# Tagged Questions

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.

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### Ratio and Proportion Question: Income and Expenditure

The ratio between the incomes of Suman and Chaman is $2:3$ and the ratio between their expenditures is $3:2$. The saving of Suman and Chaman is directly proportional to their incomes and inversely ...
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### Ιnequality relationship

Let $a,b,c,d$ positive numbers. They are connected with the relations $$b<d,\quad a<c,\quad b<a,\quad d<c$$ Is it possible to prove that $a-b<c-d$?
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### Calculating new median if one of the observations from original calculation is removed

find new average if removing one element from current average Hey guys, found an old question that I would like to build on if possible, would appreciate your help. To piggyback on this old ...
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### Tokens in boxes problem

Tokens numbered $1,2,3...$ are placed in turn in a number of boxes. A token cannot be placed in a box if it is the sum of two other tokens already placed inside that box. How far can you reach for a ...
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### Daily exercises to speed up my mental calculations?

When I was a kid in school my father prevented me from using a calculator when solving my math homeworks. However at that time I was not convinced as of why not to use such a useful tool! So I kept on ...
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### Last digit of $1234 \cdot 5678$

How to find the last digit of this multiplication $1234\times5678$. It may seem like homework but its not. I can do simple multiplication to get the result but I see some patter here, the digits are ...
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### Can all programs reducible to ones with only arithmetic operations on inputs be simulated with polynomial overhead by arithmetic machine?

In Can all programs be modeled as operations of elementary arithmetic operations on inputs? and computability theory, I asked: we treat all inputs and intermediate results and final outputs as ...
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### How can I find the square root using pen and paper?

Okay, I know this is very basic question. I learned 2 methods in school. But now, I forget one. Here is a simple method that I know. Find the prime divisors of the number Omit the half of numbers ...
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### Remembering multiplication of these two numbers: $7 \times 8 = 56$ and $9 \times 6 = 54$

I have almost mastered multiplication table up to 9x9 however, I'm having problems with the following two. 7 x 8 = 56 and 9 x 6 = 54 For some reason my brain thinks that 56 and 54 are somewhat the ...
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### Arithmetic series relationship with difference of two consecutive cubes. Is this a thing?

Excuse my dodgy notation and my write-up in general, this is the first proof I've done since leaving school a while back. Anywho, has anyone come across anything like this before? Read the whole thing,...
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### Summation that gives perfect squares

For $n=1,2,3,4$ upto $50$. How many $s(n)$ will be perfect squares? The answer given is $3(n=1,8,49)$. What will be the approach for such questions?
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### Given a range [a, b], how to find the x middle numbers?

Given a range [$a$,$b$], how can I find the $x$ middle numbers? For example: [$1$,$10$] Now I know that the middle $2$ numbers start with "$5$", but is there any way I can find the starting ...
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### How would one be able to prove mathematically that $1+1 = 2$?

Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically?
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### why does double rounding 9.46 give 10 but “regular” rounding gives 9?

What's the correct way to round, or estimate, a number to a specified precision? Starting with wikipedia: Rounding a number twice in succession to different precisions, with the latter ...
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### Proof from axioms of $\mathsf{PA}$: every natural number has remainder $0$ or $1$ or $2$ when divided by $3$

Using only the axioms of $\mathsf{PA}$, I want to prove this fact. It came up in a previous year's exam paper, and seems more difficult than I had anticipated... The question was to sketch the idea, ...
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### Square root confusion?

Last year in Pre-Algebra we learned about square roots. I was taught then that $\sqrt{64}=8$ and $\sqrt{100}=10$, which I understood and accepted. I was also taught that $\pm\sqrt{64} = 8,-8$ because ...
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### Antisymmetric asymptotic curve with only simple binary arithmetic?

I'm looking for an s-curve formula with similar properties to $Sigmoid$ or $\tan^{-1}$, but without 'expensive' unary functions or their binary generalizations (e.g. $^x\log y$). The only allowed ...
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### Division with decimal in the divisor

I understand HOW to do division with a decimal in the divisor, but my question is MUST we remove the decimal in the divisor and if so, why? Thanks.
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### Inverse Proportion on a graph

The force of attraction(F newtons) between two magnets is inversely proportional to the square of the distance , d centimetres , between the magnets . Sketch a graph to show relationship between ...
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