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.
-4
votes
2answers
27 views
partial fraction calculus [on hold]
https://pasteboard.co/If83kIk.png
I couldn't understand this. Can you explain to me please?
0
votes
1answer
27 views
moving fraction into denominator
Hello Mathematics Stackexchange I had a quick question. I do sincerely apologize if this type of question was asked before. Im having trouble simplifying this fraction specifically I am not sure how ...
0
votes
1answer
26 views
How to I simplify this to a single fraction?
I don't know how to fully simplify this and get rid of the seven at the end. If anyone could help I would greatly appreciate it.
0
votes
1answer
48 views
How to simplify $\frac{e^x}{1+e^{x}}$ to $\frac{1}{1+e^{-x}}$?
The two are equivalent, as a check with wolfram alpha shows.
I can also solve $\frac{e^x}{1+e^{x}} = A+ \frac{1}{1+e^{-x}}$? and I get that $A=0$.
But is there a way that I can directly simplify $\...
2
votes
3answers
86 views
Number of possible integer values of $x$ for which $\frac{x^3+2x^2+9}{x^2+4x+5}$ is integer
How many integer numbers, $x$, verify that the following
\begin{equation*}
\frac{x^3+2x^2+9}{x^2+4x+5}
\end{equation*}
is an integer?
I managed to do:
\begin{equation*}
\frac{x^3+2x^2+9}{x^2+4x+5} ...
-1
votes
1answer
42 views
Pell's Equation and Continued Fractions [closed]
For each of the following equations, determine whether there are no solutions, finitely many solutions, or infinitely many solutions with $x, y$
justify your answers.
$$x^2-5y^2=3 \\\ x^2+7y^2=...
0
votes
1answer
30 views
How do I get 1/15 of something, only by divide with 2 or 3 and add the result back together?
I'm currently playing the game Satisfactory, where I need to balance the conveyor belts to ensure a 100% efficient factory.
To help me in this job I have Merger and Splitter. The Splitter can split ...
0
votes
1answer
36 views
How do expressions of the form $\frac{a}{b}+\frac{c}{d}+…$ compare to $\frac{a+c+…}{b+d+…}$, for positive $a,b,c,d…$?
Is the question too general to answer? I'm talking about when the former expression will be greater (or smaller) than the latter?
Here's an extension:
Compare expressions
$$p\frac{a}{b}+q\frac{c}{d}...
0
votes
2answers
52 views
Help me solve this precalculus algebra expression!
Expression and my attempt at solution:
$$\frac{3ab}{c^{-1}}:\left(\frac{b}{c^{-1}}+\frac{a}{c^{-1}}-\frac{a}{b^{-1}}\right)-\frac{(a-1)a^{-1}+(b-1)b^{-1}+(c+1)c^{-1}}{a^{-1}+b^{-1}-c^{-1}}=$$
$$\frac{...
0
votes
1answer
40 views
Simplify $9((x^2-15x+50)/84)-12((x^2-8x-20)/-35)+33((x^2-3x-10/60)$
Hi I am trying to simplify the following I found online
$9\left(\dfrac{x^2-15x+50}{84}\right) + -12\left(\dfrac{x^2-8x-20}{-35}\right) + 33\left(\dfrac{x^2-3x-10}{60}\right)$
to
$= x^2 -6x -7$
...
0
votes
3answers
78 views
Is the following result true? Or Is there any known result about fractions like this?
Is the following result true? Or Is there any known result of fractions like this?
Let $n$ be fixed.
There are infinitely many integer solutions for $$\sum_{i=1}^n \frac{1}{x_i} = 0,$$ where $x_i \...
8
votes
2answers
232 views
Why does this procedure terminate? Or are there any numbers for which it doesn't?
I don't really have good formal education in theoretical mathematics, so please don't be upset if this is obvious question, but on the other hand I don't believe I am the first one to think of such ...
0
votes
1answer
38 views
simplifiy complex expression [closed]
How to simplify the following expression:
$$\frac{z-1}{z+1}~, \quad \text{where} z\in \mathbb{C}\setminus \{-1\}$$
There is just nothing i can come up with, neither in cartesian, nor in polar.
0
votes
1answer
17 views
Find whole numbers of which's average is given
I was trying to calculate something, when I came across with something I couldn't solve. I needed to "reverse an average", find whole numbers, of which's average is 0,625. I feel like this is a thing ...
0
votes
1answer
34 views
How do I simplify $\frac{(bS)^{2}}{(bS)^{2} + y}$ to $\frac{1}{1+\left[\frac{y}{bS}\right]^{2}}$?
As the above mentions I have the fraction $\frac{(bS)^{2}}{(bS)^{2} + y}$ and the next step in the equation I am following simply states "it works out to equal" $\frac{1}{1+\left[\frac{y}{bS}\right]^{...
1
vote
1answer
53 views
I tried answering this question but my answer is in decimal. How can a number of muffin be in decimal?
Mrs Ho baked a total of 60 banana muffins and chocolate muffins. After she gave away 5/7 of the banana muffins and 1/2 of the chocolate muffins, she had twice as many as chocolate muffins as banana ...
1
vote
2answers
60 views
Find the minimum value without using derivative
Find the minimum value of
$$f(x) = {3\over \sqrt{x}+1} - {12\over \sqrt{x}+3}$$
The domain of $f(x)$ is $x ∈ (0,∞)$. Then, using derivatives, I can find the minimum value is $f(1)=-1.5$. However, ...
1
vote
2answers
46 views
Stuck on candy bowl fraction
I am really stuck on this problem because I'm not even sure where to start.
