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

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2answers
56 views

Multiplication problem.

What would be the value of z in this question? If $z=2,$ the relation becomes $22\cdot wx = 594,$ which gives $wx=27.$ Partial product of $22\cdot 27$ is $154 + 440.$ It's incongruous with the ...
0
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0answers
32 views

Arithmetic progressions in subset

Let $S$ be a subset of $\{1,\dots,n\}$. Does there exist a good algorithm to find a partition of $S$ into "reasonably long" arithmetic progressions? Many thanks!
2
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4answers
42 views

$10$ Distinct Integers from a set and their sum equals to $954$

$10$ distinct integers from the set $ \left \{1;2;...;100 \right \} $ are chosen such that their sum is $954$. What is the smallest of the $10$ integers? How do I start this question? I have no idea ...
0
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0answers
28 views

Calculate new least common denominator

A parcel (lot) has an area of $547$ with co-owners that own a certain share in factions: Person $1$ has $\frac{1}{8}$, Person $2$ has $\frac{1}{8}$, Person $3$ has $\frac{2}{8}$, Person $4$ has ...
2
votes
0answers
35 views

How to reduce exponentiation expressions?

It is a simple question but I am afraid of its simplicity. Is that correct : $2^{30}+2^{30}+2^{30}+2^{30} = 2^{30}(1 + 1 + 1 + 1) = (2^{30})\cdot 4 = 2^{30}\cdot2^2 = 2^{32}$? I am doing complex ...
1
vote
1answer
76 views

How to find the nth term of this sequence?

How do I find the $n^{th}$ term, and what is it? $$ 1, \dfrac{1}{4}, \dfrac{1}{9}, \dfrac{1}{16}, \dfrac{1}{25},\dots$$ I mean I want to find out the relation how $n^{th}$ term depends on $n$. I'm ...
1
vote
1answer
67 views

Why is 0*0 is termed as indeterminate? [closed]

Why is 0 multiplied by 0 is termed as indeterminate? My idea about division by 0 is clear but not in the case of multiplication. Please help me by solving the equation : 0*0=indeterminate
2
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1answer
46 views

How to get the amount of digits after the decimal point

How can I easily find the amount of digits after the decimal point? For example: ...
0
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6answers
117 views

8 / 4 (4-2) = ? What is answer? [duplicate]

What is answer for 8 / 4 (4-2) = ? My answer is 4. But some says it's 1. And arguing each others. They even using some calculators for prove them. Even those calculators showing both 1 and 4 as ...
6
votes
3answers
71 views

Simplify $\left(\sqrt{\left(\sqrt{2} - \frac{3}{2}\right)^2} - \sqrt[3]{\left(1 - \sqrt{2}\right)^3}\right)^2$

I was trying to solve this square root problem, but I seem not to understand some basics. Here is the problem. $$\Bigg(\sqrt{\bigg(\sqrt{2} - \frac{3}{2}\bigg)^2} - \sqrt[3]{\bigg(1 - ...
1
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0answers
21 views

Arithmetic picard rank of smooth cubic surfaces

Assume a smooth cubic surface is defined over a field $k$ characteristic $0$, that it has line defined over $k$ and that its arithmetic Picard rank over $k$ is maximal i.e. $7$. Does this imply that ...
2
votes
3answers
36 views

How to calculate value of expressions when $a = 22$

$a = 22$ Round the answer to three significant figures: $\dfrac{77}{3a}$ for this one I am not sure if I do $\dfrac{77}{3(22)} = 1.17$ or $\dfrac{77}{3(22)} = 56$. Sorry if this is written in a ...
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votes
2answers
18 views

Don't understand adding a system of compound inequalities

I'm reading a proof of the Division Theorem and one line that comes up is Since 0 ≤ r1 < b and 0 ≤ r2 < b , we have −b < r1 − r2 < b. I do not ...
1
vote
1answer
28 views

First 10 digits of large sum

There is a debate about this Project Euler problem in the discussion thread for the problem. The debate is whether you only have to add the first 12 digits of each number in order to get the answer. ...
0
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2answers
39 views

How to make a value scale with a probability?

Say I have a 50/50 chance to win/lose, and I have another value which is strength which starts at 0 but rises up by 5 every win to a max of 95. And every 5 strength ups my odds to win up to 95/100. I ...
0
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0answers
10 views

An inequality related to Brun's sieve

My question is about the presentation of Brun's sieve by Gelfond & Linnik's Elementary methods in the analytic theory of numbers. The authors denote by $P(\Delta~;~D~;~x~;~a_1p_1b_1, \ldots, ...
1
vote
5answers
69 views

Is it possible to split a division problem into parts, like in multiplication?

