# Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

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### Integer solutions to fraction equation

I am having trouble finding all solutions (or at least proving I have all the solutions already). The equation is $$\frac{1}{a}+\frac{1}{b}+\frac{2}{c}=1$$ *a,b,c are positive I tried to base it on ...
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### On common repeating expansions of coprime pair?

Let $a,b>0$ be coprime and not divisible by $2$ or $5$. Now $$\frac1a=0.00\dots00r_100\dots00r_100\dots00r_1\dots$$ $$\frac1b=0.00\dots00r_200\dots00r_200\dots00r_2\dots$$ where $r_1$ and $r_2$ ...
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### How to expand a fraction to 100 as the denominator.

I'm working with some code that calculates point values based on computer hardware. On one computer as an example, the computer ends up with 29 possible points. Now lets say that I run the same code ...
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### The numerators in partial fraction decomposition involving repeated factors

So I'm confused about the partial fraction decomposition of fractions that involved repeated factors in the denominator. From what I've been taught, when you are breaking your fraction into partial ...
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### Estimate the value as a whole number or as a mixed numeral where the fractional part is 1/2

I got into a math problem, where it asked the following question: I’m not asking for the answer, but I want to know what it means by: “where the fractional part is 1/2”
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### Can you solve for the value of x?

I don't remember where I saw this equation but it was difficult to solve. The equation was: $$\frac{\tan(x)}{1+\sin(x)} = q$$ where $q$ is a constant. When I started to solve this equation it made ...
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### How do I interpret [blank] per unit [blank] per unit [blank]?

For example, if I have the energy per unit time per unit area, do I formally interpret that as: $$\frac{E}{(dt)(dA)}$$ and intuitively interpret it as how much energy is in an infinitesimal area in ...
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I need to prepare a number of questions for my homework on numbers and fractions. Not being a native English speaker, I'm stuck on constructing a question. Everyday a student solves questions in the ...
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### double series and integral resulting in an indetermined answer

I have the following: $$P = \sum_{j=1}^{6} \sum_{k=1}^{6} A(k,j) \int_0^h e^{(\alpha^{(k)} -\overline\alpha^{(j)})x} dx$$ Where A is a constant that depends on $j$ and $k$. Taking the integral ...
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### Under which conditions maximizing a ratio of functions is equivalent to minimizing its reciprocal?

Assume two non-linear functions, $f(x)$, $g(x)$ respectively, both positive and monotone non-decreasing, $f(x)$ is concave, $g(x)$ is convex. I am trying to maximize their ratio, $\frac{f(x)}{g(x)}$, ...
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### How to split the denominator of a fraction into another fraction plus the rest of the denominator?

I know the title is a badly formulated, but I have an example, that should show my Problem better: ${y^2\over(2c+2)} = {y^2\over 2c} * x$ Through Brute-Force I found out that x should for example ...
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### Euler's Continued Fraction Theorem for fractions

