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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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Is there something similar for division as this Japanese multiplication method?

In this youtube link, a really cool method to multiply two big numbers is given. Only works of integers. I was wondering if something unconventional and similar to this exists for dividing two big integers? I'm hoping someone from the Japanese…
sprajagopal
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Arithmetic sequence and a rectangular triangle

Task: Calculate the smallest angle in a rectangular (or right) triangle whose sides form an arithmetic sequence. That's it.. and I can't solve it. The solution is 36°52'. p.s.: thank you in advance!
cherry8.8vanilla
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How to show that the given equation has at least one complex root ,a s.t |a|>12

How do I show that the equation $x^3+10x^2-100x+1729$$=0$ has at least one complex root $a$ such that $|a|$$>$$12$.
liesel
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Bocce league: How many wins to advance to playoffs?

In our bocce division, we have $14$ teams (including us). Everyone plays each other $1$ time during the $13$ week season ($13$ games for all). At the end of the $13$ weeks, the top $6$ teams advance to the playoffs. What is the minimum wins a team…
Jill Keogh
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Solving system of 5 equations

\begin{align*} x\lambda_{1}&=-\frac{1}{2}\\ y\lambda_{2}&=\frac{1}{2}\\ z\lambda_{1}+z\lambda_{2}&=1\\ x^{2}+z^{2}&=1\\ y^{2}+z^{2}&=1\\ \end{align*} I wonder if there's any simple method of solving such systems of equations...is there? I've been…
khernik
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sum of a positive series

For sufficiently large $m$, I want to calculate the following series. $\displaystyle\sum_{i=0}^{3m}\sum_{j=0}^m \sum_{k=0}^m\sum_{l=0}^m \min(i,j+k+l)$ Except considering all case by case, is there any clever trick?
user46185
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Arithmetic operations in ternary number system

In a ternary number system, how are the $4$ arithmetic operations defined?
Bruna Gabrielly
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Scaling numbers cleverly to prevent arithmetic overflows or rounding errors

Let's say I have an integer position $p$ inside some integer range $r$, such that $$ 0 \le p < r \;\;\;\textrm{with}\;p, r \in \mathbb{N} $$ I need to scale a position $p$ from a small range where $0
Markus A.
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What does it mean for media to play at "1.5x" or (Nx) speed?

Suppose I have a video that plays for 60 minutes at normal "1x" speed. I know that if I set the video to play at "2x" speed, then it should play for 30 minutes. Now, what if the video is set to play at "1.5x" speed? Intuition leads me to two…
stackoverflowuser2010
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real mechanism behind addition, subtraction, multiplication, division

we all know the basic rules for operations of addition, subtraction, multiplication and division. but what i don't know is why these rules (of addition, subtraction, multiplication and division) works. as if we have been given algorithm to do these…
Pratik Aman
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Order of operations (BODMAS)

$$40-20/2+15\times1.5\\\hspace{.1in}\\40-20/2+15\times1.5=\\ 40-10+22.5=7.5$$ I'm studying and this is from an example. In BODMAS, aren't addition and subtraction have same level? So, in the 3rd line, it should be from left to right, correct?
Stalker ka NOOB
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Question regarding arithmetic: When am I to simplify?

Perhaps this one is a silly question but how do I know I am to simplify an expression? For instance: Suppose $a=5+3$, why on earth I am to perform the addition and make $a=8$. Are there rules to know when not to simplify an expression: sums,…
ceip7bavSi ceip7bavSi
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sum of ten squares

You are given an unlimited supply of $1\times 1,2\times 2,3\times 3,4\times 4,5\times 5,6\times 6$ squares.Find a set of ten squares whose areas add up to $48$.If not the whole solution,even a little prod in the right direction would help.
rahul
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Is it safe to say the following about the odd prime numbers other than 5.

I am studying basic number theory and have a habit of writing down interesting facts whenever I conclude something from the text or a problem itself. I was wondering whether I can write it down too: All odd prime numbers other than 5, either…
Adil Mayank
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$5 \frac {3}{*} \times 3 \frac {*}{2}=19$?

One of my friends gave me this apparently easy-looking problem which I do not know how to crack. The problem is to find the values of "*" where $$5 \frac {3}{*} \times 3 \frac {*}{2}=19\text{ ?}$$ I can rearrange the problem as $5 \frac {3}{x}…
learner
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