Division Definition and 469 Threads

So using the multiplicative inverse axiom we have : 1) x . x^-1 = 1 2) x . (1/x) = 1 I have no idea why do mathematicians define the multiplicative inverse of a number x to be the "fraction" 1/x. But I know for sure that multiplying any number a for example by the multiplicative inverse of x is...

I am Sorry it's a silly question but its been bothering me, So I needed to ask... In the process of division, when there is a condition like- 4/5 when the divisor is greater then the dividend. why is the Remainder 4 ? as when the divisor is greater then the dividend then the division goes in...

Why does, 4√64÷2√4 =2√16 ? I can see the method (4÷2=2, √64÷√4=√16) But why is it not; 4 times √64 divided by 2 times √4 (as per BODMAS) i.e, 4 times 8 divided by 2 times 2, which = 32 Nb. When I put it into my calculator that way it gives 32 as the answer (4*√64÷2√4)

I understand the mathematics that 1 divided by infinity is virtually zero and so equals zero. I look on the internet and that is the answer that I get. Is this a simplification for early mathematics learning and, if I continue, will I find a more complex answer? The reason that I ask is that I...

For example what is ##\frac {169}{13} = ?## This says “When ##169## is divided into ##13## groups how many there are in each group?” This can be converted into a multiplication problem like this “##13## groups of how many in each group makes ##169##?” This is ##13 * ? = 169##. It can be solved...

So the confusion here is that division by zero is often said to be undefined. So whereas, the point (0,0) certainly appears in the set of values where x=y, does the point (0,0) appear in the set of values where 1=y/x. Why or why not? In other words are the set of points where x=y the same as...

A division by zero is a mathematical oddity, , if a computer or calculator etc performs a 1\0 they would crash, the OS prevents the execution, and displays ERROR or UNDEFINED, , , some versions of windows calculator display positive or negative infinity, , try it Any ideas on this ?

What I think I should do: 1 = 0001 7 = 0111 3 = 0011 First block = 00010111 Second Block = 00110000 Now, I do binary division 00010111/11010 = find the answer 00110000/11010 = find the answer This is what I think I should do, but I am not sure if this is correct. Is this basically CRC? Any...

-1 -2 3 | 1 2 4 9 -31 15 | -1 -7 5 1 2 -3 7 9 -31 15 7 14 -21 -5 -10 15 5 -10 15The quotient has the coefficients -1, -7, 5. Now here is the problem. I assumed the variables would thus be...

Curious to know why...

I grok, am NOT asking about, the answers below. Rather, how can I calculate the final answer DIRECTLY, without division? I don't know why my Latex isn't rendering here? Please see: [web link redacted by the Mentors] Orange underline 1. Unquestionably, $\color{#FFA500}{4 \times 3/2} = 3!$ But...

Consider the division problem $\dfrac{99}{33}$ a. Which interpretation do you think would be easier to use if you need to draw a picture? $\circ \quad$ partitioning equal subsets $\circ \quad$ repeated subs traction ok I tried to look up some definitions for this question but didnt see how it...

use doubling method $\dfrac{972}{69}$ $1 \to \boxed{69}+\boxed{a}=\boxed{?}$ $2 \to \boxed{138}+\boxed{b}=\boxed{?}$ is a 100 then what is b?

Theorem: Let ## f(x), g(x) \in \mathbb{F}[ x] ## by polynomials, s.t. the degree of ## g(x) ## is at least ## 1 ##. Then: there are polynomials ## q(x), r(x) \in \mathbb{F}[ x] ## s.t. 1. ## f(x)=q(x) \cdot g(x)+r(x) ## or 2. the degree of ## r(x) ## is less than the degree of ## g(x) ## Proof...

I have the following integration - $$\int \frac{2}{x - b \frac{x^{m - n + 1}}{(-x + 1)^m}} \, dx $$ To solve this I did the following - $$\int \frac{1 - b \frac{x^{m - n}}{(-x + 1)^m}+1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx $$ Which gives me -...

Use factor theorem and syntheitc division and its conjugate to decide whether the second polynomial is a factor of the first $x^3-5x^2+3x+1;\quad x+1$ \item \textit{apply synthetic division} \item$\begin{array}{c|rrrrr} 1 &1 &-5 &3 &1\\ & &1 &-4 &-1\\ \hline &1 &-4 &-1 &0...

Hello, all I'm a rising senior who's about to apply for grad school. However, this year has been a rough year for me as my overall grade has declined a bit, especially in that I did not do well in 3 core major courses: mechanics B and EM II I got a B and STAT MECH B+(sadly, I thought i deserved...

Here's the diagram of the circuit: And here's the solution I found on a site on Google: I tried to follow through the solution given, but can't understand how it is applying current division rule to find current in QA and QB, and subtracting current values to find the current in AB is still...

##x^{2017} + 1 = Q(x) . (x-1)^2 + ax + b## where ##Q(x)## is the quotient and ##ax+b## is the remainder ##x=1 \rightarrow 2 =a+b## Then how to proceed? Thanks

The main problem is the verse of the 2 currents ## i1 ## and ## i2 ## . I think they both go clockwise, so in the node A we should have ##i1+i2=20A##. Now let's apply the second law (going clockwise). So ##ΔV1-R1*i3 - R2*i4 + ΔV2=0##, where ##i3## and ##i4## are the currents which pass through...

Hi everyone, I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track. If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...

Our teacher said that powers in division have to be subtracted when the same base , but still , I am not getting the right answer.

As we all know that division simply means how many parts of the whole we have (or splitting into equal parts) 1)Example:- if we have 12 apples and there are 3 people so each will get 4 apples right. Easy! Now my question is how does this definition makes sense in term of physical quantities ...

