What is quotient: Definition and 355 Discussions

In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division (in the case of Euclidean division), or as a fraction or a ratio (in the case of proper division). For example, when dividing 20 (the dividend) by 3 (the divisor), the quotient is "6 with a remainder of 2" in the Euclidean division sense, and



6



2
3





{\displaystyle 6{\tfrac {2}{3}}}
in the proper division sense. In the second sense, a quotient is simply the ratio of a dividend to its divisor.

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  1. D

    How to Correctly Apply the Quotient Rule in Differentiation?

    Homework Statement X / 1+sinX The Attempt at a Solution Quotient rule (1+sinX)(1)-X(1+cosX) / (1+sinX)2 To: 1+sinX-X-XcosX / (1+sinX)2 But when I look at the answer in the back of the book, it's wrong.
  2. D

    Find derivative using Quotient rule

    Homework Statement Differentiate f(x) = 6-5x-x2 / x2-1 ------- A) -5-5x / x2-1 B) 5 / (x+1)2 C) -5-5x / (x2-1)2 D) -5 / (x+1)2 E) -5+5x / x2-1 F) None of the above The Attempt at a Solution (x2)(-5-2x)-(6-5x-x2)(2x) / (x2-1)2 Simplified to: 5x2-10x+5 / x4-2x2+1...
  3. quasar987

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  4. R

    How to find the difference quotient and simplify the answer

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  5. M

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  6. B

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  7. MathematicalPhysicist

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  8. M

    Understanding Quotient Vector Space: Collapsing to Zero

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  9. Peeter

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  10. J

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  11. J

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  12. H

    Can We Identify Quotient Groups as Subgroups of the Original Group?

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  13. E

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  14. J

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  15. T

    Discrete Mathematics with possible Quotient Remainder Theorem

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  16. C

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  17. P

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  18. K

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  19. RyanSchw

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  20. M

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  21. M

    Taking the Second Derivative w/ the Quotient Rule: What if Numerator = 0?

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  22. L

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  23. D

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  24. P

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  25. T

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  26. L

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  27. M

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  28. T

    Using the Quotient Rule with the Chain Rule

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  29. P

    Problem with Differentiation Using Quotient Rule

    I am attempting to find the second derivative of a function: h(x) = [(x^2)-1] / [2x-(x^2)] I proceeded by using the Quotient Rule, and I found the following as the first derivative. (It is correct.) h`(x) = [2(x^2)-2x+2] / [2x-(x^2)]^2 Next, I tried using the Quotient Rule again, and...
  30. G

    Finding units in polynomial quotient rings

    Is there a simple method for finding all the units in a polynomial quotient ring over a finite field? For example: {F_2[x] \over x^7-1} I can see the easy ones like 1, and all power of x, but I wanted a general rule or method for finding all of them if it exists (besides testing each...
  31. A

    Problems with the quotient property of logarithms

    My test here asks me to: "Use log5 2 =0.4307 and log5 3=0.6826 to approximate the value of log5 12." According to my textbook I would solve this by subtracting (using the quotient property): 0.6826-0.4307. That = 0.2519. But that number isn't right! log5 12=1.544 (about) Which I found...
  32. W

    Explaining Quotient Topology: Step-by-Step with Examples

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  33. G

    Understanding Quotient Spaces in Topology: Exploring Attachments and Retractions

    Let X,Y be two spaces, A a closed subset of X, f:A--->Y a continuous map. We denote by X\cup_fY the quotient space of the disjoint union X\oplus{Y} by the equivalence relation ~ generated by a ~ f(a) for all a in A. This space is called teh attachment of X with Y along A via f. i) If A is a...
  34. F

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    Say for example, to differentiate x/(x²+1) I would use to quotient rule. However, would it be legal to bring up the denominator to: (x)(x²+1)-¹ and use the product/chain rule instead?
  35. S

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  36. T

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  37. M

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  38. B

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  39. H

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  40. M

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  41. M

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  42. N

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  43. A

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  44. E

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  45. S

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  46. S

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  47. M

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  48. S

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