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

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3answers
61 views

Given a rational, how to find the integers whose quotient it is?

I haven't found an answer to this anywhere. Excluding brute force, given a rational $q$ in its decimal form ($1.47$, for example), is there a good algorithm to find integers $m$ and $n$ such that ...
1
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1answer
31 views

how many questions did the answer in each round?

yolanda went on a quiz show. the question in the first round were worth 6 points. the questions in second round were worth 10 points. yolanda answered a total of 5 questions and earned 34 points. how ...
2
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2answers
92 views

Calculate f(n+1)-f(n-1) based on f(n)???

Being: $$f(n) = \left(\frac{5+3\sqrt5}{10}\right)\cdot\left(\frac{1+\sqrt5}{2}\right)^n+\left(\frac{5-3\sqrt5}{10}\right)\cdot\left(\frac{1-\sqrt5}{2}\right)^n$$ Calculate: $$f(n+1)-f(n-1)\\ ...
7
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7answers
1k views

Is it possible to calculate the arithmetic mean from the geometric mean?

An estimation method would be acceptable, doesn't need to be exact (but obviously that would be preferable). I have a dataset of geometric means, need to calculate the arithmetic mean.
2
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3answers
34 views

I need help with an average question

My brother and I are going on vacation. We need to rent a car. We will rent the car for $10$ days. However, I will only be on the vacation for $5$ days. My brother will be on vacation for the full ...
2
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1answer
61 views

maths question for level 2 maths essential skills.

In Seville, Sue sees some wall tiles that she would like for her kitchen. The big tile measures $20 \text{ cm}\times 20 \text{ cm}$. The small tile measures $10 \text{ cm}\times 10 \text{ cm}$. How ...
1
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1answer
39 views

What's a more optimal native C-language algorithm to set bit $k$? [closed]

Let $n$ be an integer (for example an unsigned int which is usually 32- or 64-bits), let the number of bits be $|n|$. Let $0 \leq k \lt|n|$. I usually do: ...
0
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2answers
96 views

Prove that if $n^2 - 1$ is divisible by a prime number $p$ such that $n - 1$ is not divisible by $p$, then $n + 1$ is also divisible by $p$.

If this proposition is false, please give at least $3$ counter-examples, and try to modify the proposition so that it becomes true. If the proposition is true, please try to prove this even more ...
9
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4answers
467 views

Calculate the product

$$\left( 1 + \frac{1}{2} \right) \left( 1 + \frac{1}{3} \right) \left( 1 + \frac{1}{4} \right) ... \left( 1 + \frac{1}{99} \right) $$ Of course I could do it factor for factor but there has got to be ...
0
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1answer
14 views

Show that if $a=bq+r $ and $d|a$ and $d |b $, then $d|a-bq $

Show that if $a=bq+r $ and $d|a$ and $d |b $, then $d|a-bq $ That is show that if $d $ divides $a $ and $a=bq+r $ then $d $ divides $a-bq $. Here $d |a $ means "d divides a", that is $ a=dk $ where ...
1
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1answer
96 views

A question using arithmetic progression.

Water fills a tank at a rate of 150 litres during the 1st hour, 350 litres during the 2nd hour, 550 litres during the third hour and so on. Find the number of hours necessary to fill a rectangular ...
3
votes
2answers
127 views

I want to learn math from ground-up, basic to advanced, beginner to expert

I want to learn math. I've learned math long time ago, but i hardly remember anything. I really want to relearn but have no idea where to begin. I want to learn math by reading through good books, ...
0
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7answers
148 views

How to derive $\;a^3 + b^3 = (a + b)(a^2 - ab + b^2)\;?$

I'm studying in 8th grade in India. I saw the question in my FIITJEE textbook, but it was not shown how to derive it. Please help. My mid phase examinations are coming up.
1
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1answer
30 views

How to express the relationship between two numbers by dividing?

I recently edited an image to bring it from 194px high to 140px high I'd like to describe how much shorter the image is (or, how different the two are in general) There are two ways to compare the ...
3
votes
0answers
30 views

question in product

can any expert just check my solution You bought a car for $\$2500$ down and made payments of $\$299.50$ each month for $36$ months. (a) Find the amount of the payments over the $36$ months. (b) Find ...
0
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2answers
45 views

B is 40% of A , C is 10% of B. How many percent of is C of G? [closed]

Would you please be so kind as to delete. Similar (exact copies) are readily available all over the internet. Thank you.
9
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2answers
270 views

Multiplying using reciprocal, addition and subtraction

Let $a,b\in\mathbb{R}$. How can we compute $a\times b$ using only the following operations only (with any reals) : $\frac{1}{*}$ (inverse) $*+*$ (addition) $*-*$ (subtraction) ?
0
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0answers
12 views

How can I know the number of steps required to get to a single digit number when adding the digit of a number repeatedly?

