Questions on fractions, which are expressions (not values) of the form $\frac pq$.

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2
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1answer
36 views

Fraction simplification Rules

I am studying for GRE and One of the practice questions is a division. After converting my Mixed numeral I get 90/72 now I just have to simplify. What I understood is that you divide by Least common ...
2
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1answer
57 views

The elementary question on sign of Rational numbers

The image below can be used to show that $+\frac{8}{3}=\frac{+8}{3}$. Similarly we can show $-\frac{8}{3}=\frac{-8}{3}$. Now how can we show that $$-\dfrac{8}{3}=\dfrac{8}{-3}?$$
1
vote
1answer
25 views

Partial Fraction Decomposition - Multiple Answers-Question

Now I do understand how partial fraction decomposition works and why you can do it, but there is one case that I don´t understand. And that is, the following: $$\frac{A_{1}}{(x-x_{1})} + ...
1
vote
1answer
19 views

Auto loan calculator website widget

I was going to try my luck on StackOverflow, but I have a feeling my issue here is on order of operations. I'm using the loan calculation found here to build a loan calculator for a clients website. ...
1
vote
1answer
26 views

Is this fraction non-terminating?

I recently stumbled upon an observation: the fraction $\frac{x}{y}$ terminates if and only if $y$ only has prime factors $2$ and $5$. For example: $$\frac{1}{20} = \frac{1}{2\cdot2\cdot5} = 0.05$$ ...
11
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0answers
307 views

To how many decimals is $\sum_ {k=1}^\infty \frac{k}{\sqrt{k!}} = \frac{49850839\,\pi}{29567947}$ correct?

Consider: $$\sum_ {k=1}^\infty \frac{k}{\sqrt{k!}} = \frac{49850839\,\pi}{29567947}$$ This is, as far as I'm able to check with my software, correct to at least 167 decimals. If anyone has the ...
5
votes
0answers
61 views

Is there any elegant formalization of fractional numbers?

The question is just what is on the title, but I'll describe the context for completion: Natural numbers can be encoded quite elegantly on the Lambda Calculus as church numbers, that is, a function ...
3
votes
0answers
28 views

Origin/history of mixed number notation with misleading hyphen, e.g. 1-1/2

So there is a system of writing mixed numbers (that is, a combination of whole number and fraction, used instead of an “improper” fraction) used in cases where typing vulgar fractions (e.g. ½) ...
3
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0answers
68 views

All those unit fractions add to 1?

Consider $$S(n)=\{x \mid x=(a_1 ,a_2,a_3 \cdots a_n) \text{ where } \sum_{r=1}^{n}\frac{1}{a_r} =1 \}$$ Now let $|S(n)|$ denote the cardinaly (order) of set $S(n)$. Thus: $S(1)= \{(1)\} \implies ...
3
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0answers
691 views

Four candle problem: Using candles as timers

The candles each take one hour to burn completely. Cutting off bits of the candles is forbidden, but the candles are placed on a raft of fork handles so they may be burnt at both ends (e.g. to time ...
2
votes
0answers
37 views

Pull constant out of a summation of fractions

General problem $$ \sum_{i=1}^n \frac{a_i + x}{b_i + x} = 0 $$ Is it possible for solve for $x$? Some context I've hit a road block in my derivation... At this point, I need to pull the model ...
2
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0answers
46 views

How to do this ratios problem without algebra?

Dinesh had some fiction and nonfiction books. The number of fiction was $4/9$ of the total number of books. After he had donated $80$ fiction books and $25$ nonfiction books, there were $20\%$ as many ...
2
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0answers
112 views

Trigonometric functions of rational fractions of pi

Consider rational numbers $\frac{m}{n}$ and $\frac{m'}{n'}$, where $0<\frac{m}{n}, \frac{m'}{n'} <1$. Then $$\sin^2 (\tfrac{m}{n} \pi) = 2 \sin^2 (\tfrac{m'}{n'} \pi)$$ When $\frac{m}{n} = ...
1
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0answers
12 views

unique ringhomomorphism from the Field of fractions to another field

$R$ is a ring, $L$ a field and $K$ the fraction field constructed from $R$. For any injective ring homomorphism $f=R \rightarrow L$, there is a unique ring homomorphism $\tilde{f}:K \rightarrow L$ ...
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0answers
35 views

How much information is missing?

If we know the value of $\frac{(a-b)}{(c-d)}$, can we calculate the value of $\frac{(a-d)}{(c-b)}$ That is : Let $\frac{(a-b)}{(c-d)}=k$ , can we calculate $\frac{(a-d)}{(c-b)}$ in terms of $k$ And if ...
1
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0answers
42 views

Reverse engineer numerical results to fractions of remarkable numbers?

Numerical methods output decimal numbers that oftentimes result from the division of two (or more) numbers: $1.5708... = \frac{\pi}{2}$ $0.3679... = \frac{1}{e}$ $0.7071... = \frac{\sqrt2}{2}$ ...
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0answers
31 views

How to make continued fractions of any number?

