Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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-1
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1answer
33 views

company as none-binary tree [closed]

Company's structure is depicted as none-binary tree where each node represents an employee. Root of the tree is CEO of the company and every node that has children is their supervisor. When assigning ...
11
votes
3answers
762 views

How to raise -1 to non-integer powers

How do you calculate $(-1)^x$ where $x$ is some real number. For example, what is $(-1)^{\sqrt{5}}$. This question came as I was trying to computer $e^{i\pi a}$ where $a$ is irrational.
-3
votes
4answers
41 views

Prove Summation to Some Number $n$ [duplicate]

Let $n\in \mathbb{N}$. Can someone help me prove this by induction: $$\sum _{i=0}^{n}{i} =\frac { n\left( n+1 \right) }{ 2 } .$$
3
votes
1answer
32 views

How many divisors of N ended by 5

I must know how to find how many divisor of N ended by 5 ? In my exercise, I have $\ N=63'000 = 2^3*3^2*5^3*7 $ and I can found the number of divisors of N using $\ (3+1)*(2+1)*(3+1)*(1+1)=96$ Among ...
0
votes
0answers
21 views

Binary Overflow Detection

I am trying to solve several problems, which are binary and encoded using the 2's complement system. One problem has stuck out to me: 0111 + 0001 Both are positive, with 0111 being 1+2+4 or 7, and ...
21
votes
12answers
5k views

Is there a law that you can add or multiply to both sides of an equation?

It seems that given a statement a = b, that a + c = b + c is assumed also to be true. Why isn't this an axiom of arithmetic, like the commutative law or associative law? Or is it a consequence of ...
3
votes
0answers
22 views

Finding lower bounds for solution of linear Diophantine equation in two varuables

I am currently encountering the following arithmetical problem : given four nonzero integers $A,B,C,D$, let $\Omega=\bigg\lbrace (x,y)\in{\mathbb N_{\geq 0}}^2 \ \bigg| \ \frac{Ax+By}{Cx+Dy} \in ...
0
votes
4answers
100 views

What is $10 \times 10-10+10$? [duplicate]

I was just surfing a social site and found this question posted by someone. People were arguing or different answers like 80, 100, 120. So, what is the correct answer for $10 \times 10-10+10$? I used ...
4
votes
6answers
145 views

Show that $\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$

Show that $$\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$$ Playing around with the expression, I found a proof which I will post as an answer. I'm asking this question because I ...
6
votes
7answers
184 views

why is $\sqrt{-1} = i$ and not $\pm i$? [duplicate]

this is something that came up when working with one of my students today and it has been bothering me since. It is more of a maths question than a pedagogical question so i figured i would ask here ...
4
votes
1answer
123 views

Can someone prove why $\sqrt{ab}=\sqrt{a}\sqrt{b}$ is only valid when a and b are positive?

I have seen many people say that a and b can't be positive for example in this false proof : $$1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{-1} \sqrt{-1} = i^2 = -1$$ Trust me, I understand that $1\neq -1$ and ...
5
votes
9answers
210 views

How do I explain why multiplying $0.8 \times 0.8$ is less than $0.8$?

I'm math is very rusty so forgive me for a trivial question. In my daughters home work she had the sum $4.8 \times 4.8$. Her thought process was to multiply $4 \times 4 =16$ and then $0.8 \times 0.8$ ...
0
votes
1answer
29 views

Multiplying numbers splitting the number into 4 digit numbers

Doing some programming exercise how to sum big numbers,I split the numbers into $n$ numbers of $4$-digit numbers $1240135981395813958$ I split into $1240$,$1359$,$8139$,$5813$,$958$ and summing with ...
2
votes
2answers
62 views

get 100 with the help of five 2

how to get 100 with the help of +, -, /, * and five 2s? 22222 = 100 I should put arithmetic operants between two s and get 100. PLease help
11
votes
7answers
190 views

Arithmetic pattern $1 + 2 = 3, 4 + 5 + 6 = 7 + 8$, and so on

I am noticing this pattern: \begin{align} 1+2&=3\\ 4+5+6&=7+8\\ 9+10+11+12&=13+14+15 \\ 16+17+18+19+20&=21+22+23+24 \\ &\vdots \end{align} Is there a general formula that expresses ...
1
vote
0answers
73 views

Can you subtract two integers using multiplication and division?

The multiplication operation is traditionally defined as "repeated addition", and division (with remainder) can be defined using repeated subtraction. Can we define subtraction the other way round? ...
2
votes
1answer
45 views

Order of Operations Game Solution

My AP Computer Science teacher likes to play a game with his students where he writes 4 random numbers on the board and a fifth, target number. The objective is to use the four basic operations ...
2
votes
2answers
52 views

Why does the limit behavior of this function take over at 35?

