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
6
votes
1 answer

Finding the sum of numbers between any two given numbers

I tried to derive this type of formula and ended up with this . But it's not holding true for all the numbers. Can you please tell what I've done wrong !!
Amritanshu
  • 961
6
votes
3 answers

Arithmetic: Prove that is multiple of 30

Prove that $n^{19}-n^7$ is multiple of $30$ I've seen $6$ can divide it because $$n^{19}-n^7=n^7(n^{12}-1) = n^7(n^6+1)(n^6-1)=n^4(n^6+1)(n^3-1)n^3(n^3+1)$$ And there are three consecutive numbers, so, at least one is multiple of $3$ and up to…
Ricardo
  • 280
6
votes
3 answers

Question on some arithmetic calculations

When $6272$ is multiplied by $0.94$ the answer is $5895.68$. When it is divided by $1.06$ the answer is $\approx 5916.9811$. Why is it so? Just as a little background, I am using the default Microsoft calculator for this calculation. I haven't…
Confused
  • 63
6
votes
4 answers

Multiplication convention rules

Student was asked to convert the following statement into multiplication format $$7+7+7+7+7+7$$ She wrote the answer as $7\times 6=42$ and was marked wrong as the teacher expected $6\times 7=42$. Is there any rule that can clarify the answer…
derik
  • 61
  • 2
6
votes
1 answer

"there exists" and "for some" are the same, right?

I think "there exists" and "for some" are the same, but still want to make sure. Ex: $x > ky$ for some k or there exists a k such that $x > ky$
user262959
  • 141
6
votes
1 answer

Why is multiplication treated differently to addition?

I am a grade 11 student in South Africa. Just so you know, this is my first time posting here. My understanding is that multiplication is simply a shorter way of writing addition problems. E.g. $$4\cdot 4 = 4+4+4+4 = 16$$ Also, subtraction is just…
Matt
  • 61
6
votes
2 answers

Find $x;y$ such that: $\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$

Let $x,y \in \mathbb{Z}$ such that: $$\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$$ Find $x,y$ I don't have any ideas about this problem.
Lê Tấn Khang
  • 1,113
6
votes
3 answers

How to get all the decimals on a division with decimal point and without remainder?

I divided 4.18 by 5 by hand, like this: As you see I removed the decimal point since I was dividing by a whole number, then I put the decimal point back and got 0.83 as result. It's correct, the point is that often on this kind of division I get a…
Ezequiel Barbosa
  • 499
6
votes
8 answers

Which is larger, $\sqrt{3} + \sqrt{5}$ or $\sqrt{2} + \sqrt{6}$?

The clue given by the text is to "use the fact that $\sqrt{x}$ is increasing." I was able to get the correct answer here by squaring both expressions. But I don't think I made use of the text-prided clue, so am wondering if perhaps I'm missing the…
drzaius7
  • 61
6
votes
7 answers

On the commutative property of multiplication (domain of integers, possibly reals)

$ab = ba$ This is, inherently, true. Some texts drop it like an axiom without any justification. But I'm a bit curious where it stems from or basically why/how it works. If anyone could enlighten me a bit further, I'd be most grateful. Peano axioms?…
Wannaknow
  • 71
  • 1
  • 3
6
votes
1 answer

Elementary operations

There are four elementary arithmetic operators. Are all operations in mathematics derived from the four elementary arithmetic operators? I'm studying linear algebra and noticed that some exercises define a new operation such as "adition between…
0 kelvin
  • 542
5
votes
3 answers

How to put 9 pigs into 4 pens so that there are an even number of pigs in each pen?

Put 9 pigs into 4 pens so that there are an even number of pigs in each pen. Read this for inspiration.
principal-ideal-domain
  • 6,106
5
votes
2 answers

Interval arithmetic for open intervals

I found a detailed paper which outlines the rules of interval arithmetic for closed intervals, including unbounded closed intervals, but it makes no mention whatsoever about open intervals. I'm hoping to write a package of software which handles…
Arkanon
  • 151
5
votes
5 answers

Prove that for all real numbers $x$ and $y$, if $x+y \geq 100$, then $x \geq 50$ or $y \geq 50$.

I'm confused about the following question in my math textbook. Prove that for all real numbers $x$ and $y$, if $x+y \geq 100$, then $x \geq 50$ or $y \geq 50.$ The or is what gets me. For or to be true don't we need only one of the statements in the…
Dunka
  • 2,787
  • 12
  • 41
  • 69
5
votes
1 answer

Intuition for rules of rounding numbers

My textbook says that while rounding a number, if the digit next to the digit to be rounded is a 5, then increment the digit to be rounded by 1 if it is even odd, else do not increase. I don't understand the logic behind this rule. Why such a…
Shaurya Gupta
  • 4,339
1 2 3
…
99 100