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

learn more… | top users | synonyms (1)

4
votes
2answers
384 views

How many positive integers N are there such that the least common multiple of N and 1000 is 1000?

How many positive integers N are there such that the least common multiple of N and 1000 is 1000? I did found the solution to this problem , but I did it by brute force. When I was tackling ...
0
votes
2answers
66 views

Prove that if $N =\overline {xyz}\in\boldsymbol N$ (natural number) and if $x+y+z=9$ then $9$ divides $N$.

Prove that if $N =\overline {xyz}\in\boldsymbol N$ (natural number) and if $x+y+z=9$ then $9$ divides $N$. My try: $100x+10y+z=(99+1)x+(9+1)x+(10-9)z=99x+x+9y+y+10z-9z=9(11x+y-z)+x+y+10z$ Then I ...
5
votes
2answers
180 views

What is the total number of distinct sums possible from tossing six, six-sided dice?

I was reading The Ascent of Money by Niall Ferguson, and he writes "... he [John Law] wagered 10,000 to 1 that a friend could not throw a designated number with six dice at one throw. (He probably ...
0
votes
4answers
91 views

negative number divided by positive number, what would be remainder?

my question is If $-27$ is divided by $5$, what would be the remainder? thanks in advance.
1
vote
3answers
175 views

could not able to understand Project Euler 18. “Maximum path sum I”

According to question, By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. ...
0
votes
3answers
75 views

How many even numbers are there in a set $\{x_1, x_2 … x_n\}$

For example how to calculate how many even numbers are in a set $\{45, 46, 47 ... 456\}$. General question is how to calculate how many even numbers are in a given set of natural numbers which doesn't ...
3
votes
3answers
123 views

Explanation of minus × minus = plus

I've seen numerous explanation of why two negatives make a positive and I did understand most of them. Now, I found the following explanation : If now we consider the product arising from the ...
2
votes
4answers
100 views

Division misconception

I'm having trouble understanding division when the divisor is greater than the dividend, for ex 1/4. I think of division as "how many times can the divisor fit into the dividend evenly". ...
1
vote
1answer
43 views

Euclidian division of polynomials

I have to find the remainder of the division of $X^n$ by $X^2-6X-16$ for all positive integer $n$. I know how to do a euclidian division with polynomials but I am confused with the $n$ since I don't ...
1
vote
1answer
79 views

Exponent Law Question: $\left(x^2\right)^\frac{1}{2} = |x|$

Quick easy question! I was always taught at school that $(x^m)^n=x^{mn}$. However, I've only just noticed when computing something (two years into an undergrad course..) that for example ...
0
votes
3answers
57 views

Are there any identities linking arithmetic functions and $\pi$?

The question is self-explainatory. For example are there any known identities involving Euler Totient function and $\pi$ ?
0
votes
3answers
110 views

Find $x ^{ 2013} + 2013x ^{ 2010}$

Q. If $\large {\space x^2 + x + 1 = 0\space } $, Find $ x ^{ 2013} + 2013x ^{ 2010}$. I have tried finding the roots of $x$ from the given equation but that does not work.
0
votes
3answers
137 views

How to remember multiplication/times table of numbers greater than 12 but smaller than 21?

Is there any technique to permanently remember multiplication/times table of numbers greater than 12 but smaller than 21? For example, 13x1 = 13 .....through..... 20x10 = 200 ?
0
votes
1answer
29 views

Arithmetic-Division [closed]

how do you divide any two decimal numbers? condition: not by multiplying using 10 on both sides(Numerator and Denominator)
0
votes
1answer
90 views

Problem with my floor…

Let the set of numbers $A,n$ be of defined as $A_n = \text{the }n\text{'th value of }x\text{ such that }2\not\mid\lfloor{ x^2 - \sqrt{x}}\rfloor$, and $n$ is a positive integer. So as the first 10 ...
0
votes
1answer
101 views

A logical problem I can't solve. Please help. (About money) [closed]

I borrow 25 euro from 2 people that means I have 50 euro. I go to a restaurant, I eat and I pay 45 euro that means I have 5 euros remaining. I give 2 euro to each and that means I have 1 euro ...
1
vote
0answers
58 views

A question from Tom Korner's 'The Pleasures of Counting'

Merchant ships sailing independently take 75% of the time to complete voyages compared to ships sailing in a convoy but lose 14% of their number to submarines on each voyage, whilst convoyed ships ...
1
vote
1answer
69 views

