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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1answer
24 views

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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2answers
22 views

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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1answer
47 views

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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3answers
6k views

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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1answer
66 views

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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0answers
137 views

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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5answers
13k views

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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5answers
187 views

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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1answer
63 views

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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1answer
25 views

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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3answers
43 views

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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2answers
4k views

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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3answers
779 views

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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0answers
25 views

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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10answers
4k views

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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1answer
38 views

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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3answers
54 views

Can $0$ be added to any equation without changing the outcome?

I was thinking about adding $0$ to an equation, e.g.: A very simple one: $$2x + 2 = 10\\ 2x = 8 \\ x = 4 .$$ If you add "$+ 0$" to any side it does not change the outcome. $2x + 2 + 0 = 10 \...
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3answers
28 views

counting numbers you know a short method?

How many number of form $\overline{abc}$ exist such that $a<b<c$? A teacher said that this problem is very easy ,and i can't find his method. Thanks!
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1answer
138 views

Find the sum of $1^{n}-2^{n}+3^{n}-4^{n}+\cdots+m^{n}$

After seing this question I started wondering about a generalization of a similar sum. The sum is $$ S(m,n)=\sum_{r=1}^{m}(-1)^{r-1}\;r^{n} $$ I gave this to WA to crunch and it gave $$ S(m,n)= (-1)^...
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0answers
49 views

Limit of a sequence in $\mathbb{Z}_p$ (J.-P. Serre, p-adic equations)

In a proof of a theorem in chapter 2 "p-adic equations" in "A Course in Arithmetic" from J-P Serre there is one conclusion that I don't understand. Here is the theorem I'm talking about (excluding the ...
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1answer
19 views

Problem solving involving profit and loss

A fruit seller buys a large quantity of apples for $\$150$. $200$ of the apples are rotten and he sells each of the remaining apples at $10$ cents more than what he paid and makes a profit of $\$50$. ...
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2answers
59 views

Can fractions be written as over 1?

I know that all whole numbers can be written as the whole number divided by one. I was wondering if fractions could be written the same way, for example.. Can $1\over2$ be written as $1/2\over1$ ...
3
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1answer
103 views

Close approximation for absolute value function

I made a very acurate approximation function for $\sqrt{n^{2}+1}$ It is $\sqrt{n^{2}+1}\approx\frac{2n(n^{2}+1)}{2n^{2}+1}+\frac{2n^{2}+1}{n(4(2n^{2}+1)^{2}+1)}$ From this I can make a very close ...
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3answers
855 views

find the largest number

I have a question regarding this problem that is to find the largest number. Just by looking at the problem, I know the answer should be (d), but how can I prove that (d) is larger than (c) in a ...
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5answers
176 views

Significance of multiplying $-1$ by $-1$

Maybe this is a weird question but it's been bugging me. In the childhood we were taught that $4 \times 3$ means $4+4+4$ i.e. adding 4, 3 times. My question is then how would you explain $-1 \times ...
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1answer
27 views

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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1answer
10 views

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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2answers
24 views

Equation between the greatest common divisor and the least common multiple

the symbols $(a,b,c,...,g)$ and $[a,b,c,...,g]$ are denote the greatest common divisor and the least common multiple, respectively for the positive integers $a,b,c,...g$. Example : $(3,6,18)=3$ and $...
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1answer
22 views

Trying to prove $f(n) = |\{n' \in A| n' < n\}|$ is surjective ($A$ is infinite set of integers

As title says, I have some infinite set of integers $A$, a function $f:A \to \mathbb N$ defined by $f(n) = |\{n' \in A| n' < n\}|$ is surjective. I'm having problems proving it. I'm not entirely ...
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3answers
97 views
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1answer
4k views

How to find the number of x per second given the time elapsed?

I'm benchmarking a websocket server and I am very poor at math so please forgive me. I am recording the amount of messages sent, and the elapsed time: ...
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3answers
22 views

Find the Capacity of the Water Tank?