Hello, I got a very basic question... A number n is dividable by 15 and 18. Can I assume from that that it is dividable by 27? (dividable - you can divide it by 15 and get no reminder). If it is dividable by 15, it is by 3 and 5. If by 18, it is dividable by 3 and 6, which means 3 and 2...

I'm curious if anyone has either shared a similar experience or has input regarding this. I was planning to take Stat Mech my second semester junior year, but heard the prof is AWFUL and unorganized, so I signed up for solid state instead (upon hearing that the solid state prof is awesome). My...

above video states that arg(z1/z2) = arg(z1) - arg(z2) this is seems very similar to Log rules but these are inverse function for angles right? And log rules only apply to logarithms, not sure where he got this from? What am i missing?

Hello everyone, I am in an upper division undergraduate electronics and circuits class right now and the textbook that were using (Eggleston: basic electronics for scientists and engineers) is not resonating with me. I was wondering if anyone had recommendations for a textbook that explains...

I came across a significant figures problem today that I need information on. The problem is this: "What volume of water can a cylindrical container hold of it is 13.0 cm tall and 12.0 cm in diameter? Show your work and express the answer in scientific notation using significant figures." Of...

On the right paragraph it says "The trial divisor 1200 goes into the dividend 13952, 8 times" Clearly 1200 goes into 13952, 11 times. I don't understand why 8 is (arbitrarily?) chosen. Please help. Thanks.

Hi I know that division of a real number by zero is not defined. I just came across the following in a textbook on Complex Analysis by Priestley , " we are allowed to divide a complex number by zero as long as the complex number ≠ 0 " Is this correct ? What happens if the complex number is...

In many books on number theory they define the well ordering principle (WOP) as: Every non- empty subset of positive integers has a least element. Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it...

In many books on number theory they define the well ordering principle (WOP) as: Every non- empty subset of positive integers has a least element. Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it possible...

I'm reading a book where the author gives the long division solution of ##\frac 1 {1+y^2}## as ##1-y^2+y^4-y^6...##. I'm having trouble duplicating this result and even online calculators such as Symbolab are not helpful. Can anyone explain how to get it?

Why is the division of zero by itself not equal to one,since it is conventional that any number divided by itself is equal to one?,or maybe is zero not a number?

If the euclid division lemma was not discovered by euclid himself, then why was the name "euclid lemma"? (https://en.wikipedia.org/wiki/Euclidean_division#History)

Hi all, I was working the following example: where I need to find the currents. I tried solving using the traditional V=IR => I=V/R, and then I tried with the current division rule. However with the current division rule the answers don't match. Also according to the answers on the book the...

1. A capacitor with a capacity of C= 20μF is connected to a source with a voltage of V=24V. We unplug the source from the capacitor and we then connect it with a wire and the capacitor gets charged in a time of Δt=0.2s. Figure out the number of electrons that pass go to the capacitor and the...

What's the best way to demonstrate Synthetic division with Latex I tried an array but too much open space Mahalo

Hello Consider the following code in Python3 n = 226553150 m = 1023473145 n*m = 231871064940156750 int(n*m/5) = 46374212988031352 n*m//5 = 46374212988031350 Now since ##n*m## is divisible by ##5##, both should be give the same answer. But the first is wrong and second is correct. What is...

what is the use of multiplying and dividing a vector by a scalar?

Hi, In about two weeks I'm starting my Junior year at a UC, after transferring from a community college. I want to review/get ahead before the quarter officially starts, but I'm at a loss of how to do so. I feel like I may be at a disadvantage to other students because my previous courses...

Hi. x2 = x3 / x but x2 is defined for all x and equals zero at x=0 but what happens for x3 / x at x=o ? Is it defined at x=o ? Does it equal zero ? If not what is causing this anomaly ? Thanks

Homework Statement Let a, b be natural numbers then there exists a unique pair (q,r) that are elements of the non-negative integers such that b=aq+r and 0 is less than or equal to r which is less than a I have a question regarding the existence part of the proof, now if I assumed a is less...

11. Given a polynomial with the degree 3. If it is divided by x^2+2x-3, the remainder is 2x + 1. If it is divided by x^2+2x, the remainder is 3x - 2. The polynomial is ... A. \frac23x^3+\frac43x^2+3x-2 B. \frac23x^3+\frac43x^2+3x+2 C. \frac23x^3+\frac43x^2-3x+2 D. x^3+2x^2+3x-2 E. 2x^3+4x^2+3x+2...

Say I have a given problem that states: Does the Intermediate Value Theorem guarantee that the following equation has a real solution between ##(\frac{7}{2})## and ##(\frac{9}{2})##? $$3x^4-27x^3+177x^2+1347x+420=0$$ Now what I want to do is determine the sign of x=##(\frac{7}{2})## and...

How do you write each line of long division in LaTeX on here ? Thanks

Homework Statement (1+2i+3i2)/(1-2i+3i2) answer options : a : 1 b: -i c: i d: 0 Homework Equations what is the most easy method to solve it , The Attempt at a Solution are they conjugate to each other ? if they are than z/zconjugate =1 , but how can...

So I just changed my major from Math to EE this semester and I really would like to continue taking some math. I have completed the entire Calc 1-3, LA, DEQ's, and a intro stats course. I only need 1 more course for a math minor. (intro proofs won't count for this though). My university doesn't...

I am reading "Algebra: An Approach via Module Theory" by William A. Adkins and Steven H. Weintraub ... I am currently focused on Chapter 2: Rings ... I need help with an aspect of the proof of Corollary 2.4 ... ... Corollary 2.4 and its proof read as follows: In the above proof of Corollary...