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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The sum of numbers being unexpected squares

We have the following result: If $a$, $b$ and $c$ are pairwise coprime integers, such that $$\frac 1a+\frac 1b=\frac 1c$$ then $a+b$, $a-c$ and $b-c$ are perfect squares. What I did. I tried to prove first that $a+b$ is a perfect…
E. Joseph
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Sum of all the digits from 1 to 10000

I need to add up all the digits in the numbers $1$ to $10000$. How would I do that without using a calculator? I don't get it one bit. We are doing something in our math class about this.
Ali Ragb
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4 answers

How to put brackets into $10^2÷10÷10÷10÷10 = 10$ to make it correct?

My son was given a challenge division sheet to be done during a school lesson. He said he struggled for ages with question 14: Put brackets into this expression to make it correct. $10^2 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 10$ I tried to help but I could not…
Peter de Rivaz
  • 287
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What is the rigorous definition of addition?

I hope this is not a stupid question, but can we have a 'rigorous' definition of addition of two numbers? I am asking this because I haven't seen one. Almost all resources talk about addition being 'the sum of two numbers'. Understanding it becomes…
codetalker
  • 2,419
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Help Converting Octal to Decimal

I'm having trouble understanding the conversion of Octal Numbers to Decimals Numbers. It mostly comes down to the decimals I have most trouble with and was hoping someone could explain more in depth. I have this number: 4.5 in octal that translates…
Anon
  • 41
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How to calculate the sum of an incremental string of numbers

How do I calculate the sum of 1+2+3+..up to 50? I knew the answer to this at one point in time but have since forgotten the formula.
I0_ol
  • 143
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Get the modulus of a Number N concatenated N times.

I don't know if this is the right forum. Is there a Mathematical approach to get the Modulus of a Number N which is concatenated N times? I had the following scenario today on an Interview for a Developer Job, this was one of the questions, and only…
Orejano
  • 143
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How to determine the remainder of $ \frac{7^{369}}{350} $?

How to determine the remainder of the following : $$ \frac{7^{369}}{350} $$ Is there any tricky way to determine this? I start as $$\frac{7^{368}}{50} \ \ , $$ This type of problem are highly asked in aptitude exam.
Hailey
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Order of precedence, multiplication vs. division

Recently I had this doubt about the order of precedence of mathematical operations multiplication and division. Given that we have a simple question like this 80 / 10 * 5 without parenthesis, what should be the answer? Should it be 40 considering…
Rajith Gun Hewage
  • 143
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5 answers

What is the value of $3-3\times 6+2$?

Please could someone help me and my brother settle our dispute? We have been looking at the following equation: $$3-3\times 6+2=$$ This may look familiar but I have yet to find a fully conclusive explanation. We are both using BODMAS, might I…
R Alqo
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Simplify $\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}$

Simplify $\displaystyle{\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}}$. I get this when I was doing another Q, but I don't know how to further simplify it. Can anyone help me, please?
JSCB
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  • 123
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Can you encode if-then-else in arithmetic

Is there a general way to encode if-then-else/ITE in arithmetic, i.e. using the usual mathematical operators? Example: let $f(x) = x^2$ if $x < 10^{30}$ and $log x$ otherwise, shortly written as $f(x) = ITE(x<10^{30},x^2,log x)$.
mrueg
  • 153
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Least value for addition

We know that $$0\leq a \leq b \leq c\leq d\leq e\,\,\text{ and}\,\, a + b + c + d + e = 100$$. What would be the least possible value of $\,\,a + c + e\,\,$ ? I apologize for poor syntax.
fosho
  • 1,491
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How do I express 108 as the product of powers of its prime factors?

How do I express $108$ as the product of powers of its prime factors? I've got $2^2 \times 3^3$ is this correct?
greg
  • 341
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Count number of values between two numbers

I am finding with some formulas for my web application. I need a formula that counts the number of values between two number, e.g. there are four numbers (3,4,5,6) between 2 and 7
Cudos
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