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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2
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3answers
52 views

Determining parity of a number

I have this function: $$f(n) = \frac{(-1)^n + 1}{2}$$ For $n \in Z$ It seems be equal to $1$ if $n$ is an even number and $0$ otherwise: $$ \begin{array}{c|c} n & -3 & -2 & -1 & 0 ...
3
votes
0answers
22 views

Sum of integers and zêta functions

I am working on generalizing some works from the usual rational case to general number fields. That implies some technical changes I am not really at ease with. For instance: $$\sum_{m \leqslant X} m ...
-3
votes
1answer
37 views

Problem about water and time

You can fill a container with water from a hot water tap in $80$ minutes. The container can be filled with water from a cold water tap in $48$ minutes. How long does it take to fill the tub, if you ...
0
votes
3answers
82 views

Why is $-3^4 = -81$ and $(-3)^4 = 81$?

How do you express $-3^4$ to get an answer of $-81$. And how is $(-3)^4$ expressed to get the answer of $81$?
1
vote
2answers
63 views

Bizarre question given to student at learning center [on hold]

I work at a learning center and this problem came up during a lesson. The student stared at it for a while, and after looking at it myself, I am also puzzled. An average of 368 students attend ...
2
votes
0answers
26 views

Creating arithmetic expression equal to 1000 using exactly eight 8's and parentheses

I would like to find all the expressions that can be created using nothing but arithmetic operators, exactly eight $8$'s, and parentheses. Here are the seven solutions I've found (on the Internet) so ...
2
votes
2answers
74 views

Prove that $108^3-7^3$ is a multiple of $101$

Encountered the next problem: prove that $108^3-7^3$ is the multiple to $101$. As I understand if $c$ is the multiple to $a$ it means that there exist $b\in\mathbb{N}$ that $ab=c$. So i want to ...
0
votes
0answers
19 views

Solutions in $\mathbb Q_p$ leads to solution for congruences equations?

Let $p$ be a prime number such that $p\equiv1\pmod 3$. Let $n$ be an integer such that the equation $x^3=n$ has a solution in $\mathbb Q_p$. In fact with our assumptions, the others solution are in ...
1
vote
3answers
37 views

Adding 100 different number

How do I compute ...
0
votes
0answers
34 views

Why diferent calculators give different values for same expression?

So I was working with this expression: $1111 = 5 * 2^t$ after working it out until here $2.346744/0.301029 = t$ I decided to use a calculator to know the value of $t$ just for fun. Using windows ...
1
vote
1answer
39 views

Is expression $(1/x)/(2/x^2)$ is fraction expression or rational expression?

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions. $$\dfrac{6}{x-1}, ...
0
votes
1answer
24 views

Integers that squared have the same last two digits

I need to find the integers that when squared they maintain the las two digits, I've started like this: being b and a the last two digits of the number $(10b+a)²\equiv 10b+a \mod(100) \Rightarrow 20ab ...
1
vote
2answers
16 views

How is `round to the nearest` calculated using number expansion

Suppose I have the number 0.342543 and I want to round it to the 2 places after the radix point using round to the nearest ...
0
votes
0answers
10 views

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 ...
0
votes
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 $a-b<c-d$?
6
votes
1answer
43 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 ...
0
votes
1answer
23 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?
1
vote
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, ...
1
vote
3answers
50 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 ...
1
vote
3answers
25 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!
1
vote
0answers
45 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 ...
-1
votes
0answers
49 views

Using continued fraction find square root of even number [closed]

We can approximate the square root of 2 using the method of Continued_fraction_representation The square root of 2 is calculated using (1+r) where 1 is the lower ...
8
votes
3answers
831 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 ...
0
votes
3answers
42 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 ...
0
votes
1answer
6 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 ...
0
votes
2answers
23 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 ...
1
vote
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 ...
16
votes
2answers
177 views

Finding properties of operation defined by $x⊕y=\frac{1}{\frac{1}{x}+\frac{1}{y}}$? (“Reciprocal addition” common for parallel resistors)

I have recently found some interesting properties of the function/operation: $x⊕y = \frac{1}{\frac{1}{x}+\frac{1}{y}} = \frac{xy}{x+y}$ where $x,y\ne0$. and similarly, its inverse operation: $x⊖y = ...
2
votes
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: ...
0
votes
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. ...
3
votes
1answer
100 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 ...
0
votes
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) ...
5
votes
2answers
58 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 $1/2\over1$ ...
2
votes
3answers
94 views

If sum of n natural number is 20 then what is their max. product?

If sum of n natural number is 20 then what is their max. product ?
0
votes
1answer
20 views

Binary addition and subtraction

Assuming the sign-magnitude representation of binary numbers, what is the result of the -6+29?! ...
1
vote
1answer
26 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 ...
3
votes
1answer
57 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" ...
0
votes
0answers
13 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 ...
0
votes
0answers
7 views

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 $P(A)\subset A$.
1
vote
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 ...
2
votes
2answers
21 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 ...
1
vote
1answer
20 views

Ratios question involving 3 factors

An Alloy A contains copper and tin in a ratio of 3:5 by weight . Another alloy B contains tin and zinc in the ratio of 3:7 by weight . Find the ratio of copper : tin : Zin in a new alloy containing ...
2
votes
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 ...
1
vote
1answer
21 views

Question involving profit and loss

A shopkeeper brought 1840 oranges for 350 dollars . He threw away 52 rotten oranges and packed the rest in boxes of 6 each . He sold these boxes at 1.85 each .calculate the total profit he made if the ...
0
votes
1answer
17 views

Compounded interest quarterly

Calculate the compound interest earned when 8000 is invested for 9 months at 5% per annum compounded quarterly. I'm confuse with this question because compounded quarterly means that every 4 months ...
0
votes
0answers
11 views

Profit and loss question

A shopkeeper buys 240 pears for 60 dollars . Some of these pears are bad and they are thrown away. The remaining pears are sold at 35 cents each , thus making a profit of 19.80 dollars . Calculate the ...
0
votes
3answers
34 views

Hire purchase problems

A bank offers loans at interest of $12\%$ per annum , compounded monthly. Jack took a $\$50,000$ loan and makes a monthly installment payments of $\$4200$ at the end of each month . Find his ...
0
votes
1answer
18 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 $\$50$. ...
1
vote
2answers
36 views

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 ...
1
vote
1answer
12 views

Clearing concepts for compound interest

A man banked $\$50,000$ into the bank which pays compound interest if $7.6\%$ per annum compounded every 3 months. The formula is $$ A = P \left( 1 + \frac r {100} \right)^n $$ where $P$ is the ...