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
3
votes
0 answers

What's a simple, natural function that is "halfway" between addition and multiplication?

What's a simple, natural function that is "halfway" between addition and multiplication, in some sense? Can you think of a way to make that precise? $$ x + y \quad\longrightarrow\quad ? \quad\longrightarrow\quad x \cdot y$$ Alternatively, what's…
Bjørn Kjos-Hanssen
  • 2,915
3
votes
2 answers

What does it mean to divide?

So I'm in year 11 (10th grade for americans) and I have a really stupid question.. What does it mean to divide in maths? I recently looked it up and it said "To divide means to slit the number up into equal groups". However, other sites said "To…
JamesM
  • 175
3
votes
6 answers

I have difficulty counting

Take this example: $$84 + 87 + 90 + 93 .. + 180 + 183$$ If we want to use Gauss' way of finding this sum, we have to find the number of elements in this. What I do is just take the difference of the highest and lowest sum (99) and divide by 3, but…
Gallus
  • 33
3
votes
2 answers

Patterns in the repetend in $1/121$

$$ \frac{1}{121} = 0.00\ \overbrace{8264}\ \overbrace{4628}\ 09\ \overbrace{91735}\ \overbrace{53719} \ldots $$ The entire $22$-digit repetend appears here. It begins with the first digit after the decimal point. The sequence $8264$ gets…
Michael Hardy
  • 1
3
votes
1 answer

Repeating Decimals and Rounding

I have stumbled across the proof that $0.\overline{9}=1$. The proof is as follows. Let $x=0.\overline{9}$ $10\cdot x = 9.\overline{9}$ $10\cdot x = 9 + 0.\overline{9}$ Now that $0.\overline{9}=x$, $10\cdot x = 9 + x$. We get $9x=9$ and $\therefore…
Jaden Lee
  • 409
3
votes
1 answer

Problem about a simple division

My little sister wants me to divide $135628$ by $339$. I can not make her understand that quotient is $400$ and remainder is $28$. She does not understand how one last $0$ comes after $40$. She knows the relation among divisor ,dividend,quotient and…
user53386
3
votes
2 answers

Is there a general theory about repetition of the same operator?

Is there a theory about repeating the same arithmetic operation? E.G. multiplication is a repetition of addition, and exponentiation is the repetition of multiplication.
Ilya Grushevskiy
  • 181
3
votes
3 answers

Mod question: $2^{-1} \bmod 5 = 3$

According to Wolfie: $2^{-1} \bmod 5 = 3$ http://www.wolframalpha.com/input/?i=2%5E-1+mod+5 Why is that?
Buddha
  • 31
3
votes
3 answers

Definition for multiplication

I am serious. What is the definition for multiplication ?. Every book and resources online(the one's I have seen) tells multiplication is repeated addition. But that's only some defintion that can be called valid when one of the numbers is a…
hrkrshnn
  • 6,287
3
votes
1 answer

Difference between Percentage value calculation

Here's one more question I need help with. Samir has some amount of rupees with him, the difference between $45.45$% and 36.36% of which is Rs. $789435689$. Find the amount. a) $8683792579$ b) $8673792579$ c) $7573781479$ d) $88667292579$ e) None…
Electrifyings
  • 189
3
votes
4 answers

Prove that if $(x+y)^5$ is congruent to $2$ (mod $5$) then $(x+y)$ is congruent to $2$ (mod $5$)?

I need a proof of the above. I understand that it is just an application of Fermat's Little Theorem, but how do I prove this without the theorem?
Jeanine
  • 31
3
votes
3 answers

Additive inverse: priority in expressions

What is the order of operations in expressions like $-x^2$? For example, Google returns $-3^2 = -9$, but Excel returns $-3^2 = 9$. Furthermore, is $-x! = -(x!)$ or $-x! = (-x)!$ ?
Abionics
  • 133
3
votes
3 answers

Square root of 1

I know this is a dumb question but I can't get the answer to another follow up question, What is the square root of 1? If the square root of 1 is itself then why does other square root of number not equal to themselves? Is there other square root…
Richeve Bebedor
  • 219
3
votes
4 answers

Problem: Predict the remainder when 11111...(100 ones) is divided by 1111111

this very same problem appeared in a different thread but the questions was slightly different. In my case, I'm looking precisely for the answer. This is how I solved it, I only need confirmation of whether this actually is correct: So I assumed…
LocoVoco
  • 85
3
votes
2 answers

How is a - (b - c) = c - (b - a) called?

What is the following property of a subtraction operator called? $a - (b - c) = c - (b - a)$ Having a name for this property is important for algebraic structures defined with a subtraction operator but no addition operator. And these are important…
ismael
  • 689
1 2 3
…
99 100