I've been working with this function on an semi-related question: $$f(N)=\left\lfloor \frac{10N}{\lceil \frac{3}{4} N \rceil} \right\rfloor$$ It's clear that $10\leq f(N) \leq 13$, and that ...
3
votes
2answers
102 views

Is there a name for property $n+k=m+k\implies n=m$?

Monoid of natural numbers with addition have such property, that for any $n,m, k \in \mathbb{N}$ if $n+k=m+k$ then $n=m$. Does this property have some name in English?
0
votes
3answers
43 views

Explanation of calculator percentage key

I would really appreciate some help with this question. I have asked few people but nobody could explain. When you use calculator and enter these values you get different results. Why? Example: 100 ...
1
vote
0answers
32 views

Mathematical term or equation to describe arithmetic pattern

First off, this is a badly titled question because I'm unsure of how to word the problem. Please suggest a better title. The sum of $55,555$ and $33,333$ is $88,888$. If I change the first digit of ...
1
vote
2answers
35 views

If five geometric means are inserted between 8 and 5832, what is the fifth term in the geometric series?

If five geometric means are inserted between 8 and 5832, what is the fifth term in the geometric series? Again i don't understand the wording of the problem. So in general: what does it mean for $n$ ...
1
vote
1answer
32 views

If $64$ is divided into three parts proportional to $2$, $4$ and $6$, what is the smallest part?

If $64$ is divided into three parts proportional to $2$, $4$ and $6$, what is the smallest part? The problem I have is with understanding what the question means. What does it mean for a number $N$ ...
13
votes
2answers
116 views

Six of a kind .

$$\begin{align} ...
0
votes
5answers
40 views

Dividing Numbers Into Rations

The question is: Suppose 60 is divided into 3 parts in the ratio of 1:3:6. What s the value of the middle part? I tried to take 60, divide it into 3 parts and divide those 3 parts accordingly to ...
0
votes
1answer
29 views

Why Sum square of each pair of a group of numbers is N factor of sum squares of its elements difference from mean?

Consider we have some numbers for example $3,4,8$ that its mean is, $5$. It is easy to follow that, $$\left(3-4\right)^2+\left(4-8\right)^2+\left(3-8\right)^2 = 3\cdot\left( (3-5)^2+(4-5)^2+(8-5)^2 ...
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votes
1answer
61 views

Arithmetic Series, when $n$ tends to infinity the limit is $24$ [closed]

The $n$-th term of a sequence is $U_n$ $$U_{n+1}=pU_n+q$$ $p$ and $q$ are constants the first two terms are $U_1=96$ and $U_2=72$ the limit as $n$ tends to infinity is $24$ a) show that ...
6
votes
2answers
132 views

Defining addition in second order logic

(before saying it's duplicate, read whole question) I was told by someone that we can define addition and multiplication purely in terms of successor function, provided that we work in second order ...
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votes
1answer
64 views

Why is $\,c^2-2bcd+b^2d^2=(c-bd)^2\,$? [closed]

How would you explain, using simple arithmetic, that $$c^2-2bcd+b^2d^2=(c-bd)^2\;?$$ (I'm trying to explain this to a student I tutor.)
0
votes
2answers
42 views

Division by Multiplication of Reciprocal

I'm trying to prove the following: $${ad\over bc} = {\frac ab \over \frac cd} $$ First, $${\frac ab} = ab^{-1} $$ and $${\frac cd} = cd^{-1} $$ So the compound fraction above equals $$ ...
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votes
3answers
64 views

Find algorithm for equation [closed]

I need algorithm for this problem: Find $x,y$ from the equation: $c=ax+by$, where a,b,c are given natural numbers and $(a,b)=1$ (the greatest common factor of $a$ and $b$ is $1$).
-4
votes
4answers
118 views

Does the commutative property of addition hold when we're dealing with infinity? [closed]

I was wondering, if I evaluated some kind of algebraic expression and I got the following: $-\infty+\infty$. Is infinity commutative like it is with real numbers? Could I say that $$-\infty+\infty = ...
1
vote
2answers
45 views

Is combinatorics a part of arithmetics?

I wonder how arithmetic, combinatorics and discrete mathematics are related.
8
votes
2answers
119 views

Given dividend and divisor, can we know the length of nonrepeating part and repeating part?