I recently found an continued fraction representation of $\pi$, and I wondered how can I make an continued fraction that converges into a number? The MAIN question is: how do you make a continued ...
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0answers
41 views

quotient of two differentiable functions is differentiable

I have two functions $k(t)$ and $l(t)$ in a certain closed interval $[a,b]$ both functions are continuous and differentiable in the interval. In addition we have: Both functions are increasing with ...
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0answers
25 views

Stern-Brocot Tree and sum of coefficients of continued fraction

Suppose we are given a continued fraction $$\frac{p}{q}=a_{1}+\frac{1}{a_{2}+\frac{1}{a_{3}+\frac{1}{a_{4}+\cdots}}}$$ I am trying to find an expression, possibly asymptotic, for the sum of the ...
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0answers
41 views

Is this a mistake on my part or theirs?

I'm not sure if I'm the one making the mistake, or my math book. It looks like the negative sign completely disappeared. $$\frac{3x^2}{-\sqrt{18}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = ...
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0answers
103 views

three fractions between π and 22/7

three fractions between π and 22/7 π=355/113 =3.14159 22/7=3.1428 using a/b 355/113<22/7 then a+b/c+d 1) 355+22/113+7 =377/120~ 3.14166 2) 377+22/12+7 =399/127~3.14173 3) 399+22/127+7 ...
1
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0answers
178 views

How many elements are in the following set?

The set is $$\{ x \in Q:x^2 =64/25 \} $$ I thought the answer was $\{ \frac{8}{5}, -\frac{8}{5} \}$ but I am told there are in fact 4 distinct elements: $$\{ \frac{8}{5}, \frac{8}{-5}, \frac{-8}{5}, ...
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0answers
19 views

Extracting a function of a variable from an expression

I have this expression: $\frac{d+2wd}{2w+3wd-3d-w^2-1}$ Is there anyway I can write it just as a function of f(d)? [To me this looks like it is already a function of d, but I want to confirm if ...
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0answers
99 views

exponential integration with fractional powers

I am trying to solve the following integral $$\int_{-\infty}^a \frac{\beta_1 \beta_2}{y^2(c-y)^2} e^{-\beta_1/(c-y)} e^{-\beta_2/y} \, dy$$ where $a<0$, $c>0$, $\beta_1>0$, $\beta_2>0$ I ...
1
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0answers
27 views

MultiEquations (with fractions)

Can you please help me solve these equations i don't understand how to solve them with fractions. 1=n-2/15 151/20 =2a+1 3/4 -3/5 -2 1/5k = - 26/25
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0answers
64 views

Prove that there exists a subset with sum >=1 such that the remaining integer sum reduces by 1

let $ n \in \mathbb{N} $ and $ \frac{1}{w_1},\ldots, \frac{1}{w_n} $ for some (not necessarily distinct) $ w_1,\ldots,w_n \in \mathbb{N} $ and $ w_1,\ldots,w_n \ge 2 $ be given. Assume that $ ...
1
vote
0answers
31 views

Rational exponentiation?

Consider the following operation: $\left(\frac{a}{b}\right)^\frac{n}{m}$ where $a, n\in\mathbb{Z}$ and $b, m\in\mathbb{N^*}$. My question is: when the result is a rational number, how (formula or ...
1
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0answers
63 views

Does there exist an operation which partitions any fraction into the sum of the minimum number of unit fractions?

Motivation : I've been interested in finding an operation which partitions a fraction into unit fractions. The following is one of the operations which I've found. Let's start a rational number $q_0$ ...
1
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0answers
90 views

Turn a number $x$ into a fraction with a denominator with no more than $k$ digits

Is there a function for turning any number $x$ into a fraction with a denominator that has a maximum of $k$ digits? (I'm sure there is, since Excel has one built in, I just can't figure out what it ...
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0answers
43 views

Computability of division of large numbers

What is the largest computable mathematical division in terms of the number of digits that can be handled by a typical desktop computer using the best available big number libraries, assuming input is ...
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0answers
1k views

Contribution (weighted average) of change in rate over time

I'm trying to determine the weighted average impact of one customer's change in rate on the total change in effective rate. Let's say I have two customers and two time periods: ...
0
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0answers
22 views

Simplifying MATLAB fraction to make numerator equal to 1

I have a function which returns this fraction, which is not in the needed format. $$\frac{36893488147419103232*z^2}{36893488147419103232*z^2 - 672282507639892864*z + 6656262451880127}$$ I need it to ...
0
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0answers
15 views

Term for “Remainder in the Whole”

If I have a proper fraction I want to know what the name is for the amount remaining in the whole. So given $\frac1 3$ I want the name of the term $\frac 2 3$.
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0answers
40 views

