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

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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
215 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
14 views

Ratio of sums vs sum of ratio

Is anyone aware of any general (or perhaps not so general) relationship (inequality for instance) relating $A(x,y)= \frac{\sum_z f(x,y,z)}{\sum_z g(y,z)}$ and $B(x,y)= ...
0
votes
1answer
25 views

Find original cost based on fractional purchase

How would I go about finding the original cost of bitcoin knowing that $20 purchased .0531401 of bitcoin? I would like to know what the cost of 1 bitcoin was at the time of purchase? ...
0
votes
1answer
41 views

How to do rational expressions

Never was much of a math student but I am brushing up on my arithmetic and algebra for college. I am using sample questions from Accuplacer and then using video lectures and practice on Khan ...
0
votes
1answer
22 views

Factors that Impact a Weighted Average the Most

I am trying to determine how to calculate the factors that have the most significant impact on a weighted average. For example, let's say I am reviewing the number of patients that responded to a ...
0
votes
1answer
89 views

Subtracting or Multiplying Fractions 3/4-1/2

This is the given scenario to help visualize the problem at hand. A bird feeder is filled with 3/4 of a full bag of seeds. The birds ate 1/2 of what was in the bird feeder. What fraction of a full ...
0
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1answer
35 views

Simplifying this expression, trigonometry

I have been having trouble understanding how $$6-6\cos\left(\frac{\pi}{4}\right) = 3\sqrt{2}.$$ My main problem is the conversion of the two separate terms into one.
0
votes
1answer
102 views

Converting a negative decimal with fractions to binary and hex

I am asking the question even though it has been answered before because I am looking at 3 different pages with 3 different answers right now. I am wondering how to convert a negative decimal with a ...
0
votes
1answer
50 views

Choosing suits of cards in a row

Three cards from a standard deck are dealt. What is the probability that the first is a heart, the second is a spade, and the third is another heart? I have figured out so far that you can use ...
0
votes
1answer
33 views

How to calculate $n$th term in terms of constants?

The expression is $$\large t_n=\frac{(x\times t_{n-1})^2}{((x-t_{n-1}\times y)^2+4\times x\times t_{n-1})\times t_{n-2}}$$ where $x$ and $y$ are constants. $t_0$ , $t_1$ , $t_2$ , $t_3$ and $t_4$ ...
0
votes
1answer
110 views

Equivalent forms of expressions with complex numbers

Which expressions are equivalent to $ {1\over{(9i+z)^4}} + {1\over{(9i-z)^4}}$ Select all that apply. $ {18i\over{(81−z)^8}}$ $ {−18i\over{(81+z)^8}}$ $ {18i\over{(81+z)^8}}$ $ ...
0
votes
1answer
62 views

Recursive formula for partial fraction decomposition of a specific kind of fractions

I need to make a partial fraction decomposition of the following fraction : $$ \frac{1}{(x-a)^2(x-b)^2(x-c)^2(x-d)^2(x-e)} $$ The problem is that Wolfram doesn't give any answer : ...
0
votes
1answer
27 views

Second Order Approximation for a Polynomial

if I have an expression: $L=\frac{12a^3d^3-4wa^3d^2+16a^2d^2-4wa^2d+6ad+1}{12a^3d^3-4wa^3d^2-4a^2wd+16a^2d^2+7ad-aw+1}$ what is the second order approximation in $\frac{d}{w}$? I know that ...
0
votes
1answer
25 views

Is there a value for $a$ other than a factor or a multiple of $c$ in $\frac{a}{b}=\frac{c}{d}$

Suppose $a,b,c,d$ to be whatever quantities whatsoever that satisfy the proportion $\frac{a}{b}=\frac{c}{d}$. Is there a value for $a$ other than a factor or a multiple of $c$. Or, is there a value ...
10
votes
0answers
288 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
56 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
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
votes
0answers
672 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
43 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
votes
0answers
104 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
37 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}} = ...
1
vote
0answers
98 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
150 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}, ...
1
vote
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 ...
1
vote
0answers
86 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
vote
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
vote
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
vote
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 ...
1
vote
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 ...
1
vote
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
votes
0answers
48 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.
0
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0answers
25 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
15 views

Sum of finite number of terms of the series $\sum\limits_{L=2}^{L_{max}}\frac{1}{e^{i \phi / L} -1}$

Good day everyone. Are there any chances to get a compact formula for the following sum of finite number of terms? $$\sum\limits_{L=2}^{N} \dfrac{1}{e^{ \frac{i \varphi}{L}} -1}$$ N and $\varphi$ ...
0
votes
0answers
6 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, ...
0
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0answers
72 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, ...
0
votes
0answers
24 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 = ...
0
votes
0answers
46 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 ...
0
votes
0answers
48 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: $$ \frac{4mlt(c^2 - c \sqrt{c^2-v^2})}{\sqrt{1-\frac{v^2}{c^2}}} $$ ...
0
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0answers
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 ...
0
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0answers
30 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
votes
0answers
53 views

How to calculate the Integer portion of a fraction using only +, -, $\div$ and *?

I made something in excel that calculates the days left until a given date, and from that how many weeks were left. I had it so that 9 days displayed as 1.2 using this formula: ...
0
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0answers
21 views

GCD and fraction problem

If x/y = 1/a + 1/b + 1/c and GCD of a , b and c is 9 then find a) minimum of x and y which do not cause x/y repeating decimal b) the best of x and y that cause x/y nearly to 3/10 many ...
0
votes
0answers
49 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
votes
0answers
113 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
votes
0answers
144 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
25 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
votes
0answers
112 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 ...