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

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3
votes
2answers
158 views

How is “1” defined in various branches of mathematics?

Wikipedia does not elaborate much on the concept of "One" in such branches as graph theory, ring theory, algebra, topology, measure theory, formal logic, etcetera. How can one grasp the concept of ...
0
votes
1answer
39 views

Least Squares Equation (Change in Estimated Value)

The specified Least Square regression line is Price=5.2+2.5*Value If I was told that the estimated Value had changed from ...
0
votes
3answers
271 views

Two easy proofs by contradiction

Check the validity of the statements below using contradiction method (i) p: The sum of an irrational number and a rational number is irrational (ii) q: If $n$ is a real number with $n ...
4
votes
5answers
2k views

If the first 10 positive integer is placed in a circle(any order), 3 integer in consecutive locations around the circle that have a sum > 17?

If the first 10 positive integer is placed around a circle, in any order, there exists 3 integer in consecutive locations around the circle that have a sum greater than or equal to 17? This was from ...
0
votes
1answer
212 views

Cancellation Law, If $ax=ay$ then $x=y$

It's about cancellation law. if $ax=ay$ then $x=y$, provided that $a \neq 0$ It says that this only true if it applied in whole integers not just positive integers, I'm not really sure, if I put ...
2
votes
1answer
170 views

Don't understand casting out nines

Let n be a positive integer. If the sum of the digits of n is divisible by 9, then n is divisible by 9. I got upto here, ...
1
vote
2answers
188 views

How to do long division of 5555 / 55

I know this might seem silly, but I am having trouble performing step-by-step long division on $5555 \div 55$. My main problem is that I don't know when or what the rule is about putting the zeroes. ...
3
votes
2answers
212 views

Number base conversion

How can I convert a number from one base, $b_1 \neq 10$ to another base $b_2 \neq 10$ without going through base $10$ i.e. $b_1\rightarrow 10 \rightarrow b_2$?
1
vote
1answer
163 views

Uncertainty When Multiplying by $\pi$

When multiplying a number with an uncertainty by $\pi$, does the certainty differ, and if so, how? Example: $a = 10$ $\delta a = 1$ What is the uncertainty of $b$ where $b=\pi a$?
-1
votes
2answers
2k views

convert 0-255 into decimal between 0-1 [closed]

What I am trying to do is convert the color values 0-255 into a decimal form between 0-...
2
votes
3answers
72 views

linear equations

A shopkeeper buys a number of books for Rs.1200. If he had bought 5 less books for the same amount, each book would have cost him Rs.20 more. How many books did he buy? I have this question found in ...
3
votes
0answers
211 views

How does my $10\times10$ abacus work?

How does this $10\times10$ abacus work? More specific: Counting: is it common to count from 1 to 100, or from 1 to 9.999.999? How does addition work? How does multiplication work? Are there any ...
3
votes
1answer
2k views

How do you work with the IEEE 754 32-bit floating point format?

I'm having trouble completing a question that deals with the IEEE 754 32-bit floating point format, primarily because I don't know how to use it. I was hoping someone here could clarify for me using ...
4
votes
4answers
105 views

Arithmetics ; $p-1 \mid q$ equivalent to $(p-1)^2 \mid p^q - 1$

I have a problem with this exercise : prof that $p-1|\space q \iff (p-1)^2|\space p^q - 1$ I succeed to prof that $(p-1)^2|\space p^q - 1 \implies p-1|\space q$ thanks ^^
73
votes
14answers
4k views

Formal proof for $(-1) \times (-1) = 1$

Is there a formal proof for $(-1) \times (-1) = 1$? It's a fundamental formula not only in arithmetic but also in the whole of math. Is there a proof for it or is it just assumed?
0
votes
2answers
113 views

Mathematical transpose in excel

I'm currently working in excel, and I have to mathematically transpose a few cells (10*10 or 5r*10c): ------------------------------- | .. | .. | .. | .. | .. | .. | | 21 | 22 | 23 | 24 | 25 | .. | | ...
0
votes
1answer
91 views

Generate unique integer from $n$ integers and solve to get the integers from result

What could be the best way to generate a unique integer from $n$ integers in order $(n_1,n_2,\ldots)$? Further, from $n$, we should be able to get back each $n_1, n_2,\ldots $ etc. For example, from ...
17
votes
5answers
5k views

Is 'no solution' the same as 'undefined'?