How to find the common denominator with multiple variables

Find $\frac{zf^{'}(z)}{f(z)}$, where $-1 \leq \alpha \leq 0 $ and $0< v < 1$ Given: $f(z)= \frac{1}{\pi}(-\log (1-vz)+ \alpha \log(1-vz^{-1}))$ and $f^{'}(z)= \frac{1}{\pi}\left(\frac{v}{1-vz} ...
0
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0answers
28 views

simplifying fractions

I have the following equation: $$ \omega_m(s) = \frac{K_{\omega} \frac{K_m}{\tau_m s + 1}}{1 + K_\omega K_p \times \frac{K_m}{\tau_m s + 1}} V_r(s) $$ and I have been trying to bring in the following ...
0
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0answers
27 views

Approximate ratio with a small fraction so that numerator multiplied by denominator give enough rectangular area?

I would like to layout given number of objects (like plots) into rectangular area (like computer operating system window on screen). I would like to calculate the width and height of the window (in ...
0
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0answers
50 views

How to simplify an expression?

I have tried to simplify this expression for quite a long time now but I can't find how to do it. Can someone help me with it.
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0answers
33 views

Inverse Laplace Transform by Partial Fraction Expansion

I've been trying to solve this partial fraction for a Laplace transformation but I can't. Is there any way to solve it? $$\frac{(s-t)^2}{((s-t)^2-1)((s+1)^2+4)}$$ Could somebody help, I've been ...
0
votes
0answers
7 views

What are all of the possible fractional forms an offspring's genetic makeup?

I am wondering what fractions are considered to be "impossible" and "possible" for describing the genetic composition of an offspring. This is what I mean: Example: Say one parent is 1/2 Polish, ...
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0answers
146 views

Simplifying a ratio to lowest form: How to tell which number to divide by both quantities of the ratio to get to lowest form in just one step?

The question is to simplify the following ratio 72 is to 48 which can be written as 72 : 48. Now if I knew the table of 24, ...
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0answers
25 views

Variable value estimation for given product/fracture values

I have a data set (time series) with given values for certain fractions xy = x/y (where x,y are not constant over time) Thus, there are following fractions: AB = A/B CB = C/B AD = A/D CD = C/D AE = ...
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0answers
52 views

Euler Totient Function and new fraction numbers

Euler’s Totient Function can be used to calculate the count of new fraction numbers [below 1] as the divisor increases. New fractions identified are always either odd/odd, even/odd or odd/even. With ...
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0answers
50 views

Can This Expression Be Simplified? (Involves Square Roots)

I started with the expression $$ \frac{4mlt(1-\sqrt{1-\frac{v^2}{c^2}})c^2}{\sqrt{1-\frac{v^2}{c^2}}} $$ and have ended up at: $$ \frac{4mlt(c^2 - c \sqrt{c^2-v^2})}{\sqrt{1-\frac{v^2}{c^2}}} $$ ...
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23 views

Calculating enrichment

My question concerns how enriched something is as im trying to combine several lists of uneven group size and the answer is escaping me. So basically, I have 6 groups and I want to compare them with ...
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0answers
33 views

Long division for multipolynomial expression, little o notation

I have this expression: $$\mathrm{Exp}=\frac{d^3(-12a^4)+d^2(4a^4-16a^3)+d(4a^3-6a^2-a)}{d^3(-12a^4+12a^3)+d^2(4a^4-20a^3+16a^2)+d(4a^3-11a+7a)+(1-2a+a^2)}$$ Is there any way I can take the second ...
0
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0answers
52 views

Identity for fractional summation

I would like to know if there's an identity to represent the following summation $\sum_{i=0}^{n}\frac{x_i}{y_i}$ Where x and y are non integer values. The result of this is being calculated using ...
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0answers
223 views

How to find maximum and minimum of $\frac{x+y+z}{ax+by+cz}$ where $0\leq x \leq y \leq z \leq 1$ for given positive real numbers $a,b,c$

How do I find the maximum and minimum of $$\frac{x+y+z}{ax+by+cz}$$ where $0\leq x \leq y \leq z\leq 1$ for given positive real numbers $a,b,c$? I guess those are one of $\frac{3}{a+b+c}$ or ...
0
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0answers
146 views

If I have $\lfloor\frac{E}{K}\rfloor =\lfloor \frac{E}{K + m}\rfloor$, what is the upper limit of 'm' in terms of 'E' and 'k'

Given that E, K, m > 0, then is there a way to find out value of m in terms of E and ...
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0answers
28 views

Question on passing from rational to exponet

it's not a question itself, but I'd like to check if am I doing this passage from rational numbers to the exponent form right: From: $\sqrt{a\sqrt{a}}$ Evaluete to: $\sqrt{a*a^{\frac{1}{2}}}$ = ...
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0answers
113 views

Point me the primordial and intuitive concepts about this operations on physics

Warning: Layman question. Treat me as a 10 years old child The question was based on this page. I could write this on the physics channel, but despite the context, my problem is intrinsically ...