What is Division: Definition and 486 Discussions

A division is a large military unit or formation, usually consisting of between 6,000 and 25,000 soldiers.
In most armies, a division is composed of several regiments or brigades; in turn, several divisions typically make up a corps. Historically, the division has been the default combined arms unit capable of independent operations. Smaller combined arms units, such as the American regimental combat team (RCT) during World War II, were used when conditions favored them. In recent times, modern Western militaries have begun adopting the smaller brigade combat team (similar to the RCT) as the default combined arms unit, with the division they belong to being less important.
While the focus of this article is on army divisions, in naval usage, "division" has a completely different meaning, referring to either an administrative/functional sub-unit of a department (e.g., fire control division of the weapons department) aboard naval and coast guard ships, shore commands, and in naval aviation units (including navy, marine corps, and coast guard aviation), to a sub-unit of several ships within a flotilla or squadron, or to two or three sections of aircraft operating under a designated division leader. Some languages, like Russian, Serbian, Croatian and Polish, also use a similar word, divizion/divizijun/dywizjon, for a battalion-size artillery or cavalry unit.

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  1. Mr Davis 97

    Division for Ratios: Explaining Value of Fractions

    Why is division used for ratios? For example, if we have 1 dog for every 2 cats, then why can this relation be modeled by the division? Since the ratio can essentially have the value of 1/2 or 2, then what is the significance of these two distinct numbers in relation to the ratio? How does the...
  2. Mr Davis 97

    What is Division? An Intuitive Explanation

    Although of course I have been using division since my elementary years, I still can't out my finger on exactly what division is from a computation standpoint. For example, addition is adding objects (very intuitive), subtraction is adding the additive inverse of an object, and multiplication is...
  3. N

    Division by 0: A Puzzle That Has Baffled Us for Years

    Hello This is question is bugging me for years. Why is division by 0 undefined and not multiplication by 0 undefined? If any number multiplied by 0 is 0 then the logical answer for any number divided by 0 would be ∞ (for me at least). If you "define" N/0=∞ and N*0=undefined then there are...
  4. gfd43tg

    MATLAB Understanding Matrix Division in Matlab: Solving Linear Systems

    Hello, I am confused about a concept, Suppose I am trying to solve a linear system ##Ax = b## I want to know why is it when I solve for x, the command is x = A\b. Why would it not be x = b\A. One could see that if you divide x on both sides, then b/x = A. Is this not true for the matrix?
  5. TheSodesa

    Polynomial long division -- How does it work?

    Let's say I wanted to do the following calculation: (x^2 + 2x + 1) / (x+1) I've scrolled through some online guides, and they all show how to do it, but not the principle behind it. I'm specifically having trouble with the fact, that instead of dividing the largest degree term with the entire...
  6. S

    MHB Doing polynomial long division

    rewrite using polynomial long division \frac{x^3 + 4x^2 + 3}{x+4} so I did x+4 \sqrt{x^3 + 4x^2 + 0x + 3} and got x^2 + 1 - \frac{1}{x+4} What am i doing wrong? How is that incorrect?
  7. M

    Array multiplication and array division

    Hi, in Matlab I encounter with two new operations for me which are array multiplication and array division. I want to learn that do they have physical applications in real world physics problems or are they be related with banking and accounting.
  8. P

    Preparation for Upper Division Physics (general advice in doing well)

    and grad school as well. Hi, I'm a physics major at UCSD (3rd best UC school; behind UCLA and UC Berkeley) , and I'm looking for general advice in doing well in my upper division courses, since I'm fairly nervous. I know I will be in smaller classes filled with the next Einsteins and Feynmans...
  9. J

    What is the relationship between two vectors in terms of rotation and scaling?

    I want find a value M such that given v and u, satisfies the equation v=Mu. Well, the vector u has a modulus u and a direction α wrt x-axis; the vector v has another modulus v and another direction β wrt x-axis. What is happened is a change of magnitude and direction of the vector u...
  10. kq6up

    Upper Division (Junior Sr. Level) Mechanics Textbook Recommendations?

    I am reviewing to go back to grad school, and I need suggestions on a mechanics book to review. Having a readily available solutions manual is a huge plus since I am self studying. Recommendations? Thanks, Chris Maness
  11. J

    How is the division of the current for all passive elements?

