Questions on fractions, numbers of the form $p/q$ where $p$ and $q$ are integers, and $q$ is not zero.

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3answers
54 views

Basic algebra, isolating the variable

So I have the equation $$\tan30=\frac{4.9t-\frac{10}{t}}{\frac{8.77}{t}}$$ And I want to find t, but my algebra has failed me. This is my working so far. ...
2
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2answers
35 views

How to identify whether a fractional part of a number contains more that 2 digits.

EX. I want to accept numbers which have maximum of 2 digits after decimal points. i, e, 10.23 should be allowed and 10.233 should not be allowed. What mathematical operations can be done to ...
0
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2answers
27 views

Fractional Power Interpretation

I have a following query in my mind. It has been in my mind since i was a kid. I know that 2^3 means that multiply 2 three times,3^-2 means multiply (1/3) two times.What does 2^(0.22) means. multiply ...
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2answers
50 views

Fraction Cross Multiply

Students first learning about fractions are often taught to "cross-multiply" when dealing with fraction with non-like denominators, however, in Mathematica, with the function ...
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2answers
22 views

Help Reducing simple fraction

This has got to be easy, but for some reason I just don't see it, probably because it's late. Solution key to a quiz we took online says that: $\frac{A^2 + A + AB}{(A + B)(A + B + 1)}$ can get ...
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2answers
86 views

Finding modulus of two numbers

Let $\frac xy$ be a fraction in reduced form, $y\geq x$, and $m=y \mod x$. How do you find $x$ mod $m$?
8
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1answer
382 views

IMO 1979 problem

The question is $$\text{If }\, p, \ q\in \mathbb{N}, \;1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}=\frac{p}{q}.\qquad \text{Prove that } 1979\mid p.$$ So my solution went like ...
6
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1answer
130 views

How to best understand Euclid's definition of equal ratios? How does it relate to Dedekind cuts?

This is something I've been wondering about. When I think of "ratios" $x/y$ and $z/w$ as being "equal", with $x$, $y$, $z$, and $w$ being real numbers, this means the results of dividing the real ...
1
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1answer
115 views

If I add a constant $c$ to each fraction's numerator and denominator in a sequence of fractions, how is the sequence affected?

Given a sorted ascending sequence of fractions, if I add a constant $c$ to each fraction's numerator and denominator, how is the sequence affected? For example, if I have a sequence in ascending ...
0
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1answer
24 views

Solving function in difference quotien equation

I have the problem Find the difference quotient $\frac{f(2 + h) - f(2)}{h}$ for $f(x) = \frac{1}{x^2}$. The answer they gave is $\frac{-(4 + h)}{4(2 + h)^2}$ So far I've done: $$\frac{[1/(2 + h)^2 ...
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1answer
132 views

Deradicalization of denominators

Task: Develop a fraction equivalent to $$ 1\over{\sum\limits_{i=0}^{n-1}c_in^{i/n}} $$ in which the denominator is rational.
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1answer
30 views

Rearranging algebraic formula when subject is on both sides

I have run into some difficulty with a question on making a variable the subject of an equation where the variable is on both sides. I am really struggling to find a method for making "a" the ...
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 ...
0
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1answer
21 views

Comparing Fractions that contain epsilon

Given $\epsilon$ a constant s.t. $0<\epsilon<1$, and $n,p$ positive integers, $n >= 2p$, is the following true: $\frac{(1+\epsilon)n}{(2+\epsilon)p} \geq \lceil\frac{n}{2p}\rceil$
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1answer
35 views

What's the difference between “continued fractions” and “compound fractions”?

What should we call a fraction which includes another fraction in its numerator or denominator, like $${ab\over {c \over d}}$$?
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1answer
38 views

Reducing an inquality with fractions

can you help me reduce the following inequality (i need to get a relation between x and y -- express x in terms of y) $\frac{n}{2x} < \frac{n}{(4+\epsilon)y}+1$ I would like to show somehow that ...
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1answer
45 views

formula to apportion cost of transport among three people in a liftshare

I share lifts with Sed and Awk to work every day. We tally journeys owed on a spreadsheet. A week might look like this: ...
0
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1answer
40 views

How to work out these fractions?

$\dfrac{-x^4 + 4x^2 + 6}{x}$ $\dfrac{7x^8 - 5x^5 + 9x^3 + x^2}{x}$ I have no idea how to do this. I was first thinking of doing $-x$ or collecting up the $x's$ but I'm not sure as I haven't dealt ...
10
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0answers
221 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 ...
2
votes
0answers
60 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 ...
2
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0answers
93 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} = ...
2
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0answers
521 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 ...
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0answers
21 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
60 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
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0answers
48 views

Name of rational numbers of the form $p/q$ with $p,q$ prime

For the life of me, I cannot think of whether there is a name for fractions of the form $\frac{p}{q}$, where $p,q$ are both prime. Fractions such as $\frac{4}{5}$ are sometimes said to be in "reduced ...
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0answers
21 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
53 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
76 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
33 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
570 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: ...
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0answers
29 views

