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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Why does this math trick work?

35 by 11 is 385 because 3+5 is 8, so it's the digit in the middle. Same for: 72 by 11 is 792 because 7+2 is 9, so it's the digit in the middle. I see it works because 35 by 10 is 350, or 72 by 10 is 720. The 0 is replaced with the extra digit. The…
Jossie Calderon
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Reverse addition

I have a number 46 which is the result of addition of 12+17+17. Is there a way, given the result 46 and 12 , 17 as the numbers used to get the result, to find out in what combination 12 and 17 was used to get the result 46
user10183910
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Rightmost digit of $ \left \lfloor \frac{10^{20000}}{10^{100}+3} \right\rfloor $

How could I find $$ 0 \leq a \leq 9 $$ such that $$ \left \lfloor \frac{10^{20000}}{10^{100}+3} \right\rfloor \equiv a \mod 10 $$ ?
Chon
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Equal theoremisu

On the label of the tiramisu pie I was eating with my roommates, it said: 3.5 equal parts. This raised a question. Can you divide a pie in 3.5 equal parts?
Nro
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What is the calculation to find the total break time and work time using the Pomodoro technique?

I am testing pomodoro efficiency and would like to learn the proper equation for finding total break and work time in a set duration of hours. My sample is: If I work 90 minutes, break for 15 minutes, inside of a 9.5 hour time, how can I figure out…
Victor Bureau
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The height in metres of a cuboid shaped room when only the areas of the floor, side wall and end wall are know.

A sports hall is in the shape of a large box or cuboid. The area of the floor is 200m2, the area of one of the side walls is 150m2 and the area of an end wall is 48m2. What is the height, in metres, of the hall? I was helping my young daughter with…
Local Worker
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When asked to solve a question without using a calculator, how much mental computation is reasonable?

Recently, the following question was asked: Without calculator, find out what is larger: $60^\frac{1}{3}$ or $2+7^\frac{1}{3}$. (Apologies; I don't know how to link to that question, but it is not essential for the question I am asking.) Most people…
Keith Backman
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Evaluate: $3\cdot9^{\frac{1}{2}}\cdot27^{\frac{1}{4}}\cdot81^{\frac{1}{8}} \ldots$

Evaluate: $3\cdot9^{\frac{1}{2}}\cdot27^{\frac{1}{4}}\cdot81^{\frac{1}{8}} \dotsb$ Trial: Let $$\begin{align} P &= 3 \cdot 9^{\frac{1}{2}} \cdot 27^{\frac{1}{4}} \cdot 81^{\frac{1}{8}} \dotsb\\ \implies \ln P &=\ln3+\frac{1}{2} \ln…
A.D
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GRE Cumulative addition problem.

The following problem is quoted from Manhattan 5lb Book of GRE Practice Problems, 2016ed. Question: Molly worked at an amusement park over the summer. Every two weeks she was paid according to the following schedule: at the end of 1st $2$ weeks,…
user366312
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$n$-th element in a pattern of repeated elements of a set

If I have a set of letters $\{a,b,c\}$ which will repeat five times, i.e. $$a,a,a,a,a,b,b,b,b,b,c,c,c,c,c,a,a,a,a,a,\cdots,$$ how can I determine what letter will be in a given position, i.e. $168$?
DecentGradient
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For which positive integers $n$ is $2^n+1$ divisible by $n^2$

I would like to show that if $n\in\mathbf{N}^{\star} = \mathbf{N}\backslash\{0\}$ is such that $n^2$ divides $2^n + 1$ then $n=1$ or $n=3$. If $n$ is a prime number $p$ it by obvious (and then $p=3$) by writing $2^p = (1+1)^p$ and using the fact…
11house
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Dividing by 10 not sure about formula

I have 2139 and I want to divide it into 10 people where 1 should get 3 times more than the 9 other. Solutions below: Solution A: What I did is get 30% of the total and give it to the that person and divide the rest to 9 equally solution is 2139 *…
guradio
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Is there a Quick Way to Evaluate $\pi^3$ By Hand?

We ran into a question on a computer science test that basically asked what is $\pi^3$ rounded up to the nearest whole number. The value of $\pi$ as defined by the programming language was $3.141592653589793$ and afterwards, we found out we would've…
Badr B
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Ten people are sitting in a row, and each is thinking of a negative integer no smaller than $-15$.

Ten people are sitting in a row, and each is thinking of a negative integer no smaller than $-15$. Each person subtracts, from his own number, the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing…
ddswsd
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Prove that gcd(n, mp) = gcd (n, m) if n and p are relatively prime

Let $n, m$ and $p$ non-zero natural integers, with $n$ and $p$ relatively prime. Prove that $\gcd(n, mp) = \gcd (n, m)$. This problem had three questions. First, to prove that if $d$ divides $n$ then $d$ and $p$ are relatively prime. That's done.…
Calin Toderas
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