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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Are $+, -,\times,\div$ the "base" calculations?

My friend told me that every equation possible with modern mathematical notation boils down to only $+, -,\times,\div$ What that means is that you can take any function and if you dive deep enough into it it will only have those operators For…
user169330
4
votes
3 answers

What is $9-5+2$?

What is 9-5+2 ? 9-5+2 = 6; //With Calculator 9-5+2 = 2; //Using BODMAS If you evaluate from the right it give you "2" which follows the law: Brackets-Of-Division-Multiplication-Addition-Subtraction Why don't calculators follow that…
Tawani
  • 231
4
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6 answers

Solve $x + y + z = xyz$ such that $x , y , z \neq0$

I came across the equation $x+y+z=xyz$ such that $x , y , z \neq 0$. I set $x=1, y=2, z=3$ but how can i reach formal mathematical solution without " guessing " the answer ? Thank you
sharon
  • 59
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Find prime numbers $p,q$ such that $p^n+p^{n-1}+...+p+1=q^2+q+1$

Let $p,q$ are prime numbers and $n$ is a even number such that : $p^n+p^{n-1}+...+p+1=q^2+q+1$ Find $p,q$? I think : $p^n+p^{n-1}+...+p+1=q^2+q+1\Rightarrow p^n+p^{n-1}+...+p=q(q+1)\Rightarrow p|q(q+1)\Rightarrow p|q$ or $p|q+1$ If $p|q$ then…
Lê Tấn Khang
  • 1,113
4
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1 answer

Significant figures during intermediate steps in a calculation

If I have some values to use in a calculation, which all have 3 significant digits, then I know that the result will also have no more than 3 significant digits. Am I allowed to round up/down to 3 digits during intermediate steps in the calculation?…
Steeven
  • 749
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Fraction - to be or not to be?

In a recent year 6 maths test my daughter was asked to write a fraction equal to half of 11/40. Her response was 5.5/40 which was not accepted as a correct answer- the model answer used for marking was 11/80. Does the numerator or denominator in a…
Dan Stewart
  • 41
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How does mutliplication work?

I was wondering how Al Khwarizmi's method of multiplication worked? I was hoping for a simple explanation in layman's terms. For those of you unfamiliar with the method its basically this: If you have two numbers, x and y, write them beside each…
user26649
4
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1 answer

Is $\sqrt{3}^\sqrt{5}$ rational or irrational?

Is $\sqrt{3}^\sqrt{5}$ rational or irrational? One way is to let $x$=$\sqrt{3}^\sqrt{5}$ and then calculate $antilog \ (log (\sqrt 3) \times \sqrt(5))$ which gives irrational number. But is there a way to check it without calculators..
Bhaskar Vashishth
  • 11,279
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Understanding the concept of multiplication

Since multiplication is such a basic algorithm in math we rarely stop to think about what it really is about, so please, help me understand? When we multiply two numbers we are basically increasing the number of units of one number by the other.…
reddead
  • 43
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$4^{101} \mod 101$ without Fermat's little theorem

Can anyone tell me how to find the remainder of $\frac{4^{101}}{101}$ without using Fermat's little theorem ? I tried doing $$4^{101} \equiv 2^{202} \equiv (5\cdot 101 + 7)^{22} \cdot 2^{4} \equiv 7^{22} \cdot 2^4 \mod 101$$ but after this I can't…
questioner
  • 392
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1 answer

"Alternating" sums of fourth powers.

Problem: Show that any integer $n$ can be written as: $$n = \sum_{k = 0}^N \epsilon_k k^4$$ where $N$ is a nonnegative integer and $\epsilon_k$ is in $\{\pm 1\}$ for every $k\leq N$.
user193599
  • 41
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Is it allowed to use "equal to" and "approximately equal to" in the same sentence?

Let's use the following example: $$17! = 16!*17 \approx 2 \cdot 10^{13} * 17 = 3.4 \cdot 10^{14} $$ Are you allowed to do this? I am in doubt whether or not this indicates that $17! = 3.4 \cdot 10^{14}$, which is obviously not true, but I think it…
Bruhihihi
  • 33
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What is the remainder when ${2222}^{5555}+{5555}^{2222}$ is divided by $7$?

The question is multiple-choice. What is the fastest approach to solve it? One suggested solution is: It can be seen that $[2222\equiv3\pmod7]\wedge[5555\equiv4\pmod7]$ Therefore…
lliB the Lizard
  • 61
3
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1 answer

Adding repeating decimals

(intimidated newbie here, please be gentle) I got curious about adding repeating decimals while working on a "convert degrees/min/sec to degrees" problem. To convert 5°13'11'' to degrees, I can add $$5 + \frac{13}{60}+\frac{11}{3600}$$ to get…
sloopie72
  • 75
3
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3 answers

How addition and multiplication works

Lets say i am doing 12 + 13 by using the addition method that we know. i mean first we write 13 below 12, then we do 2+3 and then 1+1. The result can be validated as 25 (or true) by doing the counting manually. But for larger numbers, what is the…
user3243180
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