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.

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  1. anemone

    MHB Find the value of the ratio of m/n

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  2. K

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  3. R

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  4. D

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  5. S

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  6. C

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  7. H

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  8. R

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  9. J

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  10. M

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  11. E

    MHB Determine the ratio of the base to the perimeter.

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  12. T

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  13. N

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  14. D

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  15. S

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  16. E

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  17. Saitama

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  18. E

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  19. H

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  20. B

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  21. T

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  22. M

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  23. T

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  24. adjacent

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  26. N

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  27. N

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  28. Albert1

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  29. T

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  30. N

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    hi friends, can anybody clear my concept about the following sentence. " if we use substrates with higher permittivity, like quartz or GaAs that has been used in previous successful experiments, the unit cell will have smaller unit-to-wavelength ratio".
  31. Spinnor

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  32. N

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  33. N

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  34. Z

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  35. B

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  38. O

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  39. B

    Limit of Ratio Function with Dots and Filled Numbers: Understanding the Results

    Homework Statement This is not homework Could you help me understand what happens to this function \frac{1}{\sqrt{100..1^2+199...9}- 100...1} when the dots are filled with 0's and 9's , shouldn't the result be 1/.99999...)= 1.? but if to this input...
  40. C

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    Velocity ratio is defined as the ratio of the distance moved by effort and load, in the same time interval. It is said and known : that in the first order of lever, velocity ratio is usually greater than 1 but could be less or equal to 1. Why do we say that? And what does it mean? In the...
  41. S

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  42. tartaneto

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    Hi guys. I have something stuck in my head since a few days and I'd like to have your opinion about that. I don't know if I am missing something in my assumptions so please feel free to enlighten me. Here's the thing: considering two protons (or electrons), one fixed at the origin of the frame...
  43. anemone

    MHB Proving Area Ratio of Equilateral Triangle Divided by Line

    A line divides an equilateral triangle into two parts with the same perimeter and having areas $A_1$ and $A_2$ respectively. Prove that $\dfrac{7}{9} \le \dfrac{A_1}{A_2} \le \dfrac{9}{7}$.
  44. W

    Calculating Ratio of Electrical Current to Light Speed: A Challenge!

    Homework Statement If a 0.505m long wire is excited into its lowest electrical resonance by a 2.2E7 Hz electrical oscillator, what is the ratio of the speed of the electrical current to that of light? Assume that the wire is like a tube with both ends closed. f=2.2E7 L=0.505 v=...
  45. J

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  46. R

    Determining the damping constant from the ratio of amplitudes

    Homework Statement I have measured the amplitude between the first and tenth oscillations for a damped harmonic oscillator (spring with a mass attached). I also have measured the period. First question. Is an (underdamped) harmonic oscillator periodic? Like I know that the solution to the...
  47. K

    MHB Solve Ratio Word Problem: Find Value of x

    hi , this is one simple math but i am not getting the answer. the work done by (x-3) men in (2x+1) days and the work done by (2x+1)men in (x+4) days are in the ratio of 3:10.find the value of 'x'.
  48. K

    MHB Solving Ratio and Proportion Problem: (a+b+c)^2/(a^2+b^2+c^2)

    hi , i am stuck with a problem . the problem is if a , b , c are in continued proportion ,then prove that (a+b+c)^2/(a^2 +b^2 +c^2) =(a+b+c)/(a-b+c) i have tried solving the problem in different way like breaking the formula of (a+b+c)^2 =a^2 +b^2 +c^2 + 2ab +2bc+2ca , then used...
  49. J

    MHB Proportions and Equations: Can You Prove a Ratio with this Equation?

    if x/(b+c-a)=y/(c+a-b)=z/(a+b-c) prove that.. x(by+cz-ax)=y(cz+ax-by)=z(ax+by-cz)
  50. A

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    Why c - 14 is radio active though n/p ratio is less than 1.5?
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