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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7 answers

Weird question about inverses

This probably seems like a really stupid question. I am no math expert; I am in an Algebra II high school class. Here it goes: addition can be interchanged such that a + b = c b + a = c but why not subtraction? a - b = c b - a does not equal c I…
coder guy
  • 203
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17 answers

What is $0\div0\cdot0$?

We all know that multiplication is the inverse of division, and therefore $x\div{x}\cdot{x}=x$ But what if $x=0$? $0\div0$ is undefined so $0\div0\cdot0$ should be too, but whatever happens when we divide that first $0$ by $0$ should be reversed…
user169330
10
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1 answer

On $1/7$ in base $12$

Remember something from seventh grade: \begin{align} & 142857 \\ {}+ {}& 142857 \\ \\ & 285714 \\ {}+{} & 142857 \\ \\ & 428571 \\ {}+{} & 142857 \\ \\ & 571428 \\ {}+{} & 142857 \\ \\ & 714285 \\ {}+{} & 142857 \\ \\ & 857142 \\ {}+{} &…
Michael Hardy
  • 1
9
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2 answers

Multiplying using reciprocal, addition and subtraction

Let $a,b\in\mathbb{R}$. How can we compute $a\times b$ using only the following operations only (with any reals) : $\frac{1}{*}$ (inverse) $*+*$ (addition) $*-*$ (subtraction) ?
Hippalectryon
  • 7,730
9
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1 answer

How can I visualize division of negative numbers

$$-4 / 4$$ I have trouble because I don't know what's happening. I can do positive because I can see in my head with $$10 / 2$$ $$2, 4, 6, 8, 10 = 5$$ But with negative numbers, I can't see anything happening, I can only guess or use a calculator.…
david
  • 171
9
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2 answers

Proof of the standard algorithm for addition?

Can anyone present or point me toward a formal proof of the validity of the standard algorithm we all use for addition (line up your numbers one over the other, add the ones-place, carrying 'excess' digits to the next place-value, etc)? This is what…
ivan
  • 3,237
9
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7 answers

How can I create an expression that uses numbers 1 - 7 to equal 100?

Sorry to post what is probably a very pedestrian question here (it's actually from my son's homework; he's eight), but it's driving us crazy and I really want to know how I'm meant to approach it. We need to write an expression that uses the numbers…
user42395
9
votes
1 answer

How to Compare powers without calculating?

Is there any rule for powers so that i can compare which one is greater without actually calculating? For example 54^53 and 53^54 23^26 and 26^23 3^4 and 4^3 (very simple but how without actually calculating)
LifeH2O
  • 379
9
votes
1 answer

$mn | m^2+n^2+m \implies$ $(n-1)$ is a square

Let $m;n \in \mathbb{Z^+}$ such that $mn | m^2+n^2+m$ Prove that $(n-1)$ is a square number. P/s : I don't have any ideas about this problems :( Thanks :)
Lê Tấn Khang
  • 1,113
8
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5 answers

Proof without calculation

Show that the product of two of the numbers $(65^{1000} - 8^{2001} + 3^{177}), (79^{1212} - 9^{2399} + 2^{2001})$ and $(24^{4493} - 5^{8192} + 7^{1777})$ is non-negative, without actually evaluating the numbers. P.S. I have found by calculation that…
Shah Tamzid
  • 91
8
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2 answers

Can an odd number $n$ divide $2^n-1$?

Clearly an even number $n$ cannot divide $2^{n}-1$, but about odd ones ? If $n$ is an odd prime this cannot happen neither since for an odd prime $p$ we have $2^p\equiv 2\pmod p$ and so $p$ cannot divide $2^p-1$ but what about the general case…
Omran Kouba
  • 28,772
8
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3 answers

Is there an efficient way to add minutes in your head?

Every week I hop on a treadmill and figure out how long I need to run. I am given the pace: Pace = 7:41/mile = (7 minutes + 41 seconds) per mile I need to add this up to calculate how long I should run to run 1.5 miles. I use the formula 7:41 +…
P.Brian.Mackey
  • 255
8
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1 answer

Is there an equivalent to the distributive law for division over subtraction and/or addition?

I understand that the the distributive law cannot be applied to division over addition/subtraction, but is there an equivalent law to expand it out. For example, I know: $$100 \times (5 + 3) = (100 \times 5) + (100 \times 3),$$ but with $$100 \div…
Xaisoft
  • 363
8
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5 answers

Is 1 + 1 = 2 a fact?

One of my colleagues tried to explain me that basic arithmetic is derived from nature. And hence its a fact. Another colleague tried to argue that humans came up with basic arithmetic and then tried to correlate with nature. All I want to know is…
mlemboy
  • 99
8
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1 answer

Are there infinitely many elements $\in \mathbb Z$ equal to digital sum times digital product

The integer 99 is unique in that it is equal to its digital sum plus its digital product. Are there infinitely many integers that are equal to their digital sum times their digital product?
Bernardo Recamán Santos
  • 1,238
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99 100