Mathematics Stack Exchange
Mathematics Stack Exchange

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).

Arithmetic is defined as operations upon numbers using $4$ main operations along with many others:

addition - the sum of two numbers

subtraction - the difference of two numbers also defined as the addition of negative numbers

multiplication - the area of a rectangle with sides of lengths equal to the two operands

division - the number of times one number can be subtracted from another before equaling zero. Sometimes it will allow decimals and in other cases there will be a remainder left over when a number doesn't go into another evenly

See Arithmetic.

6283 questions
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product of sums and other useful indexing tricks

Can you explain to me the following equalities: \begin{align} \sum_{i=1}^n \left[\left( \sum_{j=1}^n (x_i-x_j) \right)\left( \sum_{k=1}^n (x_i-x_k) \right) \right]= \sum_{i,j,k=1}^n (x_i - x_j)(x_i - x_k) = \sum_{k=1}^n \left[ \sum_{i,j=1}^n \tfrac…
dunno
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Find the total amount from a given percentage and x amount which on substraction provides the x amount

I am a freelancer and working with a firm. I provide services, for which I am taking extra 5% as service charge of the firm's amount. Suppose the firm's amount is 600, and I am chargin 5%. 600 + 600%5 = 630 This total amount (630) again goes to a…
Robin
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Equations involving Euler's $\varphi$

Let $x_1,x_2,\ldots, x_n, y_1,y_2,\ldots, y_n$ be some positive integers and let $p$ be a prime number. It is possible to show that if $\sum\limits_{i=1}^nx_i\varphi(p^i)=\sum\limits_{i=1}^ny_i\varphi(p^i)$ and…
Muffin
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In an AP if Common difference is $( -4 )$ and seventh term is $4$ then find the first term

I have tried by using the formula $$a_n=a+(n-1)d$$ And answer is coming -3 I have done it like in this way $$a_n = a+(n-1)d$$ $$4=a+(4-1)×(-4)$$ $$a=-12/4$$ $$a= -3$$
Chirag Agrawal
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How many significant figures in this negative number?

I understand that $0.03$ would have $1$ significant figure. Does $-0.03$ also have one significant figure or $3$? Thanks.
nzkiwi888
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1/998001 what is sou special about it?

Possible Duplicate: What is special about the numbers 9801, 998001, 99980001 ..? Why does 1/998001 results in : 0.00000100200300400500600700800900100110120130140150160170... And it goes on and on till 998999. What is so special about that…
Mortalus
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Keeping running total for value of stocks

This should be pretty simple but I can't think of the best way to do this. Lets say I have the history of some buys and sells for a given stock: What I want to do is keep a running number to what my accumulated cost per share is. This would be the…
Eric F
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Unknown Operator and x

I have not much of a clue about math. Is there any way that I can paste equations like this: 48 ? 27 * x * 16 = 82944 or this 85 ? 82 * x + 2 = 8 and get a value for x plus the correct operator (+ - or *). These equations do not treat…
Coffeehouse
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Question based on compound Interest

A certain amount is invested in scheme A for 6 years which offers simple interest at the rate of x% per annum. The same amount is invested in scheme B for 2 years which offers compound interest compounded annually at the rate of 10% per annum.…
Soumee
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Is there a fast and easy way to calculate high powers mentally, e.g. $ 67^{81} $?

I have done research into vedic mathematics and I was wondering if it's possible that a faster method exists than the one I already know which involves Pascal's triangle.
Jonathan Musa Mkazi
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Question on profit and loss

Ans.600 My attempt: CP1=100x SP1=120x CP2=100x-100 SP2=120x-100 P2=124% of (CP2) =>20x=$\frac{124}{100} $(100x-100) x=$\frac{124}{104}$*100 The answer is nowhere close.
Soumee
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Difference between Omitting the multiplication sign and keeping it

What is the difference between 2*a and 2a? What is the difference between 2(3+4) and 2*(3+4)? We all know that omitting the multiplication sign still means multiplication so nothing changed! This question is related to a well-known mathematical…
Yousef Essam
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hyperpower modular

How can I calculate this? ${(p-1)}^{{(p-2)^{{(p-3)}^{(p-4)...}}}} (mod {.p}) $ and so on till 1. I don't know how to write it with a Knuth or Ackerman or more compact notation. I've tried to find a pattern evaluating it with Mathematica, Pari, GMP,…
skan
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When to use significant figures

Often I am not sure when to make use of significant figures in a calculation. For example at the moment. I have to calculate a certain equilibrium point which is given by: $$m^* = \frac{\phi_{\mathrm o}^{*2} A}{g K^2 A_{\mathrm v}^{*2}}$$ And the…
WG-
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Addition in Cantor expansion

How to add two integers in their Cantor expansion?
Mehdi Ijadnazar
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