How can I use Euler's Continued Fraction Theorem to find the continued fraction expansion for a (ordinary, finite) fraction via its (terminating or recurring) decimal expansion, rather than via the ...
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I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this Now as I'm trying to find further exercices, I keep stumbling upon fraction-...
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When we perform a Partial Fraction Decomposition and one of the solutions of the denominator is a multiple solution (let's say quadratic), we write: $$\frac{A_{1}}{(x-x_{i})} + \frac{A_{2}}{(x-x_{i})^... 0answers 147 views ### Simplifying MATLAB fraction to make numerator equal to 1 I have a function which returns this fraction, which is not in the needed format.$$\frac{36893488147419103232*z^2}{36893488147419103232*z^2 - 672282507639892864*z + 6656262451880127}$$I need it to ... 0answers 22 views ### Term for “Remainder in the Whole” If I have a proper fraction I want to know what the name is for the amount remaining in the whole. So given \frac1 3 I want the name of the term \frac 2 3. 0answers 84 views ### How to find the common denominator with multiple variables Find \frac{zf^{'}(z)}{f(z)}, where -1 \leq \alpha \leq 0  and 0< v < 1 Given: f(z)= \frac{1}{\pi}(-\log (1-vz)+ \alpha \log(1-vz^{-1})) and f^{'}(z)= \frac{1}{\pi}\left(\frac{v}{1-vz} ... 0answers 147 views ### Approximate ratio with a small fraction so that numerator multiplied by denominator give enough rectangular area? I would like to layout given number of objects (like plots) into rectangular area (like computer operating system window on screen). I would like to calculate the width and height of the window (in ... 2answers 742 views ### How to cancel out a negative in a denominator? The question was to make y the subject in x=5-3y (i.e. solve for y). My working was this:$$\begin{align*} x&=5-3y \\ -3y&=x-5 \\ y&=(x-5)/(-3) \end{align*}$$But this was ... 1answer 40 views ### Simplifying this expression, trigonometry I have been having trouble understanding how$$6-6\cos\left(\frac{\pi}{4}\right) = 3\sqrt{2}.$$My main problem is the conversion of the two separate terms into one. 1answer 109 views ### Fractions and decimals Ten companies sponsored a tournament and decided to give M rupees collectively.Two companies dropped and remaing agreed on paying their share equally.What was the increase in share of each company? ... 1answer 287 views ### Choosing suits of cards in a row Three cards from a standard deck are dealt. What is the probability that the first is a heart, the second is a spade, and the third is another heart? I have figured out so far that you can use ... 1answer 39 views ### How to calculate nth term in terms of constants? The expression is$$\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}}$$where x and y are constants. t_0 , t_1 , t_2 , t_3 and t_4 ... 0answers 59 views ### Can This Expression Be Simplified? (Involves Square Roots) I started with the expression$$ \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}}} $$... 0answers 37 views ### Calculating enrichment My question concerns how enriched something is as im trying to combine several lists of uneven group size and the answer is escaping me. So basically, I have 6 groups and I want to compare them with ... 0answers 52 views ### Long division for multipolynomial expression, little o notation I have this expression:$$\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)}$$Is there any way I can take the second ... 1answer 219 views ### Equivalent forms of expressions with complex numbers Which expressions are equivalent to  {1\over{(9i+z)^4}} + {1\over{(9i-z)^4}} Select all that apply.  {18i\over{(81−z)^8}}  {−18i\over{(81+z)^8}}  {18i\over{(81+z)^8}}  {−18i\over{(81−... 1answer 77 views ### Second Order Approximation for a Polynomial if I have an expression: L=\frac{12a^3d^3-4wa^3d^2+16a^2d^2-4wa^2d+6ad+1}{12a^3d^3-4wa^3d^2-4a^2wd+16a^2d^2+7ad-aw+1} what is the second order approximation in \frac{d}{w}? I know that (\frac{d}... 1answer 28 views ### Is there a value for a other than a factor or a multiple of c in \frac{a}{b}=\frac{c}{d} Suppose a,b,c,d to be whatever quantities whatsoever that satisfy the proportion \frac{a}{b}=\frac{c}{d}. Is there a value for a other than a factor or a multiple of c. Or, is there a value ... 1answer 47 views ### How to calculate a whole amount with fractions? A contractor first completes 7/16 of a building. Then he completes 1/4 of it. And finally completes 2/5th of the remainder of the building. If there is 36 days left to finish the construction ... 1answer 44 views ### Regarding +/- fractions: what are some mental tests you can apply to uncommon fraction denominators? When adding and subtracting fractions: what if there is no uncommon factor (for example 4=2,2 and 6=2,3). Does that always mean to use the LCM? What if the LCM is too big or time consuming to ... 1answer 30 views ### Solving \frac12 (3y+2)-\frac58=\frac34y for y using LCD method I am solving$$\frac12 (3y+2)-\frac58=\frac34y$$for y using LCD method. Can't figure out what I did wrong! The answer in the back of the book is -1/2. PS: In the first line that is a 1/2 in ... 1answer 50 views ### Solving function in difference quotien equation I have the problem Find the difference quotient \frac{f(2 + h) - f(2)}{h} for f(x) = \frac{1}{x^2}. The answer they gave is \frac{-(4 + h)}{4(2 + h)^2} So far I've done:$$\frac{[1/(2 + h)^2 ...
Task: Develop a fraction equivalent to $$1\over{\sum\limits_{i=0}^{n-1}c_in^{i/n}}$$ in which the denominator is rational.