Today in class my teacher wrote something along the lines of: $6^x = 0$ And proceed to heed a response from the class. A few people shouted undefined. So the teacher then writes: no solution ...
5
votes
1answer
132 views

Direct proof of the non-zeroness of an Eisenstein series

Question: Can you show directly from its formula that $G_4(i)\neq0$? Recall that the holomorphic Eisenstein series of weight $2k$ is defined by: $$G_{2k}(\tau)= \sum_{(m,n)\in\mathbb{Z}^2\setminus ...
1
vote
2answers
1k views

Formula for Snake Draft pick numbers

Hello I am trying to come up with a formula to calculate the overall pick number in a snake style draft. For example in a snake draft every other round the pick order reverses. So in a 10 team league ...
-1
votes
1answer
34 views

Changing Numbers To Prescribed Values Under Special Limitations

$x = 1825 + \large \frac{91}{1217}$ $y = 7 + \frac{2}{3}$ $z = 1827 + \frac{2}{3}$ Is there any way to turn $x$ into $z$ only using the first two terms, and/or a constant, and the ...
0
votes
2answers
54 views

How to find bounds for $x$ and $y$ for this triple integral?

I want to find the volume of the region enclosed by $z=x^2+y^2$ and $z=x+y$. How can I find the bounds for $x$ and $y$?
0
votes
1answer
79 views

simplifying “$\prod_{a\in A}\sum_{b\in B_a}{h(a,b)}$”

Is this equality correct? For finite sets $A$ and $B_a$ (where $a\in A$), we have: $$\prod_{a\in A}\sum_{b\in B_a}{h(a,b)}=\sum_{f\in \prod_{a\in A}B_a}\quad \prod_{a\in A}{h(a,f(a))}$$
6
votes
1answer
121 views

Arithmetic; count + divisibility

Let there be $101$ numbers arbitrarily chosen from the first $200$ whole numbers $1,2, \ldots ,200$. Prove that among the chosen numbers there is a pair of numbers such that one them is divisible by ...
5
votes
3answers
271 views

Interesting tea-time problem

Problem A: Please fill each blank with a number such that all the statements are true: 0 appears in all these statements $____$ time(s) 1 appears in all these statements $____$ time(s) 2 appears in ...
2
votes
2answers
115 views

Rightmost digit of $ \left \lfloor \frac{10^{20000}}{10^{100}+3} \right\rfloor $

How could I find $$ 0 \leq a \leq 9 $$ such that $$ \left \lfloor \frac{10^{20000}}{10^{100}+3} \right\rfloor \equiv a \mod 10 $$ ?
1
vote
2answers
705 views

Arithmetic Series

In a race, 8 apples are placed 5 meters apart on straight line, the first being 5 meters away from a basket. A contestant starts from the basket and puts one apple at a time into the basket. Find the ...
3
votes
2answers
3k 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.
5
votes
3answers
241 views

What is the most mathematically sound way to define the “damage per second” for a weapon?

Consider a weapon firing shots every $f^{-1}$ seconds (i.e. $f$ is the weapon's fire rate). Each shot deals $n$ damage to is target. Consider another weapon firing every $3f^{-1}$ second, but dealing ...
1
vote
2answers
125 views

Calculating kg per box with loss

He I am not to good in math but I have a situation I need to calculate. Sorry if this looks stupid I really doubt my self if it comes to calculating numbers. I have the following numbers: gross ...
4
votes
5answers
256 views

Is it convention or a fundamental mathematical property that the product of two negative numbers is positive?

Consider the following excerpts from Ask Dr. Math : Excerpt 1 So the real question is, $$(-1)(-1) = ?$$ and the answer is that the following convention has been adopted: $$(-1)(-1) = ...
1
vote
2answers
340 views

Profit and Loss calculation: Fake currency

A store buys an item for $\$50$. They price it then, at $\$80$ ($\$30$ profit margin). A customer buys the item from them with a fake $\$100$ note. The store returns $\$20$ to the customer. My ...
81
votes
1answer
3k views

$4494410$ and friends

The number $4494410$ has the property that when converted to base $16$ it is $44944A_{16}$, then if the $A$ is expanded to $10$ in the string we get back the original number. ...
0
votes
2answers
75 views

Boolean Simplification: Identifying a rule

I'm in the process of minimizing a boolean equation, and I've gotten it into the following form: $$\lnot B \lor (B \land \lnot C) \lor C$$ Just by looking at it, I can tell that this is always ...
7
votes
4answers
468 views

Is the set of PA theorems the same as the set of solvable halting problems?

