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

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2
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2answers
29 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
26 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
35 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
21 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
59 views

Algebraic Manipulation question - trying to get alternate form

I'm currently working on algebraic manipulation, changing algebraic fractions into a chosen alternate form but I've hit a brick wall. I'm trying to get: $$\frac{2(3^x - 2^x)}{3^{x+1} - 2^{x+1}}$$ ...
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2answers
68 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 $m$?
6
votes
1answer
109 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 ...
2
votes
1answer
67 views

Simultaneous rational approximation of real numbers in (0,1)

I have a simple question the rational approximation of real vectors. Dirichlet's simultaneous approximation theorem states: Given any $d$ real numbers $\alpha_1,\ldots,\alpha_d$ and a natural ...
1
vote
1answer
88 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
25 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
39 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 ...
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1answer
35 views

Solving fractions

If two plates are cut from a piece of steel that has an overall length of 17 1/2 in. the plates are 8 1/8 in. and 7 11/16 in. long. How much material remains from the original piece if each saw cut ...
10
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0answers
193 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 ...
6
votes
0answers
249 views

IMO 1979 problem

The question is $$If\, p,q\in \mathbb{N}, \;1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}=\frac{p}{q}.\qquad Prove \,that\, 1979|p.$$ So my solution went like this: ...
2
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0answers
88 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
vote
0answers
58 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
43 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
19 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
48 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
73 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 ...
1
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0answers
31 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 ...
1
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0answers
479 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
498 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 ...
0
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0answers
11 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
16 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
23 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 ...
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0answers
21 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
62 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
65 views

difficult inequality to prove

I need help proving this inequality is correct for a homework assignment: $$\displaystyle \left(\frac{13}{4}\right)^{n} \leq ...
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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
18 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
28 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
20 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
108 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
18 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
324 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
73 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
160 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
103 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, ...
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0answers
10 views

$L_\alpha$ is a $G_ \delta$ subset of $C[0,1]$?

If $\alpha$ is a positive number, then $\alpha-m(E)$ denotes the measure of $E$ with respect to $h(x)=x^\alpha$. For each $\alpha>1$, let $L_\alpha=\{f\in C[0,1]|\alpha-m(f)=0\}$. whether ...