Addition within lambda calculus

I've been reading "The Emperor's New Mind" by Roger Penrose. He briefly introduces lambda calculus (pp. 86-92) and gives this formula for addition: $A = \lambda fgxy.[((fx)(gx))y]$ This was my ...
2
votes
1answer
31 views

Averages question

There are five sticks. The average length of any four of them is 600. What is the average of all five? Is it possible to find the average of all with just this information given?
2
votes
6answers
176 views

Limits of square root [closed]

$$\lim_{x\to\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x + \sqrt x} }}-\sqrt x\right) $$ (original screenshot) Compute the limit Can you please help me out with this limit problem
6
votes
1answer
200 views

What does the raised $^2$ stand for?

What does the raised $2$ stand for? My first guess was: $4^2$ is $2\times 4=8$? Note: Am not really good at math
-1
votes
2answers
74 views

Use of Euclid's division method (algorithm) to find answer of hard problem

Euclid's division algorithm (a=bq+r) is used to answer the following questions. Please give me answers to them including the method. ...
1
vote
2answers
73 views

Value of $ \frac{a^2 + b^2 + c^2}{ac^2 - ab^2} $

If $a + b + c = 0$ , then value of $ \frac{a^2 + b^2 + c^2}{ac^2 - ab^2} $ is? According to me if $ a + b + c = 0$, then $a + b = -c$ This implies $ (a + b)^2 = c^2$ This implies $a^2 + b^2 ...
0
votes
4answers
49 views

Is the power of 1/2 same thing as principal square root?

$\sqrt{9} = 3$ 9 has 2 square roots: 3 and -3. What is $9^\frac12$? Is $9^\frac12 = \sqrt{9} = 3$ or is $9^\frac12 = \pm3$?
0
votes
2answers
46 views

How do I express a function that takes a set of values?

I have a function that I as a programmer would express like this in pseudo-code: myFunc(int[x0, x1, ... xn]){ return 1/((1/x0)+(1/x1)+...+(1/xn)); } How is ...
2
votes
3answers
60 views

Finding the remainder when $1.1!+2.2!+3.3!+ … +10.10! +2$ is divided by $11!$

Find the remainder when $1.1!+2.2!+3.3!+ ... +10.10! +2$ is divided by $11!$ An attempt: Rearranging: $$\frac{1}{11!}+\frac{2.2!}{11}+\frac{3.3!}{11} \cdots +\frac{10.10!}{11}+\frac{2}{11!}$$ ...
0
votes
1answer
50 views

Objective questions on complex calculations.

how to solve these type of questions ? i have tried logarithm and inequalities but could not pin point the exact and correct method.
1
vote
2answers
155 views

How can a negative multiplied by a negative give positive? [duplicate]

On first look this can seem weird. But I can explain what I am looking for. We all know from elementary maths that $(-\times-)=+$. Now, lets say there are 3 cows and I say they will become doubled ...
4
votes
1answer
87 views

Sum of difference of numbers in an arrangement of the numbers $0,1,2,\cdots, n$

A seemingly interesting (easy?) problem came to mind and I thought it would be nice to ask your opinion about it. Suppose we are going to arrange numbers $0$ to $n$ in a row in such a way that the ...
2
votes
2answers
124 views

Landau's “Foundations of Analysis” - Addition of natural numbers

At the beginning of his Foundations of Analysis book (translated from German), Landau writes in his Preface for the Teacher : Peano defines $x+y$ for fixed $x$ and all $y$ as follows : $$x+1 = ...
1
vote
0answers
32 views

On the Legitimacy of Grossone [duplicate]

A paper describing grossone used to measure such things as the sierpinski carpet here:http://arxiv.org/abs/1203.3150 I'd like to discuss the legitimacy of grossone. What is the general consensus ...
1
vote
4answers
145 views

Which is larger :: $y!$ or $x^y$, for numbers $x,y$.