A water tank has three taps attached, $A,B$ and $D$. $A$ and $B$ fill the water tank completely in $\displaystyle\frac{25}{3}$ minutes and $\displaystyle\frac{25}{2}$ minutes, respectively. ...
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9answers
14k views

Can $\frac {100-100}{100-100}=2$?

\begin{align*} \frac{0}{0} &= \frac{100-100}{100-100} \\ &= \frac{10^2-10^2}{10(10-10)} \\ &= \frac{(10+10)(10-10)}{10(10-10)} \\ &= \frac{10+10}{10} \\ &= \frac{20}{10} \\ &= ...
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0answers
28 views

How to Prove? - If the interpretation of theory is consistent, then the interpreted theory is consistent

Let L1 and L2 be finite or recursive languages, and T a theory in the language of L2. A translation of L1 into T is an assignment to each sentence S of L1 into a sentence i(S) of L2 such that: (T0) i(...
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1answer
37 views

Division by rational (decimal) number meaning

When I say, that I exchanged 42 CZK into 1,5 euro. Why do I get the rate for one euro by dividing? 1) How do you explain this division in words. Like when you say when doing integer division, that ...
115
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14answers
15k views

Why does an argument similiar to 0.999…=1 show 999…=-1?

I accept that two numbers can have the same supremum depending on how you generate a decimal representation. So $2.4999\ldots = 2.5$ etc. Can anyone point me to resources that would explain what the ...
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4answers
2k views

Property of 111,111

Whilst playing on my calculator, I noticed the following pattern. $1^2-0^2=1$ $6^2-5^2=11$ ${20}^2-{17}^2=111$ ${56}^2-{45}^2=1{,}111$ ${156}^2-{115}^2=11{,}111$ To me, this is where it gets ...
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1answer
20 views

Binary addition and subtraction

Assuming the sign-magnitude representation of binary numbers, what is the result of the -6+29?! ...
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8answers
3k views

Seeking elegant proof why 0 divided by 0 does not equal 1

Several years ago I was bored and so for amusement I wrote out a proof that $\dfrac00$ does not equal $1$. I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce ...
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2answers
107 views

Is there a mathematical term for three orders of magnitude?

I've been playing this github game for a while called Swarm Simulator. I like it a lot and there are a bunch of other simulators going around either in-browser like Swarm or iOS apps, etc. These ...
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0answers
28 views

Karatsuba multiplication for $x = 123 , y = 100$

Given the numbers $x = 123$ and $y = 100$ how to apply the Karatsuba algorithm to multiply these numbers ? The formula is xy=10^n(ac)+10^n/2(ad+bc)+bd As I ...
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1answer
58 views

Can multiplication and division be treated as logical operations?

A few of my friends and I were playing around with math (more specifically, why (-1)(-1)=1) and we figured out that multiplication (with regards to signs) was an "nxor" operation (I.E. If we treat "1" ...
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0answers
30 views

Bird Travel with Relative speed

A bird starts flying from a place O towards B via A. There is no wind resistance from O to A. But there is wind resistance (in the form of uniform wind velocity) between A and B. To travel from O ...
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0answers
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Polynomials which let a set invariant

Let $A=\{\sum_{i=0}^n 10^i; n\in\Bbb N\}$ the set of integers written with only the digit $1$. Determine all the polynomials $P\in\Bbb R[X]$ such that $P(A)\subset A$.
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2answers
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Minimizing the intersection of three sets

Let the sets $A,B,C$ which are all subsets of a larger set $N$. If $N(A), N(B), N(C), N$ are the populations respectively, then i need to find the minimum value of the population of their intersection ...
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2answers
35 views

Scale a range from ($-251$ to $198$) to ($0$ to $100$)?

I have a scoring system set up, where the worst score possible is $-251$, and the best is $198$. How can I scale any results, to fit on a $0$ to $100$ scale? (I.e. if the user gets $-251$, I want to ...
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2answers
74 views

A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps

problem A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps, but the $2$ leaps of the cat are the same as $3$ leaps of the rat. Compare the speeds of the cat and the rat a)$...
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4answers
4k views

HARD Arithmetic Progression Problem

The first term is 8 and the common difference is d, where d doesn't = 0. The first term, the fifth term, and the eighth term of the progression are the first term, the second term and the third term, ...
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2answers
19 views

Ratio , proportion question

It will take 24 men working 9 hours a day each of build a house in 45 days . Given that all men work at the same rate, (A) how many days will 18 men take to build the same house if they work 8 ...