$13/92=0.14\overline{1304347826086956521739}$ In this example, the length of nonrepeating part is $3$. The length of repeating part (repeating period) is $21$. I collected some properties related to ...
-4
votes
6answers
71 views

How to simplify expression with exponents? [closed]

One question left for me to answer and I am stuck on it. How to simplify $2 \cdot 2^{45} + 6 \cdot 2^{45}$ to this: $2^{48}$?
4
votes
4answers
136 views

Find $\lim_{x \to \infty}( \sqrt{4x^2+5x} - \sqrt{4x^2+x})$

$$\lim_{x \to \infty} \left(\sqrt{4x^2+5x} - \sqrt{4x^2+x}\ \right)$$ I have a lot of approaches, but it seems that I get stuck in all of those unfortunately. So for example I have tried to multiply ...
4
votes
1answer
112 views

Is $\sqrt{3}^\sqrt{5}$ rational or irrational?

Is $\sqrt{3}^\sqrt{5}$ rational or irrational? One way is to let $x$=$\sqrt{3}^\sqrt{5}$ and then calculate $antilog \ (log (\sqrt 3) \times \sqrt(5))$ which gives irrational number. But is there a ...
2
votes
2answers
73 views

An identity that comes from computing the Wiener index of a cyclic graph

Can the below identity be proven in such a way that we can generalize it? $(1 + 1 + 2 + 2 + 3 + 3 + 4) +( 1 + 2 + 2 + 3 + 3 + 4) + (1 + 2 + 3 + 3 + 4)+ +( 1 + 2 + 3 + 4 )+(1 + 2 + 3) + (1 + 2) + 1 = ...
4
votes
0answers
84 views

Calculate $\sqrt{\frac{1}{2}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}}} \times \ldots $

$$ \sqrt{\frac{1}{2}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}+ \frac{1}{2}\sqrt{\frac{1}{2}}}} \times\ldots$$ I already know ...
3
votes
3answers
208 views

How to divide natural number N into M nearly equal summands?

How to divide natural number N into M nearly equal summands? For example, to divide 20 by 13, in geometric representation, I should get How to generate the sequence above? What is the name of ...
0
votes
2answers
34 views

Adding interest and saving to principal

I know the formula $$ K_n = K_0 \cdot (1+r)^n $$ to get the balance after $n$ years with an interest rate $r$. What if I'm adding 5 dollars to the principal each day. How can I find the balance ...
8
votes
1answer
95 views

$mn | m^2+n^2+m \implies$ $(n-1)$ 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 :)
5
votes
1answer
86 views

Can all math operations be reduced to a sufficiently complex algorithm?

Say I could only perform one operation (addition) from addition I could derive subtraction by adding a negative number. Also, from addition I could derive multiplication, like $ a n $, just add $ a $ ...
1
vote
3answers
40 views

Basic arithmetic [closed]

I can't understand how: $$ \frac {2\times{^nC_2}}{5} $$ Equals: $$ 2\times \frac {^nC_2}{5} $$ If we forget the combination and replace it with a $10$, the result is clearly different. $1$ in the ...
3
votes
5answers
89 views

Why doesn't squaring the radicand of a square root introduce a plus-minus sign here?

The question I have concerns the following problem: $\sqrt{4x-1} = \sqrt{x+2}-3$ $(\sqrt{4x-1})^2 = (\sqrt{x+2}-3)^2$ $\sqrt{4x-1}\times\sqrt{4x-1} = (\sqrt{x+2}-3)\times(\sqrt{x+2}-3)$ ...
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votes
2answers
75 views

Is this a possible reason for why 0/0=anything, meaning it's undefined? [duplicate]

I already know about this: $4\over 0$=?, so $?\cdot0=4$, so $0\over 0$=?, so $?\cdot0=0$. This can be just any number, such as five, 49, zero, or even -567 because anything times zero equals zero. ...
1
vote
1answer
45 views

Diophantine equation : two products of linear factors differ by a constant

Recently, I was asked the following question by a friend : find all $a,b,c,a',b',c',k \in {\mathbb Z}$ with $k\neq 0$ such that the identity $$ (X-a)(X-b)(X-c)+k=(X-a')(X-b')(X-c') $$ holds in ...
6
votes
1answer
548 views

What is the Scientific Notation of Zero?

This question was asked here, where the answer uses this description. The last line reads: "The special case of $0$ does not have a unique representation in scientific notation, i.e., ...
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votes
1answer
200 views

Why is it possible to find the birth year by subtracting one's age from 114?

I noticed that any person can find their birth year just by subtracting their age from the number $114$. For example, if I am $25$ years old then from $114-25=89$ I know the birth year is $1989 $. ...
1
vote
3answers
53 views

Using a decimal addition table for subtracting

I'm reviewing the math I missed in school and I've come across a decimal addition table in a book along with a description of how to use the same table for subtracting. I'm having trouble parsing the ...