Mathematics Stack Exchange
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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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How can you derive an algorithm for dividing natural numbers?

In the set of natural numbers, division is defined as ${(a/b)*b=a}$ With the help of Peano's axioms, I can find an algorithm for multiplication and addition. But how I can find an algorithm for the division operation which based on the axioms and…
Honza Prochazka
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Commutative property of subtraction and addition of negatives

Why is it that subtraction is noncommutative but addition of a negative number is? Everything I can read says that subtraction can be view as adding a negative. However, when you view it in this way the noncommutative property of subtraction is…
James Kervin
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Prove that the value $\frac{1}{2}\sqrt{2 - \sqrt{3}} = \left(\sqrt{6} - \sqrt{2}\right)/4$

Using half-angle formula, the simplest intuitive ‘exact’ answer to $\sin(15^{\circ}) = \frac{1}{2}\sqrt{2 - \sqrt{3}} $. However, using instead angle sum-addition properties the most available reduced exact form is $\frac{\sqrt6-\sqrt2}{4}$. Using…
user819279
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For number N how to find x,y where x*y = N and |x - y| is minimum?

I want to find numbers x and y such that x*y = N and |x-y| is minimum. For example; 7 = 7*1 15 = 5*3 16 = 4*4 Is there a fast way to find this?
Drethax
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Finding percentage of one of two variables in an equation composed of three

The title is probably horrible, but I couldn't think of a better sentence to describe what I'm attempting to do. I want to take the result of an equation made with 3 variables and then, with two of the variables, create the same number as if the…
Jimmy
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Math/Statistical analysis of a video on youtube

Say approx 6.3 billion people in the world: 6300000000 And the youtube video has 290 million views: 290000000 What percentage of people (of the world) have seen this video?
cwiggo
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Isolate $V$ in $\frac1b\ln(\frac V{V_0}) - \frac cb \ln \frac{b+cV}{b+cV_0} = -\frac tm$

I'm still asking for your help. I have to isolate $V$ in this equation. I have the final result in my book, but I'm not even close to get it. $$\frac1b\ln\left(\frac V{V_0}\right) - \frac cb \ln \frac{b+cV}{b+cV_0} = -\frac tm$$ I tried a lot of…
proxima
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Is it possible to create a new language that translates into words at least the basic operations of math, to make it easier to understand?

I was wondering if it's possible to make maths easier to calculate and understand, and more natural for kids and even adults. And then I realized how easy it is for human beings to manipulate words and from them make whole sentences and express…
Artur Souza
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Distributing numbers in groups

I don't understand how distributive property works in case like this: $(x_1 \cdot y_1) + (x_2 \cdot y_2) + (x_3 \cdot y_3) + \dots + (x_n \cdot y_n)$ So, how do I calculate this differently? I want to calculate $x$'s and $y$'s separately. I know…
user816590
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What extra structure is needed so that grade-school arithmetic notions of division comes out of the formal definition of integer division?

Formally, an integer $m$ divides an integer $n$ if $\exists k \in \mathbb{Z} | n = k\times m$. In grade school we took this further and say that the quotient $\frac{n}{m} = k$. However, this "equals" thing is not required in the formal…
Michael Stachowsky
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Radix 2 square root

I am trying to understand the radix-2 square root shown in Chapter 6 of Digital Arithmetic(Miloš D.ErcegovacTomásLang). I am missing something in the computation of F[j]. I am attaching the formula used for F[j] and the example given in the…
ammrra
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is someone having an idea on how "casting out twos" are been done.

Is someone having an idea on how "casting out twos" are been done? I know about "casting out nines" but I try to research for "casting out twos" and saw nothing. Thanks in advance.
Nganja
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A video with $30$ minutes length, played at $33.33\%$ faster speed that equates to $22.5$ minutes. Where are the extra $2.508$ minutes?

A video with $30$ minutes length, played at $33.33\%$ faster speed that equates to $22.5$ minutes. Where are the extra $2.508$ minutes? Yes the math is $$\frac{30}{1.3333} = 22.50,$$ but my intuition is that the result should be $20$ minutes. How…
Andy
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Find the real numbers given their product

We have four real numbers $a,b,c,d$ and their six products should satisfy $\{ab,ac,ad,bc,bd,cd\}=\{2,2.4,3,4,5,6\}$. How do we find them? The sequence of products is not necessarily in order. For example we don't know if $ab=2$ or $ac=2.4$.
Craftsman
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A and B can do a piece of work in 9 days, B and C in 12 days, A and C in 18 days. If all of them work together, then how much time will they take?

This is how I did it. $A+B=9 \tag 1$ $B+C=12 \tag 2$ $A+C=18 \tag 3$ Adding (1), (2) and (3) we get: $A+B+B+C+A+C=9+12+18$ $2(A+B+C)=39$ $A+B+C=19.5$ So, they complete the work together in $19.5$ days. But the book says this answer is…
Russell
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