For example, 82934 would give 2 because 82934 -> (8+2+9+3+4)=26 -> (2+6)=8 I want to know the number of steps depending on the number. If it's not possible, I would like an approximation of it. If ...
4
votes
3answers
1k views

Can you give me a visual representation on 1/6 of 4/5 to get 4/30?

I'm trying to understand fractions more by using a visual representation, and I having a hard time making a visual representation of the 1/6 of 4/5 and getting a visual understandable representation ...
3
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1answer
59 views

Alphametics Question

In the figure below, each distinct letter represents a unique digit such that the arithmetic sum holds. If the letter L represents 9, what is the digit represented by the letter T? ...
0
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1answer
46 views

Why is the word “of” equivalent to multiplying in fraction word problems?

I know this is a very easy problem, but I'm having a hard time getting my head around this concept, consider this example from a book. *Jerry bought a pie and ate 1⁄5 of it. Then his wife Doreen ate ...
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2answers
39 views

How to calculate value of x in (1875+y):(x+y)=165

I need to solve this equation but every time I get a different result.Ive tried "find out $x$" calculators online but they fail with "error" or "invalid [...]". The equation is $(1875+y):(x+y)=165$ ...
0
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1answer
23 views

An implication between two statements concerning integers

Does "Every non-empty bounded below set of integers has a smallest element" $\implies$ "If $m,n$ are integers with $m>n$ , then $m-n\ge1$" ? If not then what additional assumption is needed ...
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0answers
38 views

Terminology: Name for general, non-differential equations over $\mathbb{R}^n$

Let $x \in \mathbb{R}^n$ be a variable, and $f_1, \ldots , f_n : \mathbb{R}^n \mapsto \mathbb{R}$ be a sequence of functions, each having a closed form expression. Assume that we want to solve the ...
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1answer
23 views

How to add and subtract functions? [closed]

Given: $(f+g)(x)= 4x+5$ and $(f-g)(x)= -6x+3$ find $f(x)$ and $g(x)$ algebraically. Please help!
2
votes
1answer
76 views

How to solve 2 ÷ 2 ÷ 2 ? ${}{}{}{}$

$$2 ÷ 2 ÷ 2 = (2 ÷ 2) ÷ 2 \ \ \text{OR}\ \ 2 ÷ (2 ÷ 2) ?$$ Is there any standard rule which is world wide accepted for solving this type of expressions? If I process the expression from left to ...
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1answer
40 views

Getting rid of numerator in a fraction equation

Im doing Okun's law for economics. Which is $\dfrac{Y^*-357665}{Y^*} = 1.5(5.1-4.75)$ how do I find $Y^*$?
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votes
3answers
112 views

Prove that if $n+1$ is divisible by $m$ then $n^2-1$ is also divisible by $m$. [closed]

Prove that if $n+1$ is divisible by $m$ then $n^2-1$ is also divisible by $m$. And prove that if $n^2-1$ is divisible by $m$ then $n+1$ is also divisible by $m$.
6
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4answers
137 views

Prove that $2002^{2001}$ and $2002^{2001}+2^{2001}$ have the same number of digits.

I have an arithmetic exercise as follows: Prove that $2002^{2001}$ and $2002^{2001}+2^{2001}$ have a same number of digits. It seems easy but I don't know how to do. I can do it if $2002$ is replaced ...
2
votes
2answers
35 views

Timeline if 0.5 millimetres= 1.5 years how many millimetres would equal 1 year

Hi I am working on a timeline and know that 0.5 millimetres equals 1.5 years how many millimetres would equal a year thanks.
0
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1answer
31 views

Why is $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$?

I came across this statement, but can't see why it holds: $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$ I'm sure it's something simple, but I don't have a great deal of mathematical experience. I ...
0
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2answers
17 views

Know total amount. Must divide in two parts so that one part is 10% from another part.

I know total amount. Must divide the total amount in two parts. Smaller part (amount) is 10% of bigger part (amount) so that smaller part plus bigger part is total amount. So total is 17091.54 ...
0
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1answer
14 views

proof of uniqueness (hint) $f(m,n)=n+1$ only if $n \ge m$

I'm a bit confused about this proof. let define on $\Bbb N$ a binary fucntion $f$ that satisfies (1) $f(m,n)=n+1$ if $n \ge m$ and (2) $f$ is commutative if I write the values of $f$ in a 2x2 ...
0
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2answers
71 views

Logic and mathematical variables as objects

I am currently working on describing a predicate logic for which the objects are mathematical variables. Thus I can say stuff like: $\forall x: R(x) \implies \text{operator}(x)=1$ Here $x$ is a ...
0
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3answers
79 views

How do I add multiple binary numbers without using a partial sum?