In multiplication we can mentally split a problem that is too big into multiple problems. For example: 26 * 40 = (20 * 40) + (6 * 40) = 800 + 240 = 1040 This is a very quick way to multiply ...
3
votes
2answers
58 views

Find prime numbers $p,q$ such that: $pq| p^p+q^q+1$

Le $p,q$ be prime numbers such that: $pq| p^p+q^q+1$ Find $p,q$ I don't have any ideas about this problem :( Thanks :)
1
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0answers
15 views

How to analytically find these rounding issues

Let's say we have a fixed yearly amount that we have to divide equally among an amount of days. For instance for $1,600 we may have: ...
0
votes
1answer
27 views

Calculate ideal value from graph

I have a question to ask, but before I do, let me just tell you that this might be a trivial - or even downright silly question. I only have a basic understanding of math, so please do try to keep ...
2
votes
0answers
36 views

The smallest prime factor with a set of digits

I was wondering if there was a way to logically/mathematically derive what the smallest possible largest prime factor to a number was, using each of the digits 1-9 only once. An example could be ...
0
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2answers
97 views

Two minus signs make a plus [duplicate]

Why do two minus signs make a plus sign and is there a corresponding rule for division and multiplication signs?
0
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1answer
24 views

Dividing fractions [duplicate]

When dividing fractions, you can find the quotient by multiplying them with the second fraction reciprocated. e.g. 5/6 divided by 7/8 = 5/6 times 8/7. Why does this work?
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2answers
35 views

significant figures in a product

If I take a digit like $5$ (say in m) and multiply it by a digit say $5$ (in m) then I will get $25$ ($\mathrm{m}^2$---an area). Now, $5$ can be expressed in Scientific notation as $5 \times 10^0$ to ...
0
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3answers
89 views

Evaluating $6^2\div 2(3)+4$: is the answer $10$ or $58$? [duplicate]

Evaluating $$6^2\div 2(3)+4$$ I understand how people are getting $10$ but I am getting $58$ because I am not distributing the $2$ to the $3$ inside the parentheses. Is that correct?
0
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2answers
39 views

Repeating Decimal in different base

I've come across the following question. Find $0.\overline{204}_6$ as a base ten fraction. I understand that is the question asked the repeating decimal in base $10$, I would then say that: $$x ...
4
votes
1answer
62 views

Fraction - to be or not to be?

In a recent year 6 maths test my daughter was asked to write a fraction equal to half of 11/40. Her response was 5.5/40 which was not accepted as a correct answer- the model answer used for marking ...
2
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0answers
34 views

Can I have a trailing dot at the end of a number?

Is 12. a valid way to say 12.0 I was trying it with python. If I say a = 12., python will ...
4
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1answer
121 views

Simplifying $\scriptsize\sqrt{2+\sqrt{2}} + \sqrt{2+\sqrt{2+\sqrt{2}}} + \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}} + \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2}}}}$

The question is in the title: is there a simpler form or result for $$\sqrt{2+\sqrt{2}} + \sqrt{2+\sqrt{2+\sqrt{2}}} + \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}} + ...
0
votes
2answers
249 views

What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?

Can somebody help me figure out how to approach this problem and why the answer is 14.5? I already have the answer I'm just confused about how to approach these questions in general for future ...
1
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2answers
20 views

Methods to quickly compute percentages

Yesterday, talking with a friend of mine, she asked me what is a quick (and – of course – correct) way to compute percentages, say $3.7 \%$ of $149$. Frankly, I was sort of dumbfounded, because I use ...
3
votes
1answer
53 views

Tiny arithmetic trigonometry anomaly

$1.96\sin(149^\circ) + 1.00842\sin(203^\circ) + 0.61446\sin(285^\circ) = 0.02193075901$ But if I calculated each of the terms separately, then add them together, I get a result that is a tiny bit ...
0
votes
1answer
37 views

Fractional hexadecimal addition.

i have searched the web and through out the forums but, i couldn't find an exact answer. This is my first question, and please excuse my english. I am doing my CS homework which includes adding some ...
1
vote
2answers
38 views

The ambiguity of the meaning of the term “average”

Suppose $\{x_1, x_2, \ldots , x_n\}$ is a set of data of n weights. The average weight is then (the sum of these weights divided by $n$), right? Now, suppose $\{x_1, x_2, \ldots , x_n\}$ is a set of ...
1
vote
4answers
157 views

Is there anything (even something weird or fancy) that you can multiply by zero and not get zero?