    The current always prefers the path with minor resistance, but how the current reacts wrt the inductance and capacitance?
  12. evinda

    MHB How to Use Euclidean Division in $\mathbb{Z}_7$?

    Hello! :D I am given the following exercise: In $\mathbb{Z}_7$ apply the Euclidean division, dividing $[2]x^5+x^4+x^3+[3]x^2+[2]x+[2]$ by $[3]x^2+[2]x+[3]$. That's what I have done: $$\text{ the units of } \mathbb{Z}_7 \text{ are: } \{ 1,2,3,4,5,6\}$$ We want $[3]x^2+[2]x+[3]$ to be monic,so we...
  13. MarkFL

    MHB Synthetic and polynomial long division

    Until now, I have avoided trying to display techniques of division using $\LaTeX$ because there just didn't seem to be a nice way to carry it out. However, we may use the array environment for the display of synthetic and polynomial long division methods very nicely. I will demonstrate how to...
  14. chimath35

    Division as Subtraction: A New Perspective

    So, I assume to look at multiplication as addition; how should I look at division?
  15. chimath35

    Division Algorithm: Understand Unique c & d

    So, the division algorithm states that if a and b are integers with a>0 then there exist c and d integers such that 0<=d<a b=ac+d d and c are unique Now I don't understand d and c being unique. For example 4*3 + 3 = 15 where a=4 c=3 d=3 b=15 c and d are not unique, or maybe I don't...
  16. Y

    Fourier Integrals and Division

    Homework Statement (a) Find the Fourier transform f(ω) of: f(x) = cos(x) between -pi/2 and pi/2 (b) Find the Fourier transform g(ω) of: g(x) = sin(x) between = -pi/2 and pi/2 (c) Without doing any integration, determine f(ω)/g(ω) and explain why it is so Homework Equations f(ω) =...
  17. S

    Asking about matrix division

    Is it possible to compute matrix (A/B) without first finding the inverse of matrix B but ending with EITHER { A * (Inverse of B) } OR { (Inverse of B * A }...i think i discovered the trick
  18. D

    Approximating Division for X1, X2 & ΔX Expressions

    What is the name and where can I find the derivation for the following approximation? (X-(ΔX/2)) / (X+ (ΔX/2)) ≈ 1- ΔX/X Assuming ΔX << X, and X = (X1 + X2) / 2 and ΔX = X1 - X2 Thanks fellas! EDIT: Revised the expression.
  19. Duderonimous

    Help in choosing 4 upper division physics classes.

    Hello, I am a transfer student that has been admitted to CSU Long Beach in the Fall '14 for a BS in electrical engineering and I would also like to pursue a BA in physics. I reckon this will take me 4 years. A BA in physics consist of taking lower division CALC I/II/III and PHYS ABC. Also...
  20. S

    MHB Polynomial Long Division w Integrals

    I do not understand how I would do this with long division since there is only 2 terms. I can't remember the trick. Here is what I have so far. \int \frac{3x^2 - 2}{x^2 - 2x - 8} dx so I got \int 3 + \frac{x^2 - 2}{(x - 4)(x + 2)} I'm not sure if that's right? I just factored it out instead...
  21. evinda

    MHB Why do we apply the Euclidean Division, b divided by 3?

    Hey! :rolleyes: I am looking at the following exercise: "Prove that $\forall n \in \mathbb{N}$ the number $17 \cdot 3^{2n+1}+41 \cdot n^2 \cdot 3^{n+1}+2$ " is not a square of an integer." We do it like that: $a(n)= 17 \cdot 3^{2n+1}+41 \cdot n^2 \cdot 3^{n+1}+2=3 \cdot (17 \cdot 3^{2n}+41...
  22. N

    (Confused) RF circuit concepts- Voltage division?

    how could you calculate the input voltage at an input impedance from a voltage source? I saw they use voltage division law to find the voltage at the input impedance(Zin) from a voltage source(Vs). They do it like Vs * Zin/(Zin+Zs). The problem came... We all know that we can determine the...
  23. gfd43tg

