. 0.5 (we get this ans if we find (dr/r) / (dl/l) ) assuming that volume of rod always remains constant... But why it is not so ? We have different ratios for different materials..
  43. B

    Ratio of Power between Two Cars

    Homework Statement A Grand Prix race car accelerates to twice the speed of the car in sample problem 1, in the same amount of time. Calculate the ratio of the power needed by the Grand Prix car to the power needed by the car in sample problem 1. Given: initial speed of car=0m/s, final speed...
  44. B

    Signal to noise ratio in a CT scanner

    Homework Statement If the relative noise (noise divided by signal) in a region of a CT slice is measured to be N what would be the value if the tube current was halved, the pitch increased from 0.9 to 1.2, the rotation time increased from 0.75s to 1s and the slice width increased from 1mm to...
  45. J

    Finding the Radius of Convergence through Ratio Test

    Homework Statement Let f(x)= (1+x)4/3 - In this question we are studying the Taylor series for f(x) about x=2. This assignment begins by having us find the first 6 terms in this Taylor series. For time, I will omit them; however, let's note that as we continuously take the derivative of this...
  46. Glenstr

    Pulling power ratio for a cable drum at different capacities

    Prior to my life as a database administrator I was a hi lead logger in coastal British Columbia, which involves harvesting logs with machines capable of putting huge strain on cable and hydraulic systems. What got me to thinking this was a friend just let me know someone we know was recently...
  47. Bill48

    Constant Acceleration Ratio to Constant Velocity

    Homework Statement A car traveling at an unspecified constant speed passes a parked motorcycle cop. The motorcycle accelerated at an unspecified constant acceleration and reaches the car at unspecified distance d. At what point did the motorcycle's speed match that of the car, expressed as a...
  48. W

    Maximize volume-pressure ratio

    Hello, I'm making a fire-boat. The boat uses 2L bottles to supply water. The fire will be 1m from the fire fighting zone and 0.5m high. The bottles are pressurized to 300 kPa. How do I maximize the volume-pressure ratio that can be supplied at that range over 90s maximum?
  49. S

    I Effects of lug height on final gear ratio for a snowmobile....

    So, great site. I have a quick question that I think has a simple answer. On a snowmobile forum I visit there has an ongoing debate. The question is, all other factors being the same, does changing the lug height on a track, change the final drive ratio of the snowmobile? I think I know the...
  50. J

    Calculating Gear RPM: Understanding Tire and Shaft Rotation | 60 Tooth Gear

    Hey Guys, So in the attached image I'm trying to determine what the rpm of the 60 tooth gear will be given the 8.4" tire will be rotating at .68 rpm, everything else is just an assumption on my part. I'm assuming the following which is probably wong: The tire being rotated at .68 rpm will...
Back
Top