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
40 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 ...
8
votes
1answer
418 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 ...
1
vote
1answer
24 views

Can two integer divisions be unified above one whole fraction line?

Is there a way to combine two integer divisions (i.e. division with the result rounded down to the nearest integer) into a single division operation? What I mean is that, when working with with real ...
1
vote
1answer
43 views

The elementary question on sign of Rational numbers

The under picture show that $$+\dfrac{8}{3}=\dfrac{+8}{3}$$ Similarly we can show $-\dfrac{8}{3}=\dfrac{-8}{3}.$ Now How do can show that $$-\dfrac{8}{3}=\dfrac{8}{-3}?$$
1
vote
1answer
137 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
votes
1answer
28 views

Basic solving for fractions

Can someone help me with this? I am a beginner to physics and in a question i need no isolate a constant to solve for another one. A/B=C/D solve for D step by step please.
0
votes
1answer
25 views

Regarding +/- fractions: what are some mental tests you can apply to uncommon fraction denominators?

When adding and subtracting fractions: what if there is no uncommon factor (for example 4=2,2 and 6=2,3). Does that always mean to use the LCM? What if the LCM is too big or time consuming to ...
0
votes
1answer
36 views

Integration with partial fractions help please

I'm trying to work in my partial fractions chapter and some were easy but for whatever reason, I'm stuck now: ∫ (x-3) / (x2+2x+4)2 What I tried: since my denominator is of higher order and a ...
0
votes
1answer
19 views

Solving $\frac12 (3y+2)-\frac58=\frac34y$ for $y$ using LCD method

I am solving $$\frac12 (3y+2)-\frac58=\frac34y$$ for $y$ using LCD method. Can't figure out what I did wrong! The answer in the back of the book is $-1/2$. PS: In the first line that is a $1/2$ in ...
0
votes
1answer
26 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 ...
0
votes
1answer
143 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.
0
votes
1answer
65 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
votes
1answer
61 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
votes
1answer
22 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: $\frac{(1+\epsilon)n}{(2+\epsilon)p} \geq \lceil\frac{n}{2p}\rceil$
0
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1answer
44 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 $${ab\over {c \over d}}$$?
0
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1answer
39 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 ...
0
votes
1answer
64 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
41 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 ...
12
votes
0answers
87 views

Closed-form of infinite continued fraction involving factorials

Is there a closed form of this: $$ 1+\dfrac{1}{2!+\dfrac{1}{3!+\dfrac{1}{4!+\ldots}}} $$
9
votes
0answers
244 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
61 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
votes
0answers
95 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
560 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 ...
1
vote
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
1
vote
0answers
61 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
51 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
23 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
vote
0answers
56 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
vote
0answers
82 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
vote
0answers
34 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
666 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
votes
0answers
10 views

What can we say about the function $f(x)$ in this case?

Alright, I'm little bit confused about what's happening here to the function $f(x)$, i thought that the formula of $f(x)$, have nothing to do with its behavior or domain. there are two or many ...
0
votes
0answers
21 views

Freshman sum related question.

I want to prove the following: If $\frac{u_1}{d_1} > \frac{u_2}{d_2} > \frac{u_3}{d_3} > \frac{u_4}{d_4}$ and $d_1 + d_3 > d_2 + d_4$ and $u_1 > u_2$ then $u_1 + u_3 > u_2 + ...
0
votes
0answers
16 views

I need help with the method I should use for this question.

Of the fifith grade students, 15/20 went to the book fair. of the students who went to the book fair, 12/16 bought at least one book. what fraction of fifth grade students bought at least one book? ...
0
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0answers
15 views

Ideal from ring of fraction

Given $R$ is a commutative ring with $1$ and $D$ is multiplicatively closed containing $1$, I want to show that any ideal of $D^{-1}R$ is of the form $D^{-1}I$, where $I$ is an ideal in $R$. I have ...
0
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0answers
18 views

How to convert a Timestamp to fractional time (decimal)

If I have a timestamp 20114-4-1 13:24:10 what is the formula to convert this to a fractional time? I am trying to create a comparison between dates and I would like to do this using decimal. I have ...
0
votes
0answers
14 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 $x\in[0, 0.5]$, ...
0
votes
0answers
50 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 ...
0
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0answers
40 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 ...
0
votes
0answers
22 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 ...
0
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0answers
27 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
votes
0answers
33 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
votes
0answers
91 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
votes
0answers
40 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 ...
0
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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: $\sqrt{a*a^{\frac{1}{2}}}$ = ...
0
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0answers
382 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 ...
0
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0answers
96 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 ...
0
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0answers
170 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?
0
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0answers
113 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, ...