    Voltage Division: Unraveling the Mystery

    Hello, I am confused about voltage division. In reference to the circuit on wikipedia, I don't understand why Vout = R2/(R1+R2)Vin and not R1/(R1+R2)Vin. The current goes through R1 first and has a drop over that resistor, not R2. https://en.wikipedia.org/wiki/Voltage_divider#Resistive_divider
  24. JasonHathaway

    Current division, equivalent resistances and short circuts

    Hi everyone, this my first post in here. Anyway, this is a solved problem, but I can't get the answer :S Homework Statement Homework Equations * Series-Parallel combination (RT=R1+R2+R3...+Rn for series, 1/RT=1/R1+1/R2+1/R3...+1/Rn for parallel) * WYE (TEE) - DELTA (PI)...
  25. Square1

    Why Should You Divide by x-1 for Evenly Spaced Events Throughout the Day?

    Lets say you want to do something x times per day. Importantly, you want to start doing this thing at the begining of the day and end at the end of the day (start of period end of period). The first thing I think about when I want to start doing something like this is divide the day's hours by...
  26. A

    MHB Division with square roots at the base

    Hi, I am new here and I don't know if anyone is going to answer to this post, but if you do so thank you very much. I have been frowning on these kind of problems! I have been trying to solve some exercices from my homeworks. However, I don't know if I am doing them correctly. Here is one...
  27. A

    Upper Division ODE vs PDE class

    I'm trying to decide between taking an ODE class or a PDE class next. I have already done Calculus 1,2,3 so I already know some ODEs and PDEs and linear algebra. I'm a 3rd year mathematics major with a minor in Statistics and I'm interested in applied mathematics.ODE course coverage: Ordinary...
  28. MarkFL

    MHB Ray's question at Yahoo Answers regarding polynomial division

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  29. M

    Division between QM and Interpretations

    Trying to relate a bit better to where QM stops, and Interpretations begin. Especially with respect to Decoherence. Is Decoherence seen as a measurable phenomena, or, just as a "possible" explanation for measurable phenomena? Obviously when I mark a path in a 2 slit experiment I cause...
  30. M

    Why Is the Current Negative in This Circuit Division Equation?

    Can someone tell me why the current I is negative and not positive? Im guessing the equation should be: I = (-2)(6||3)/(6). But why the negative sign?
  31. S

    Relationship between division, subtraction, and limits

    Ok, so I'm not really too good at group theory and that kind of math, so I hope I can explain my question: I tried to evaluate \frac{d}{dx}e^{x}: \frac{d}{dx}e^{x} = \frac{e^{x+h}-e^{x}}{h}, h -> 0 = \frac{e^{x}e^{h}-e^{x}}{h}, h-> 0 = e^{x}(\frac{e^{h}-1}{h}), h-> 0 So I figured...
  32. paulmdrdo1

    MHB How to Properly Arrange Dividend in Polynomial Division with Multiple Variables?

    i was trying to solve this problem when i got confused on how to arrange the terms in descending powers of the literal factors because some term contain two variables and the polynomial has 3 variables. how can i properly arrange the dividend here? $\displaystyle...
  33. Ackbach

    MHB Analogy Between Long Division and Polynomial Long Division

    Hopefully, anyone who has studied polynomial long division understands the link between it and regular long division. If you divide $58$ into $302985$, you could follow the usual long division procedure and obtain the answer. Alternatively, if you divide $x+4$ into $x^{3}+2x^{2}+6x+7$, you could...
  34. C

    Polynomial Division: Simplifying with Long Division

    1. Hi I have a question I am stuck on it is: (x3 + 2x2y - 2xy2 - y3)/(x-y) Can anyone help? Homework Equations The Attempt at a Solution
  35. F

    Frequency Division Multiplexing. FM SSBSC system. Bandpass Filter

    Homework Statement Due to its bandwidth and power efficiency, SSBSC is commonly used in Frequency Division Multiplexing (FDM) systems. FDM systems are used to combine a number of separate information channels into a single transmission. Each channel uses a separate carrier frequency and the...
  36. F

    MHB Understanding Algebra Division Formulas: SPI, EV, PV, and AC

    If you rearrange this formula from SPI=EV/PV to EV=SPI*PV. Why is this formula like this: CPI=EV/AC is AC=EV/CPI Aren't they basically the same. Thanks for the help.
  37. R

    Remainder After Division Problem

    Homework Statement (-8)^4124 + 6^3101 + 7^5 is divided by 3. Homework Equations The Attempt at a Solution My original insight was that 6 raised to any power is always divisible by 3. 7 raised to any power yields a remainder of 1 when divided by 3. and the remainder from -8...
  38. T

    How to check algebraic long division?

