Questions tagged [arithmetic]

Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).

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38 views

Determining the Remainder

Is it possible to calculate the remainder of two given values with merely addition, subtraction, multiplication, and division? Is there an algorithm or formula if it is even possible? For instance, ...
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What is $1 \div 2 \times 2$? [duplicate]

In the UK where I live, we are taught the abbreviation BIDMAS/BODMAS for the order of mathematical calculations: Brackets Indices / Others Division Multiplication Addition Subtraction I know that in ...
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How to I find the correlation between to range of numbers efficiently?

How can I get 2 ranges of numbers to correlate the most efficient way? So I have these two range of numbers scoreRange = [1, 9]; achievementRange = [1, 6]; What I ...
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1answer
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Simple arithmetic in Set Theory

For example if I plot number line and add $0 + 12$, then subtract $12 -12$ (if I wrote this in one line it would be: $(0+12)-12$), how it would be implemented in set theory? $A = \{x \in R\ |\ x \in [...
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Proof of Associativity and Commutativity For Multiplication and Addition of Real Numbers.

This fundamental proof is really bothering me for a long time. I have seen the proofs on proofwiki and other sites but it uses too much mathematical jargon. I would like a nice, intuitive proof using ...
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What is the remainder left after dividing $1!+2!+3!…+100!$ by $6$? [closed]

Just came across this question today. I wonder how to solve this as it is a factorial question.
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30 views

How can you derive an algorithm for dividing natural numbers?

In the set of natural numbers, division is defined as ${(a/b)*b=a}$ With the help of Peano's axioms, I can find an algorithm for multiplication and addition. But how I can find an algorithm for the ...
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31 views

I have a range problem, when do simple arithmetic. [closed]

1 course of university, have a cognitive (maybe) problem. 3 month ago all was good, I learnt Mathematical Analysis, but soon I've thought about set of numbers when we do simple math. I have a small ...
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1answer
25 views

Coins Frame Problem [closed]

We have a square frame formed for four segments containing coins along all of them, exactly 10 in each segment distributed in the following manner: Starting at the top right vertex, we have 4 coins. ...
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Given $r,a,b,N>0$, how can we estimate $x$ such that $\frac{x}{\log(a+bx^r)}\geq N$

Given $r,a,b,N>0$, how can we estimate $x$ such that $\frac{x}{\log(a+bx^r)}\geq N$ ? (constants $a,b,N$ are supposed to be big...) We know that, for any $\gamma\in (0,1)$, $$\lim_{x\to+\infty}\...
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144 views

Which is larger $(101!)^{100}$ or $(100!)^{101}$ [duplicate]

I am supposed to tell which one of $(101!)^{100}$ and $(100!)^{101}$ is larger. I am trying to use the behavior of the function $f(x)=x^{1/x}$ as is a standard technique to dealing with questions of ...
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why peano defines 1 as natural?

as long as i have researched i have found here in this presumed book from Peano https://archive.org/details/arithmeticespri00peangoog/page/n6/mode/2up that actually peano has defined the 1 as the ...
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30 views

What is the proof behind this pattern?

Let me get to the point. We see that 121 is a palindrome, also 12321 is a palindrome. If we were to add up the digits in each palindrome, for example, 121 we get 4. If we square root four, the root is ...
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Find a perfect cube of form x+k*y [closed]

There is a number given to us x and y. You need to find a perfect cube which is of the form x + k*y. Any other alternatives rather brute force would be helpful. ...
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Does it seem right to calculate fractional powers by walking steps method?

We know that $x^y$ means $x$ multiplied by itself $y$ times or $x$ taking $y$ steps. Is this method suitable when $y$ (the power) is fractional? e.g. if $x=2$ and $y = 3.5$, we would have $$2^{3.5} = (...
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1answer
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Converting $A8B34_{16}$ to octal.

According to online calculators $A8B34_{16}=2505464_{\ 8}$, yet I keep getting $2005464_{\ 8}$. I just want to know where I'm going wrong. $A8B34_{16}=10( 16^4)+8( 16^3) + 11( 16^2) + 3( 16) + 4$ $=...
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$\frac{-5^2 + (-5^2)}{(4^2 -2^5)-2×3}$ [closed]

It is a question about order of operation where $-4^2=-16$ and $(-4)^2=16$ Please help me. Thanks in advance.
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Evaluating $\sum_{n=0}^{15}(1.6^n-12n+1)$. What am I doing wrong?

