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

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0
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1answer
333 views

Irrational inequalities question: $\sqrt { -3x+1 } + \sqrt {6x+1} < \sqrt {3x+4}$ and $\sqrt { -6x+10 } + \sqrt {-x+2} \gt \sqrt {4x+5}$

Consider the following inequalities: $\sqrt { -3x+1 } + \sqrt {6x+1} \lt \sqrt {3x+4}$ $\sqrt { -6x+10 } + \sqrt {-x+2} \gt \sqrt {4x+5}$ Attempt at a solution; after performing all the ...
2
votes
2answers
50 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 ...
2
votes
1answer
40 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 ...
4
votes
1answer
6k views

Expense and Balance Mismatch

I searched and couldn't find a post in stack exchange for this. I recently saw a calculation for rupee spend and having balance in yahoo, but i am not quiet convinced with the answer given... the ...
3
votes
1answer
57 views

The operation before addition

I asked a question about operations and one comment puzzled me. Given a binary operation $\ast$ on integers at least $2$, define $\ast'$ by $$m\ast' n = \overbrace{m\ast m\ast \cdots \ast m}^{n\text{ ...
0
votes
3answers
34 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 ...
3
votes
2answers
91 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?
1
vote
0answers
24 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
21 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
27 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 $N$ ...
0
votes
3answers
154 views

Elementary rounding

Mr. Brown rounded $14.486$ to the nearest whole number by rounding $14.486$ to $14.49$ by the "over $5$" rule. Then he rounded $14.49$ to $14.5$ by the same rule. Then he rounded $14.5$ to $15$ by ...
-2
votes
0answers
40 views

Problem with Chinese remainder theorem [duplicate]

For all $n \ge 1$ , Let $\psi(n)=\{0\le x<n \mid x^3 \equiv x+1 \pmod n\}$ be the number of elements in the group. For example, $\psi(5) =1$ because the only solution $0\le x \lt 5$ for $x^3 ...
8
votes
2answers
220 views

Are there non-equivalent cardinal arithmetics?

‎Generalizing a concept in mathematics is always a problematic situation. In most cases there are several ways to generalize a notion and it is not easy to decide if a particular generalization is ...
-1
votes
1answer
213 views

Calculate start middle and end of any number [closed]

EDIT: It appears what OP wants is this: divide a given positive integer $n$ into three parts; the parts are to be roughly equal; the first and last parts to be equal. ORIGINAL POST: I need a start, ...
0
votes
5answers
35 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
3answers
76 views

Number of $0$ in great number

For example, $11111111111111100$ ends with $2$ zeros ,when we did know the decimal representation like $100!$ also. I would like a justified answer for the following question . How many $0$ are in ...
3
votes
3answers
101 views

Finding the integer solutions of the equation $3\sqrt {x + y} + 2\sqrt {8 - x} + \sqrt {6 - y} = 14$

$ 3\sqrt {x + y} + 2\sqrt {8 - x} + \sqrt {6 - y} = 14 $ . I already solved this using the Cauchy–Schwarz inequality and got $x=4$ and $y=5$. But I'm sure there is a prettier, simpler solution ...
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 ...
-3
votes
1answer
48 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 ...
-1
votes
3answers
61 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 $1$).
-3
votes
1answer
62 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
5answers
87 views

if $a+ b = 9 $and $ab = 1$. what will be the $a^3 + b^3 =$?

How can I solve this? Or, is it given properly? If $a + b = 9$ and $ab = 1$. What is $a^3 + b^3 = $?
6
votes
1answer
119 views

About translating subsets of $\Bbb Z.$

This is a continuation of About translating subsets of R2. Is it possible to find a pair of sets $A,B\subseteq\Bbb Z$ such that A is a union of translated (only translations are allowed) copies of ...
0
votes
2answers
41 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 $$ ...
-4
votes
4answers
112 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 = ...
3
votes
3answers
196 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 ...
41
votes
12answers
5k views

Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?

I was on the tube and overheard a dad questioning his kids about maths. The children were probably about 11 or 12 years old. After several more mundane questions he asked his daughter what $1/0$ ...
1
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2answers
44 views

Is combinatorics a part of arithmetics?

I wonder how arithmetic, combinatorics and discrete mathematics are related.
3
votes
1answer
88 views

In $\triangle ABC$ , find the value of $\cos A+\cos B$

The sides of $\triangle$ABC are in Arithmetic Progression (order being $a$, $b$, $c$) and satisfy $\dfrac{2!}{1!9!}+\dfrac{2!}{3!7!}+\dfrac{1}{5!5!}=\dfrac{8^a}{(2b)!}$, Then prove that the value of ...
8
votes
2answers
106 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 ...
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votes
6answers
68 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: $2^{48}$?
9
votes
1answer
146 views

Product of permutations of consecutive numbers yields arithmetic sequence

Let $n\geq 3$ be an integer, and $a,b$ be positive integers. Let $c_1,\ldots,c_n$ be a permutation of $a,a+1,\ldots,a+(n-1)$, and $d_1,\ldots,d_n$ be a permutation of $b,b+1,\ldots,b+(n-1)$. Is it ...
3
votes
4answers
112 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
108 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 ...
3
votes
0answers
76 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 ...
5
votes
1answer
81 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 $ ...
0
votes
2answers
32 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
88 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 :)
3
votes
5answers
83 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: $\sqrt{4x-1} = \sqrt{x+2}-3$ $(\sqrt{4x-1})^2 = (\sqrt{x+2}-3)^2$ $\sqrt{4x-1}\times\sqrt{4x-1} = (\sqrt{x+2}-3)\times(\sqrt{x+2}-3)$ ...
1
vote
3answers
37 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 ...
2
votes
1answer
2k views

Square root of surds?

I got this question Find the square root of $12+2\sqrt{6}$ expressing your answer in the form $\sqrt{m}+\sqrt{n}$. I have no idea what this means and how to go about it.
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votes
2answers
66 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. ...
6
votes
1answer
499 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., ...
1
vote
1answer
41 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 ...
-3
votes
3answers
85 views

How can you use the digits 2 0 1 5 to equal 28 [closed]

you can use the numbers only once and have to use them all.
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votes
1answer
107 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 $. ...
6
votes
3answers
149 views

What does $23_4$ mean?

I just saw this on a mathematical clock for $11$, i.e $23_4=11$: http://ecx.images-amazon.com/images/I/51nsaGqFoUL.jpg I guess it is some notation from algebra. But since algebra was never my ...
5
votes
1answer
118 views

Set with distinct subset sums

The problem is as follows : Given a set A with distinct positive integer elements, prove that there always exists another set B consisting of positive integers, s.t., The size of B is less than or ...
4
votes
0answers
53 views

Extention of Euclid's GCD Algorithm. (The Art of Computer Programming, Volume 1, Edition 3, Section 1.2.1, Exercise 12)

Euclid's GCD algorithm which is used to find GCD of two input numbers, say, $c$ and $d$, needs the inputs to be positive integers. Exercise 12 provides an extension to this algorithm and allows $c$ ...
2
votes
8answers
420 views

Why Not Define $0/0$ To Be $0$?

For every number $x$, $x\times 0=0$, hence $\dfrac{0}{0}$ can be any number! So $\dfrac{0}{0}$ "is knows as indeterminate" [1]. But what if we define it to be $0$? I already have an answer, but ...