This is a generalization of this question :: Which is larger? $20!$ or $2^{40}$?. No explicit general solution was presented there and I'm just curious :D Thank-you. Edit :: I want a most-general ...
1
vote
1answer
36 views

How to calculate the interest amount per day

I need to implement this calculation in my project... Its a simple calculation But I dont know... I googled about that but can't to find the solution.... I have the following values (note:its a ...
0
votes
1answer
18 views

Ratio Questions

this question is stumping me which is a pain because it was found in a basic high school math book. When a car is moving at 108 km/hr, it travels 18km on a litre of petrol. If petrol costs €1,62 ...
0
votes
1answer
36 views

Calculate desired profit given unit price and fee

This seems simple, but I'm struggling to find the answer... How much should I sell my apple for if I want to achieve the desired profit? Cost for me to buy the apple (A) = £10 Desired profit (B) = ...
0
votes
3answers
48 views

A.P problem gaussian sum (average of terms explanation)

The question is "the sum of first n terms of an arithmetic progression,if the last term is given $S_n=\frac{n(a+l)}{2}$; what does "$\frac{a+l}{2}$" represent?
0
votes
0answers
35 views

The order of operations [duplicate]

I've scoured the internet and I have asked many people, but I can't seem to get a finite answer to the multiplication and division step in the order of operation. Does multiplication precede division ...
0
votes
1answer
29 views

Fractional exponentiation in modular arithmetic

Does raising a modular expression to a fraction mean anything? For example, $a\,\,mod \,\,N$ raised to $1/b$ where $b>0$. Does this violate the rules of modularity?
1
vote
0answers
38 views

Is undecidability of arithmetic a corollary of Tarski undefinability theorem?

Arithmetic is undecidable, in other words the set of Godel numbers of theorems of arithmetic is not recursive, and so there is no algorithm/ recursive function to decide if a statement is provable or ...
1
vote
1answer
55 views

Square root notation and lengths of vectors

I'm reading a textbook and it's going over finding the dot product of two vectors: $$u * v = \|u\|*\|v\|*\cos\theta$$ The vectors are: $$u = (0, 0, 1) \\ v = (0, 2, 2)$$ With lengths: $$\|u\| = 1 ...
2
votes
4answers
449 views

Limit of $\sqrt{x^2-6x+7}-x$ as x approaches negative infinity

What is $\lim\limits_{x\to-\infty}(\sqrt{x^2-6x+7}-x)$ ? Don't understand how to approach this question
3
votes
1answer
97 views

Understanding countable ordinals (as trees, step by step)

Even though ordinal numbers – considered as transitive sets – are perfect non-trees, it is worth (and natural) to visualize them as trees, starting from the finite ones which are given as ...
-3
votes
4answers
111 views

Which number is divisible by $7^5$ ? Circle the correct answer [closed]

A) $(210^3)(98^2) $ B) $(7^2)(17^9)$ C) $(77^4)(5^7)$ D) $(27^5)(35^4)$ Which is divisible by $7^5$? I need to do with without a calculator... How would I go about this?
6
votes
1answer
51 views

Defining natural numbers without $0$ or $1$.

Let's define Peano's axioms having $2$ as the first number: $\newcommand\Nt{\mathbb N''}2\in\Nt$. $\newcommand\next{\mathop{\mathrm{next}}}\forall n\in\Nt:\next n\in\Nt$ (or $\next:\Nt\to\Nt$). ...
3
votes
2answers
59 views

Why is the coefficient in front of $\sqrt n$ always 1 in the intermediate terms for finding the continued fraction expansion of $\sqrt n$?

After playing around on paper for a bit, I came up with a short python generator to find the continued fraction expansion of $\sqrt n$. I understand why it gets the right answer when it gets an ...
1
vote
2answers
134 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 ...
3
votes
0answers
123 views

Visualizations of ordinal numbers

I find this picture of the ordinal numbers up to $\omega^\omega$ rather hard to grasp: I wonder if the following might be a more compelling way to visualize ordinal numbers up to $\omega^\omega$: ...
0
votes
4answers
84 views

Why does $ \frac {\frac {1}{\sqrt{x}}}{x} = \frac {\sqrt{x}}{x^2} $?

A homework question recently asked for me to simplify: $\frac{1}{\sqrt{7}} \div {7}$ It's easy to see that this becomes $\frac{1}{7\sqrt{7}}$ But according to wolfram alpha this is also equal to ...
0
votes
1answer
67 views

The sum of two numbers equals 318, express the product of the numbers according to the lowest

I didn't understand the question on the title, what am I supposed to do?
1
vote
0answers
153 views

Property of arithmetic means?

$a,b,c,d \geq 0.$ It seems to me that this inequality is true and equality holds when $a=b=c=d$? $$\dfrac{a+b}{2}\dfrac{b+c}{2}\dfrac{c+d}{2}\dfrac{d+a}{2}\leq ...