Find the value of $$\sum_{n=0}^{15}(1.6^n-12n+1)$$ giving your answer correct to one decimal place. [original image] I separated the summation into two parts: The summation of $1.6^n$ and the ...
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16 views

differential arithmetic forms

i know a little about real differential forms and complex differential forms. Is it to possible to consider differential forms on other fields, and for what use ?
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What kind of function is counting (1,2,3,4 . . .)? [closed]

I am a mathematical illiterate, obviously. Is counting a recursive function, then?
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32 views

Is counting a periodic function?

Dictionary entry: "Frequency" Mathematical and Physics. The number of times a specified phenomenon occurs within a specified interval, as: a The number of repetitions of a complete ...
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How to deduce the sign changes?

Let $f$ be an arithmetical function. Suppose that there exists an integer set $A$ compromises the integers $n$ for which $f(n)>0$ and a set $B$ of integers $n$ such that $f(n)<0$ and a set $C$ ...
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1answer
46 views

Decomposing fractions

I am not sure how these two terms are equal from this wiki: $$ I(X,Y) = KL(p(x,y) || p(x)p(y)) = \sum_{x,y}p(x,y) \log[\frac{p(x,y)}{p(x)q(y)}] \\ I(X,Y) = \sum_{x,y}p(x,y) \log[\frac{p(x,y)}{p(y)}...
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1answer
51 views

Arithmetic on $ \aleph_0 $ such as $ \aleph_0 + 1 $ and $ \aleph_0 - 1 $

I was playing with $ \aleph_0 $ on Wolfram Alpha when I encountered this: $ \aleph_0 + 1 = \aleph_0 $ (see on Wolfram Alpha) $ \aleph_0 - 1 = \text{undefined} $ (see on Wolfram Alpha) I understand ...
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1answer
56 views

Sum of divisors of an integer

For $n$ a positive integer, we define $s(n)$ the sum of the divisors $d$ of $n$ such that $d \neq 1$ and $d \neq n$. For example $s(6)=2+3=5$, and $s(5)=0$, because $5$ is a prime number. Is it ...
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38 views

Motivating the multiplication of real numbers

What are some of the ways in which one can motivate the multiplication of real numbers? The sum of two real numbers can be thought in terms of jumps along a horizontal line. For example, (3)+(-2) may ...
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1answer
15 views

Commutative property of subtraction and addition of negatives

Why is it that subtraction is noncommutative but addition of a negative number is? Everything I can read says that subtraction can be view as adding a negative. However, when you view it in this way ...
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1answer
19 views

Stuck in adding growth percentage.

I have $95 dollar in hand, One I have deposited on a bank, after one year I get back the initial amount + 15% interest on it. how to calculate the total amount, I have figured out my own solutions and ...
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2answers
138 views

Can $(q,p)$ and $(p-q,p)$ be legs of a Pythagorean Triple

I'm searching to prove that there's no (or to find an example of) $p$ and $q$ coprimes, and $n,m$ integers such that: $q^2 + p^2 = n^2$ $(p-q)^2 + p^2 = m^2$ I conjecture that this case is impossible. ...
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The purpose of the question is to find out how H (harmonic mean) departs from A (Arithmetic mean).

The purpose of the question is to find out how H (harmonic mean) departs from A (Arithmetic mean). $A= \frac{x1+x2+x3}{3}$ and $H= \frac{3}{1/x1+1/x2+1/x3}$ To that end, assume that: $x1=A+e1,x2=A+e2, ...
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Prove that the value $\frac{1}{2}\sqrt{2 - \sqrt{3}} = \left(\sqrt{6} - \sqrt{2}\right)/4$

Using half-angle formula, the simplest intuitive ‘exact’ answer to $\sin(15^{\circ}) = \frac{1}{2}\sqrt{2 - \sqrt{3}} $. However, using instead angle sum-addition properties the most available ...
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29 views

Solve for x in this equation with trig and exponential functions added together?

I'm having trouble putting this equation in terms of $x$, so I figured I'd ask here: $$y=25(x+0.5)^2+150\cos(0.5x)$$ I tried to subtract $150\cos(0.5x)$ from both sides and then divide by $25$, giving ...
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1answer
17 views

For number N how to find x,y where x*y = N and |x - y| is minimum?

I want to find numbers x and y such that x*y = N and |x-y| is minimum. For example; 7 = 7*1 15 = 5*3 16 = 4*4 Is there a fast way to find this?
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period of state i, d=d(i) is the gcd of integer set: Ji = {n ≥ 0 | Pn(i, i) > 0

Define period of state $i$, $d=d(i)$ is the gcd of integer set: $J_i = \{n ≥ 0 \mid P_n(i, i) > 0\},$ $$ D_i=\{x \in \Bbb N \mid dx \in J_i \text{ which is closed under addition}\}. $$ Show that $...
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What numbers can fractional binary notation represent?