    My errors all involve multiplying numbers that look the same, for instance if there is a 2 that I'm supposed to multiply by a 2a I'll put 2 a, and not think about it till I see I got the answer wrong. Is there a way I can do something to the answer to see if it is right before I submit it?
  39. M

    Meaning of Multiplication and Division in Physics

    Mathematics is all around sciences.It is also considered a language.In language everything should have meaning. I know addition and subtraction meaning.Same things[quantities ,etc.] can add or subtract . It cannot be done on different things. What is the meaning of multiplication and...
  40. A

    Solving quartic equations using synthetic division

    Homework Statement We have a polynomial of fourth degree. I want to use synthetic division. However, is synthetic division applicable at all times? Are there cases in which the first binome extracted cannot have an integrer? What do I do at that time? Homework Equations Synthetic...
  41. matqkks

    MHB How best to teach the division algorithm?

    What is the best way to introduce the division algorithm? Are there real life examples of an application of this algorithm. At present I state and prove the division algorithm and then do some numerical examples but most of the students find this approach pretty dry and boring. I would like to...
  42. matqkks

    How best to teach the division algorithm?

    What is the best way to introduce the division algorithm? Are there real life examples of an application of this algorithm. At present I state and prove the division algorithm and then do some numerical examples but most of the students find this approach pretty dry and boring. I would like to...
  43. C

    Is Vector Division Possible in Mathematics?

    hi guys, i have a basic question on vector division..can i divide a vector by another vector to get the third vector.. i know, if it is scalar product then i can not do the reverse engineering but what happens with the vector products? like v=wxr can i get r(both direction and quantity) by...
  44. M

    Just finished my lower division physics sequence

    Hello everyone, I just wanted to make a post thanking all of those who have helped me over the past couple of years with my physics and math questions, since it would be hard to reach every individual. I am now finally done with the lower division physics sequence and managed to get an A in...
  45. S

    Looking for an upper division mechanics book, any suggestions?

    As the title says, I'm looking for an approachable upper division mechanics book. I'm starting my upper division come fall, and want to get a head start on this course. Sone background: I've taken the traditional mechanics, E&M, and modern physics (light, waves, intro to relativity and...
  46. pratikaman

    Real mechanism behind addition, subtraction, multiplication, division

    we all know the basic rules for operations of addition, subtraction, multiplication and division. but what i don't know is why these rules (of addition, subtraction, multiplication and division) works. as if we have been given algorithm to do these operations but not explained how they...
  47. E

    Polynomial Division 2: Step-by-Step Solution for (x^3-3x^2+12x-5)/(x-2)"

    Homework Statement Show by polynomial division that \frac{x^3-3x^2+12x-5}{x-2}=(x^2-x+10)+\frac{15}{x-2} The Attempt at a Solution Please see attachment
  48. E

    P.S. I did it on paperPolynomial Division: 3x^3-5x^2+10x+4 / 3x+1

    Homework Statement Use polynomial long division to determine the quotient when 3x^3-5x^2+10x+4 divided by 3x+1 The Attempt at a Solution Please see attachment as I wasn't quite sure how to write my answer here :shy:
  49. Q

    Why is (2x^2)/(x^2+1) not dividing evenly?

    I've looked examples up online and I just can't figure out what to do exactly when I have (2x^2)/(x^2+1), for some stupid reason that was probably the work of satan, EVERY problem on the internet only has the lead coefficient of the numerator equal to or less than that in the denominator and...
  50. Nero26

    External division of a line segment

    Suppose AB is a straight line segment. To divide the segment externally at point C in the ratio m:n, is it necessary for C to remain always outside of AB? I always thought C should be outside of AB, but the post in the link below confuses me...
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