I am not sure if this is a trivial question. By Post's theorem we know that every PA (first order logic) theorem is equivalent to stating that a given input C in a given Turing machine halts or ...
4
votes
2answers
126 views

selecting an arbitary digit from an integer

Let us say I have an integer of an arbitrary length such as: $209484250490600018105614048117055336$ Is there an elegant function which allows me to select the $n$-th digit such that: $f(1) = 6$ ...
3
votes
4answers
76 views

Unable To Understand The Difference Between $(-3)^4$ And $-3^4$

Why is $(-3)^4 =81$ and $-3^4 =-81 $?This might be the most stupidest question that you might have encountered,but unfortunately i'am unable to understand this.
49
votes
9answers
3k views

The last digit of $2^{2006}$

My 13 year old son was asked this question in a maths challenge. He correctly guessed 4 on the assumption that the answer was likely to be the last digit of $2^6$. However is there a better ...
1
vote
3answers
1k views

(A twist in a classical question) Sum and product of two irrational numbers is rational?

So I know that it is possible for the sums and products of irrational numbers to be rational. But, the only instances I know of that happening is when a certain combination of additive or ...
4
votes
4answers
163 views

Is the length of a segment between 0 and 1 exactly 1?

What is the length of the line segment between points A and B on a number line, where A = 0 and B = 1? Is it exactly 1? Perhaps I am thinking about it in an incorrect manner, but it seems to me that ...
2
votes
4answers
87 views

Evaluate: $3\cdot9^{\frac{1}{2}}\cdot27^{\frac{1}{4}}\cdot81^{\frac{1}{8}} \ldots$

Evaluate: $3\cdot9^{\frac{1}{2}}\cdot27^{\frac{1}{4}}\cdot81^{\frac{1}{8}} \dotsb$ Trial: Let $$\begin{align} P &= 3 \cdot 9^{\frac{1}{2}} \cdot 27^{\frac{1}{4}} \cdot 81^{\frac{1}{8}} ...
1
vote
1answer
159 views

Euclidean Division to avoid need for floating point arithmetic

In simple terms (that Google has been unable to provide the answer), is there an approach to dividing a whole integer by a quotient & remainder? As a specific example, ...
1
vote
0answers
29 views

integer S transform

I found the following integer transform, where all variables $x_0,x _1$ and $x_2$ are integers: $ y_0=x_1+floor(\frac{1}{4}(x_0+2x_1+x_2))\\ y_1=x_2-x_1\\ y_2=x_0-x_1 $ The inverse transform is ...
6
votes
2answers
781 views

Can you prove why Popsicle Stick Multiplication works?

This is a unique way of multiplying numbers by using sticks. Let's call it "Popsicle Stick Multiplication". Or maybe "Linear Algebra" quite literally. Take a look at both images that I've drawn ...
2
votes
2answers
85 views

Multiplying over Subtraction

I'd like to take maths seriously but I'm not that great at it, so I decided to learn at home. I know this is pretty basic, but as I said, I'm pretty bad at maths, haha. The worksheet gives me this ...
4
votes
3answers
206 views

Multiplying a square root by a non-square root

This is not something I do very often, so I'm a bit dicey on the rules. I just want to make sure that I understand things right... $$-\frac{1}{2}\cdot \sqrt{\frac{2}{5}} = -\sqrt{\frac{1}{4}}\cdot ...
45
votes
7answers
2k views

Computing $999,999\cdot 222,222 + 333,333\cdot 333,334$ by hand.

I got this question from a last year's olympiad paper. Compute $999,999\cdot 222,222 + 333,333\cdot 333,334$. Is there an approach to this by using pen-and-paper? EDIT Working through on paper ...
0
votes
1answer
69 views

Find the subtotal from the total including tax

If I have the Grand Total (including VAT) amount of money paid and the VAT % which was paid, how can I figure out the sub total (total before VAT)? For example If Sub Total = 70 and VAT is 18% ...
0
votes
1answer
83 views

When $(\sum_{i=1}^nk_i < \prod_{i=n}^ni^{k_i}k_i!)$?

Consider $\Omega \subset \mathbb{N}$ a finite subset of $\mathbb{N}$, $\phi: \Omega \rightarrow \mathbb{N}$ an enumeration of $\Omega$ such that $\phi(\omega)=i$ and $|\Omega|=n$, $$ ...
0
votes
0answers
23 views

How do I scale or normalise a set of numbers ranging from less than 1 to approaching a billion? [duplicate]

Possible Duplicate: Range scaling problem Apologies if title is a bit skewed, I'm assuming what I want to do is a form of scaling or normalising, but it's been a while since I've properly ...