In Computer Systems: a Programmer's Perspective: Consider a notation of the form $b_m b_{m - 1} \dots b_1 b_0 . b_{-1} b_{-2} \dots b_{-n + 1} b_{- n}$, where each binary digit, or bit, $b_i$ ranges ...
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1answer
63 views

Are the imaginary zero, the complex zero, and the real zero distinct numbers?

The additive identity element is unique. Does this imply that all zeros are not distinct? Am struggling to explain how a unique additive element does not rule out more than one number zero. I am ...
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Why does zero times zero equal zero? [closed]

When trying to prove that if $mx = 0$, $x = 0$, I had to assume that $m \neq 0$. In the case that $m = 0$, then $0 * 0 = 0$. However, it's not clear that $0 * 0 = 0$. Or is it supposed to be?
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1answer
27 views

Arithmetic mean of 4 numbers word problem

Encountered this in a timed online test, only allowing 20 seconds per question: The average (arithmetic mean) of 4 numbers is greater than 8 but less than 14. Which of the following could not be the ...
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2answers
27 views

Stumped by percentage / arithmetic / proportion word problem [closed]

One of two questions that stumped me in an online exam. Each question has more or less a 20 second time limit but I'm not entirely sure how to solve this one offline either, would love to learn how to ...
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1answer
37 views

History behind “Rainbow” Addition Facts

While trying to solve a chiming clock problem algebraically, I came across a solution which used "Rainbow" Addition Facts. Problem An old chime clock strikes one chime at 1 o’clock, two ...
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Dimension of subspace defined by $a^2+b^2=c^2+d^2 \Rightarrow f(a)+f(b)=f(c)+f(d)$

Let $V={\mathbb Q}^{\mathbb N}$ be the space of all functions ${\mathbb N}\to {\mathbb Q}$ where ${\mathbb N}=\lbrace 1,2,3,\ldots \rbrace$ is the set of all positive integers. Let $W$ be the subspace ...
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1answer
45 views

What is the value of $\log5-\log9+\log10$

Sorry it might be a stupid question but I am confused why $\log5-\log9+\log10=\log(50/9)$? By bodmas rule first if we add then it should be $\log(5/90)$?
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1answer
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Finding sets of four or five strictly positive integers that give the same result when added and when multiplied

In the book The Moscow Puzzles by Boris A. Kordemsky (ISBN 0-684-14860-6), the puzzle "Different actions, same results" (#52), asks for sets of four and five numbers strictly positive ...
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24 views

Infinite product of cosine functions [duplicate]

So I was toiling away trying to show that a sequence of random variables converges to a particular distribution by showing that the characteristic functions of the limit and the target are equal, ...
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1answer
25 views

Calculator gives a different answer than online math websites - exponents

I am quite confused with the different answers obtained when I inputed an equation into a physical calculator and an online math calculator. The equation was: (6.67×10e-11)×(5.97×10e24)×(7.35×10e22)÷(...
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1answer
38 views

How do I solve this logical reasoning problem?

A mart has $10^7$ items in stock. It has collected billing data for $10^{10}$ customer transactions. Each individual bill can have at most $10$ distinct items on it. The owner of the mart wants to ...
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1answer
49 views

Arithmetic sequence $\log(2),\log(2^x-1),\log(2^x+3),\ldots$

For which $x$ is $$\log(2),\log(2^x-1),\log(2^x+3),\ldots$$ an arithmetic sequence? Solved: For $d=\log(2)$, one gets the airthmetic sequence $$n\log(2)$$ Then you have to solve $$4=2^x-1$$ This means ...
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1answer
13 views

Foodservice calculation question. Converting weights

The question is: A 5-pound bag of cocoa powder costs $25.35. One cup of cocoa powder weighs 4 ounces. How much would 2 teaspoons cost? I first converted the 5 pounds to ounces by multiplying by 16 ...
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1answer
33 views

Numbers $N\equiv abab$ s.t. $N-1$ is a perfect square

I want to find all the numbers of the form $N\equiv abab$ (with $a\neq 0$) such that $N-1$ is a perfect square. I am stuck. I know that such N can be written as $N=101(10a+b)$, but I don't know how to ...
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2answers
46 views

Anyone know the algorithm or algebraic explanation for the long division method used to calculated square root of any number? [closed]

By Long division method, I mean the one we get the value of sqrt(5) for example where we split the number into pairs in the middle and add numbers to the left and top with a fixed mechanical procedure ...

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