I'm wondering if there's any kind of "imaginary anti-grassmann" (for lack of a better idea) or some strange object or other in math that you can multiply by zero and somehow not get something other ...
2
votes
2answers
64 views

Is there any formula for number of divisors of $a \times b$?

Let $a$ and $b$ be two numbers, Number of divisors of $a$ is $n_1$; Number of divisors of $b$ is $n_2$; How to find the number of divisors $N$ of product $a \times b$ by using known number of ...
3
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2answers
37 views

On the priority of arithmetic operations

Could someone explain the difference between these two problems: 6:2(2 + 1) and 6/2(2 + 1)? The first one should be read as ...
1
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2answers
34 views

How does $\sum (Y_i-\bar{Y})^2 = \sum Y_i^2 - n\bar{Y}^2$?

I've tried my algebra backwards and forwards and starting from the left-hand side of the equation below I just can't get to the right-hand side. I'm always left with an extra term $-2Y_i\bar{Y}$. ...
4
votes
1answer
107 views

Disjoint subsets and Number of 1's in the binary representation

For a subset $S$ of $[n]$, let $\chi(S)$ denote the $n$ bit 'characterisitc vector' of $S$, i.e., $\chi(S)=(a_1, a_2, \ldots, a_n)$ where $a_i=1$ if $i \in S$ and $a_i=0 $ if $i \notin S$. Think of ...
0
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1answer
19 views

base arithmetic conversation decimal to (+3)

I've asked the question because I've never seen a base like that before. For example, $76_{10}$ = $(?)_{+3}$ . The issue is that what does $_{+3}$ stand for ?
0
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2answers
33 views

Base-n arithmetic and multi-dimensional matrices

Interesting thing about binary numbers is to find their decimal value you can represent them as a multidimensional array, where each cell is indexed, starting from 0. For simplicity, let's start with ...
0
votes
1answer
29 views

Summation problem (probability)

I have the equation $$\Pr(X\le6)=\sum_{x=6}^{∞}\left({e^{-4.8}}\cdot\frac{4.8^{x}}{x!}\right).$$ And it is not equating to when I sum each term manually. Plugging this into my calculator I get ...
1
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2answers
66 views

How to calculate so that when width increases, height will decrease

As stated in title. Width is dynamic, hence the calculation :p The tricky part is that width can not be on the right side of the divide sign (\), as defined by the css ...
2
votes
1answer
40 views

Why does complement arithmetic work?

I'm learning about how computers store and manipulate integers, and I want to understand two's complement. Despite an abundance of web-sites demonstrating how to perform complement arithmetic, the ...
1
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2answers
46 views

Find the fraction that creates a repeating decimal that repeats certain digits

Is there any way to find the fraction $x/y$ that, when converted to a decimal, repeats a series of digits $z$? For example: ${x}/{y} = z.zzzzzzzz...$ or with actual numbers, $x/y = 234.234234234...$ ...
1
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3answers
45 views

Operations and Identities [duplicate]

We have the binary operation addition on numbers. It has an additive identity ( 0 ) and it is commutative. Multiplication is simply repeated addition. It is a binary operation on numbers. Its ...
4
votes
4answers
182 views

How to compute a lot of digits of $\sqrt{2}$ manually and quickly?

After having read the answers to calculating $\pi$ manually, I realised that the two fast methods (Ramanujan and Gauss–Legendre) used $\sqrt{2}$. So, I wondered how to calculate $\sqrt{2}$ manually in ...
4
votes
1answer
23 views

Sum of numbers in a grouping question

A person grouped numbers in the following way: $$\left \{ 1 \right \},\left \{ 3,5 \right \},\left \{ 7,9,11 \right \},\left \{ 13,15,17,19 \right \},...$$ What is the sum of the numbers in the $9$th ...
2
votes
2answers
88 views

What fraction is $\frac{2}{5}$ of $\frac{3}{4}$?

$\frac{2}{5}$ of blood donors at a centre have group O blood. $\frac{3}{4}$ of these donors are under 30. What fraction of the group O blood donors at the centre are under 30? What I did was divide ...
2
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0answers
27 views

Arbitrarily long arithmetic progressions?

I found a theorem that states that if $A\subset \mathbb{Z}$ such that the upper Banach density is non-zero, then $A$ contains arbitrarily long arithmetic progressions, this is called Szemerédi's ...