I know how to add binary numbers but what I normally do is add the first 2 binary numbers and then add the 3rd one to their sum. It is really slow. $$ 111_2 + 111_2 + 111_2 + 111_2 $$ Here is ...
5
votes
1answer
59 views

Halmos on Definability and Luzin on Division by 0

For a successful introduction of a new symbol (e.g. '$\emptyset$') into a mathematical discourse it is necessary and sufficient that the symbol refer to something (e.g. Existence + Specification in ...
0
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1answer
27 views

Confused by step in an inductive proof of arithmetical progression

In the book "What is Mathematics?" there is a section that provides an inductive proof of the arithmetic progression. Part of this proof is: $\frac{r(r+1)+2(r+1)}{2}=\frac{(r+1)(r+2)}{2}$ I don't ...
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1answer
38 views

Why does $ \frac {a}{b}$ of $c$ means $ \frac {a}{b} \cdot c$ [closed]

Why does it multiply when the preposition "of" appears?
0
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0answers
47 views

binomial coefficient as perfect powers

Bonjour to everyone. Let m be an integer. For: $ r \geq 2 \quad and \quad 4 \leq k \leq n-4, $ we know, as a consequence of the Sylvester theorem, that: $ {n \choose k}=m^r \quad (n \geq 2k) $ has ...
0
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1answer
45 views

Is there a way to simplify this equation?

$$ A = \left( 4000 \left( 1+\frac{x}{y} \right) \right)^4 \cdot \left( 1 + \frac{x+0.002}{y} \right)^4 \cdot \left(1+\frac{x+0.002+0.002}{y} \right)^4 $$
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0answers
30 views

Binary division algorithm

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1answer
37 views

Prove that there are an infinity of prime $ak+b$, $a$ and $b$ coprimes

We have to integers $a,b$. I need to show that if $a$ and $b$ are coprimes then the set of prime numbers of kind $ak+b$ is infinite. How could I show it ? I know how to do that for $4k+3$ or $4k+1$, ...
0
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2answers
39 views

How do you get from this to this formula?

I have the formula : $$3×4^{n-1}×1×\left({1\over 3}\right)^{n-1}$$ And I would like to know how to get to this one (which is equal) : $$3× \left({4\over 3}\right)^{n-1}$$ How can I do that ?
0
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1answer
61 views

What is the smallest division without a fraction?

Is there a mathematical formula to calculate the smallest division of a fraction with both numbers not being a division? I'm not a mathematician (and not English), so I hope I use the correct terms. ...
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2answers
29 views

arithmetic series problem

if $S(n)$ is a function representing the sum of an arithmetic series, determine the series with $S(13) = 507$ and $S(25) = 2025$ oh and the answer is supposed to be $$S(n) = \frac{7}{2}n^2 - ...
6
votes
1answer
402 views

What is a simple way of computing the following fraction?

Compute the value of the expression: $$\frac{(10^4+324)(22^4+324)(34^4+324)(46^4+324)(58^4+324)}{(4^4+324)(16^4+324)(28^4+324)(40^4+324)(52^4+324)}$$
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1answer
17 views

How to determine operantors between given numbers to get a given result

In a children's math book I found the following example: There are $2$ numbers: $242, 961$. You can use these numbers as many times as you want, and you can use any arithmetical operator ...
1
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1answer
25 views

Normalisation of $\mathbb{Z}$ in $\mathbb{Q}(\sqrt{d})$ is UFD…

We know that the normalisation of $\mathbb{Z}$ in $\mathbb{Q}(\sqrt{d})$ where $d\in \mathbb{Z}$ is $$O=\mathbb{Z}[\beta], \text{$\beta=\sqrt{d}$ if $d\equiv2,3 \pmod 4$}; \ \frac{1+\sqrt{d}}{2} ...
15
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3answers
400 views

About an inequality including arithmetic mean, geometric mean and harmonic mean

For any $n$ positive real numbers $a_i\ (i=1,2,\cdots,n)$, let us define $A,G,H$ as $$A=\frac{\sum_{i=1}^{n}a_i}{n},\ G=\sqrt[n]{\prod_{i=1}^{n}a_i},\ H=\frac{n}{\sum_{i=1}^{n}\frac{1}{a_i}}.$$ ...
1
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2answers
52 views

Word for the number being added-to OR subtracted-from another number

I first asked this on english.stackexchange.com, but this site would probably be a better-suited to answer it: In division, we have a dividend and a divisor. According to this page, we also ...