Comparing Fractional Numbers

Does a formula exist for comparing two fractional numbers, without resolving to using anything other than integers and fractions? (Thus not real numbers). In other words: given $\dfrac{a}{b}$ and ...
0
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0answers
13 views

proving a fraction with 2 parameters to be small

Hi I have a fraction as below $$\frac{1.623x^4+0.434x^4\sum_iy_iz_i^2+(0.014x^2+0.0027)\sum_iy_iz_i^4}{1.645x^2+(0.083-0.329x^2+0.435x^4)\sum_iy_iz_i^2+0.014\sum_iy_iz_i^4}$$ where $x\in[0, 0.5]$, ...
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0answers
39 views

L'Hospital's rule for higher derivatives

Let $u,v \in C^\infty(\mathbb{R})$, where $u(0) = 0$ and $v(0) = 0$ and $v'(0) \not= 0$. Then, one can define a function $f \in C^\infty(\mathbb{R}\setminus\{0\})$ by $f := u/v$. L'Hospital allows ...
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0answers
21 views

Adding a natural number to a normalized fraction

I am currently writing yet another rational number class where the fraction should always be normalized. When adding a natural number to a normalized fraction, it possible to get a non-normalized ...
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0answers
14 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
23 views

Calculating an average value based on separate subsamples from the same sample

I have a question coming from biological research. We routinely have to quantify on microscopic images certain values characteristic of a piece of tissue – for example the percentage of cells that are ...
0
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0answers
31 views

How can I simplify the following expression with exponents.

$$\frac{(t+1)^{\frac{1}{3}}-\frac{1}{3}t(t^2+1)^{-\frac{2}{3}}}{(t^2+1)^{-\frac{2}{3}}}$$ I found this problem from a book and its answer is $\frac{2t+3}{3(t+1)^{\frac{4}{3}}}$(as in the book's ...
0
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0answers
22 views

How to find maximum and minimum of (x+y+z)/(ax+by+cz) where 0≤x≤y≤z≤1 for given positive real numbers a,b,c

How to find maximum and minimum of $$\frac{x+y+z}{ax+by+cz}$$ where 0≤x≤y≤z≤1 for given positive real numbers a,b,c? I guess those are one of $\frac{3}{a+b+c}$ or $\frac{2}{b+c}$ or $\frac{1}{c}$, ...
0
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0answers
73 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 ...
0
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0answers
21 views

I need to find $n$ that $\frac{1}{(n+1) \cdot \ln(n+1)} <10^{-4}$

$\frac{1}{(n+1) \cdot \ln(n+1)} <10^{-4}$ So what I did is this: $(n+1)\ln(n+1) > 1000 \Rightarrow n>190$ When I put it back I see that $\frac{1}{192 \cdot ln(192)} \not < 10^{-4}$. ...
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0answers
20 views

Simplified Form for a Series

Is there a simplified form for the following sum: $Z = \frac{r_1}{c}+\frac{r_2}{c+r_1}+\frac{r_3}{c+r_1+r_2}+...+\frac{r_n}{c+r_1+...+r_{n-1}}$ I need to express it if possible in a way that I can ...
0
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0answers
38 views

Transformation of fractions

I have a problem with a certain transformation of a fraction. This is part of a reudctio ad absurdum to show that there are infinit prim numbers. $\mathrm{P} = \prod_{i=1}^{n} p_i$ as the amount of ...
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0answers
21 views

Calculating summary with variable multiplication factor

I have a formula of thermal conductance heat transfer rate. Here it is: $$ Q = \lambda{S (T_1 - T_2) \over L} \Delta t $$ For my calculations I have got some constant values available $$ Q = 0.58{1 ...
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0answers
12 views

If $d/dx_t ({\dot y}_t/y_t) > 0$ and $dy_t/dx_t < 0$ what can I then say about the sign of $d{\dot y}_t/dx_t$?

Assume that the rate of change in $y_t$ over time is ${{{{\dot y}_t}} \over {{y_t}}} = {x_t}$, where $x_t >0$. The derivative of this expression with respect to $x_t$ will be positive (well, it ...
0
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0answers
130 views

Rounding algorithm

I'm working on making some economic calculations prettier to eye, and that involves a lot of rounding, which caused me some problems. I'm aware that result of rounding depends on chosen method, but ...
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0answers
19 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
339 views

How to get approximate fraction numbers from imaginary numbers with MatLab

I'm not sure how to title this problem actually, but I have a clumsy PHP code that I've used to get approximate fraction numbers for imaginary numbers like pi, phi, square root of 2, 3 and so on. I'd ...
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0answers
84 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: ...
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0answers
164 views

Partial fraction expansion when the degree of the numerator is unknown

Hope it's not too stupid: is there any general approach to partial fraction expansion when the degrees of polynomials in the numerator are unknown?
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0answers
108 views

Fractions for use of determining ratios

When you have two processes and you want to compare the results of them, is it: (original process)/(new process) or (new process)/(old process)? There isn't a particular context for this question, ...