Ratio Definition and 1000 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

    B Understanding the relationship between ratios and fractions

    As I understand, a ratio is a comparison between two or more quantities. Ratios involve two or more numbers. Whereas a fraction is a single real number. Why are ratios and fractions the same when ratios involve two or more different numbers whereas fractions represent only ONE real number like...
  2. hraghav

    Find ratio of brightness & the distance the 6th dark fringe is from central fringe

    a) sinθ = y / L where y = 1.26 m and L = 1.29m sinθ = 0.9767 β = (pi * a*sinθ) / λ where λ = 517.4 * 10^-9 m and a= 3.96 × 10^−6 m β = 0.000012151 / 517.4 * 10^-9 = 23.485 I / Io = (sin(23.485) / 23.485)^2 I / Io = 0.0002879 which is 0.2879 * 10^-3 b) asinθ=mλ where m =...
  3. M

    Ratio test proof

    For (a) and (b), Does someone please know how to prove this? I don't have any ideas where to start. Thanks!
  4. C

    Ratio Test vs AST

    Hi, I'm having difficulty understanding why the interval of convergence is (0, 18]. When I tested x=18, I got the following conclusion using the ratio test. When I attempt using AST, the function still diverges as the lim (n -> inf) = 2^n / n ≠ 0. What am I missing? Thanks!
  5. S

    Ratio of frequency between heavier and lighter part of composite cord

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  6. flyusx

    Is a Distribution Function a Ratio of Differentials?

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  7. Z

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  8. RChristenk

    Why Might a High P/E Ratio Be Attractive to Investors?

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  9. M

    Ratio of atomic masses of two ideal gases

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  10. prithika

    I Effect of vent ratio on the drag coefficient of round parachutes

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  11. S

    Calculating Weight Ratio of PEO and LiClO4 in PEO-LiClO4-Al2O3 PE Samples

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  12. M

    B Golden Ratio in Collatz-like sequences

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  13. agm

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  14. jaumzaum

    I Difference between relative risk and odds ratio

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  15. J

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  16. M

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  17. chwala

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  18. chwala

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  19. S

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  20. RayDonaldPratt

    I How to convert density ratio of grams/ mm^3 into metric tonnes/ m^3

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  21. Pipsqueakalchemist

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  22. U

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  23. M

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  24. chwala

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  25. A

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  30. Engineering77744

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  31. Prinzmio

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  32. Leo Liu

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  33. Jason-Li

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  34. W

    Can we assume constant C14 to C12 ratio in living tissues?

    Plants prefer C12 to C13 during photosynthesis, so that the C13 to C12 ratio in plants is less than that in the atmosphere (by around 20% for most plants, but less difference in C4 plants like maize). Do plants discriminate against C14 too? If so, won't that cause a considerable uncertainty in...
  35. chwala

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  36. Ackbach

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  37. Ackbach

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  38. M

    I Gearbox Gear ratio: How to get 60 rpm to 3500rpm? help please

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  39. W

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  40. harpazo

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  41. lucaszito

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  42. S

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  43. Athenian

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  44. L

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  45. Twigg

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  46. K

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  47. F

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  48. sodoyle

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  49. hquang001

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  50. J

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