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

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2
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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
99 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
26 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?
0
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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
132 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
64 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
votes
1answer
122 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
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2answers
307 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
vote
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
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1answer
41 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
160 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
38 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
35 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
109 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
votes
1answer
21 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
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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 ...
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2answers
74 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
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1answer
60 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 ...
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2answers
48 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, $x/y = 234.234234234...$ ...
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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
184 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
28 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 ...
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1answer
52 views

How to count the number of integers with a fixed leading digit which are less than a given number?

Consider the numbers $1$ to $5000$. Numbers starting from the digit $2$ would be $2$, $20-29$, $200-299$, $2000-2999$; total would be $1111$. How can one derive a formula for the same? The first ...
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2answers
44 views

Extremely basic arithmetic simplification

For the life of me I can't understand my lecturer's working on this. I have $$\frac{1}{j\omega{L}}$$ Where $\omega=5000$ and $L=0.0001$ He somehow ended up with $$-2j$$ Whereas I simly got ...
-1
votes
1answer
76 views

How to solve a quintic congruence equation? [duplicate]

My textbook has this quadratic equation that I have to solve, any ideas how I could show that? $$15 | (21n^5+10n^3+14n),\;\forall n\in\mathbb{Z}$$
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0answers
34 views

How to find a relation between given numbers to get a given result?

I have f(2, 3, 6) = 5/6; f(4, 3, 12) = 17/6; f(3, 3, 9) = 11/6; f(2, 0, 2) = 2; How can I find the relation f for the given values?
4
votes
1answer
61 views

$f(x) = k^n$ for infinitely many integers $k$

Let $f(x)$ be a polynomial of $n^{th}$ degree with integer coefficients and let the leading coefficient be 1. Is it true that $f(x) = k^n$ for infinitely many integers $k$ and $x$ if and only if all ...
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2answers
78 views

How can I scale a value from -255 to 255 or -100 to 100 to a scale of 0-100?

For Brightness, I have a formula that takes in a value from -255 to 255 and contrast from -100 to 100. What if I wanted to use the same formula but I wanted to convert/adjust the scaling so that I ...
2
votes
1answer
66 views

Find these prime numbers $p, q$?

Let $p, q$ be prime numbers such that $p = 3p_1 + 2; q = 3q_1 + 2$; $p + q + 3$ and $3p + 3q + pq + 3$ are square numbers. Find $p, q$? P.S. I don't have any ideas about this problem :( Thanks ...
1
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1answer
24 views

re-arrange equation $L=2^{10(v-1)} v^2$

Is it possible to re-arrange this equation to make v the subject? $$L=v^2 . 2^{10(v-1)}$$ If so, what is the answer? If it helps (which by excluding zero it should)... $$0<v<1$$ I have tried ...
0
votes
1answer
17 views

How to form a 'master rank' from a list of other ranked items?

This is my first question across the StackExchange network, and it seems a lot easier than other questions I've seen on here (so I hope it doesn't bore you!), but I can't seem to come up with the ...
0
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1answer
39 views

Base three numbers and expanded form

I need help understanding this. Write each of the following base three numerals in expanded notation. $22_3$ $212_3$ $12110_3$
2
votes
1answer
21 views

order of operation

For the following expressions,why we can get the right answer even we do addition /subtraction first ? $3+4\times 11-5 = (3+4)\times(11-5) = 42$ $6+4\times7-4$ $5+2\times13-10$ $4+7\times16-6$ ...
5
votes
1answer
80 views

What's the digit sum of $4444^{4444}$? [duplicate]

For a natural number $n$ say that $d(n)$ is the sum of the digits of $n$ (in base $10$). Then what is the value of $$d(d(d(4444^{4444}))) ?$$ I have been trying with modular arithmetic, but can't do ...
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0answers
18 views

Tratchenberg Division Method

$ 743567 \div 256 =$? I get the following method: $ 7 4 3 5 6 7 \div 256 = 2$ __24, 7, 23, And since $23 \div 2 > 9$, I choose $23 \div 3$ to get: $ 7 4 3 5 6 7 \div 256 = 27$ __24, ...
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vote
3answers
75 views

How to put a fraction in simplest form, such as $140/255$?

Given the fraction $$\dfrac{140}{255}$$ How do I find a common factor so it can be easily simplified? I have already tried $2$, $3$ and $4$.
6
votes
4answers
430 views

Why is $-5^2=-25$?

If $-5^2$ is equal to $(-5)(-5)$, doesn't that mean the negatives should cancel each other out and become $25$? Why is this not the case?
2
votes
4answers
62 views

Why does the least common denominator work?

Take for instance the following problem. You have two beakers of the same height. One has tick marks that break it into thirds. The other has tick marks that separate it into fourths. The water levels ...
0
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0answers
49 views

Arithmetic, geometric and harmonic means: adding a constant to data values

If to each observation $x_i$ we add a constant $c$, then $\frac{\sum(x_i+c)}{n}=\bar{x}+c$ Can we find an expression for the new geometric mean as a function of the old geometric mean? What about the ...
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1answer
58 views

Arithmetic Progression question on finding the 25th term

In AP, sum of n terms is $\dfrac{3n^2 + 5n}{2}$. Find 25th term. My work : $S_n = \dfrac{n}{2}\left({3n + 5}\right)$ $2a + (n-1)d = \left({3n + 5}\right)$ $2a + 24d = 80$ $a + 12d = 40$ 13th ...
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1answer
49 views

Non standard vector addition [closed]

If addition was defined as $(a_1, a_2) + (b_1, b_2) = (a_1 + b_1, 0)$ over a a set $V$, the set of all ordered pairs of real numbers, does that special addition only apply to ordered pairs and vectors ...
1
vote
2answers
459 views

logic Accounting trick

Tom went to shop with a fake \$1000 for shopping.He bought items worth \$800 from shopkeeper A A.The shopkeeper had no change so he went to borrow from shopkeeper B. He came back and gave Tom his ...