Larissa has a bowl of candies. On the first day, she eats 1/2 of the candies plus one more. On the second day, she eats 1/3 ...
0
votes
4answers
43 views
Evaluating limits in fractions
When you want to find the limit of a fraction e.g. $\frac{1-x}{1-x^3}$ as $x$ tends to $1$. Why can you not just plug in x into the numerator and denominator?
Why do you have to make all the $x$ ...
0
votes
1answer
20 views
Algebraic manipulation and inequality
Given real-valued terms $a,b,c \in {R}$ with the following conditions on them: $ 0 \leq a \leq 1 $, $|b|<1$, and $|c|< 1$. And given the terms
$ X= \frac{1}{1-( (1-a)b + ac )}$ and $ Y =\frac{1}...
1
vote
1answer
39 views
Basic division problem: dividing a fraction by a fraction
I thought I clearly knew how to divide fractions by fractions until I came across this problem. Please can somebody let me know where I am going wrong?
Here is what we start with.
$(1-2x)/(2x^1/2)/e^...
2
votes
1answer
81 views
Take two numbers x and y between 1 and 100. What’s the probability that x/y is an integer?
It was stated, as an inconsequential remark, in some lecture notes I was reading that if we are to choose two natural numbers in a certain interval and divide one by the other, that it is quite likely ...
0
votes
2answers
70 views
Why can we divide by zero in limits?
Before I ask, I want to tell you that I am beginner in limits, so you may find some problems in my understanding.
Let's assume a function $f(x) = 15-2x^2$. We want to know how the function behaves ...
0
votes
1answer
39 views
Question for preparation for the IMC internationals [on hold]
Work out the addition of:
(1/(1+2))+(1/(1+2+3))+...+(1/(1+2+3+...+51))
Guys, I'm having difficulties working this one out. Using a calculator, it would have been easy, however in the internationals ...
0
votes
0answers
23 views
On the zero element of the classical ring of quotients
Assuming $R$ a ring and $S$ an Ore subset of $R$ we construct the ring $Q = S\times R/\sim$ where the relation is $(s,x)\sim (r,y)$ if and only if there exist $a,b \in R$ such that $as = br \in S$ and ...
1
vote
3answers
40 views
Help with fractions
I have attached an image of which I have a question about. I don’t understand how you can get from equation 1 to equation 2.
Could someone please explain this?
$$nRc=\left(\frac{V_{cc}-V_{BE}}{V_o-...
0
votes
2answers
45 views
How to find $\frac{146}7 \mod{7}$?
I understand that if $\gcd{(b,c)}=1$ then we can find $\frac{a}b\mod{c}$ by writing
$$x\equiv \frac{a}b\mod{c}$$
$$bx\equiv a\mod{c}$$
then reducing $a$ and solving the modular equation by finding the ...
0
votes
1answer
27 views
Possible values of $z$ in this inequality problem?
If $0<x<y<z$ integers
And $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{4}$
So it asks the possible values of $z$.
Options goes as:
A)9
B)10
C)11
D)12
E)13
1
vote
3answers
48 views
Proving $\frac{a}{b} >\frac{a+\epsilon}{b+\epsilon}$ if and only if $b<a$, for $\epsilon >0$, $a,b$ positive.
The way I use to see that this is true is to take the derivative of the LHS w.r.t to $\epsilon$. This derivative is negative if $b<a$.
I am not sure how I can use this to prove the if and only if ...
0
votes
0answers
55 views
Is there a general formula for $\int{\big(\frac {\arctan x}{x^2+1} \big )}^{\frac1k}dx$ , with $k$ is positive integer?
I'm interested to know if there is a general formual for
$$
\int\left[\arctan\left(x\right) \over x^{2} + 1\right]^{1/k}\mathrm{d}x
$$
with $k$ is positive integer may present integral of fraction ...
1
vote
1answer
74 views
Solving Fractional Diophantine Equations
As my search to create an efficient factorization algorithm continues, I stumbled upon this equation for one of my test cases:$$\dfrac{3-n^2}{2n-12}=k$$ To continue, I need to know what integer values ...
1
vote
0answers
56 views
Unit fractions pairing
(I have asked this question on stackoverflow and received a suggestion to try posting here so hey guys!)
I have been given a problem where fractions between 1/2 - 1/1000 have to be added to create ...
-2
votes
4answers
811 views
How to communicate $\frac{5}{2}$ to other people orally? [closed]
The term one third is unambiguously understood as $\frac 13$. Likewise, the term two fifths is unambiguously understood as $\frac 25$ and three sixths is understood as $\frac 36$.
But what exactly ...
0
votes
1answer
38 views
LCD of 2x+1, x^2 and x
I am given the following sum:
$$\frac{x}{2x+1} + \frac{3}{x^2} + \frac{1}{x}$$
In order to add these fractions, I must find a common denominator. I have been taught to factor each denominator and ...
2
votes
3answers
145 views
Find the value of $S$ if $S = {x\over y} + {y\over z} + {z\over x} = {y\over x} + {z\over y} + {x\over z}$ and $x + y + z = 0$
Find the value of $S$ if $$S = {x\over y} + {y\over z} + {z\over x} = {y\over x} + {z\over y} + {x\over z}$$ and $x + y + z = 0$.
This is a difficult question in my opinion and I was wondering if I ...
0
votes
1answer
33 views
How would I apply partial fraction expansion to this expression?
$$\displaystyle\frac{1}{X\bigg(1-\dfrac{X}{Y}\bigg)\bigg(\dfrac{X}{Z}-1\bigg)}$$
I want it in the form $$\frac{A}{X} + \frac{B}{(1-\dfrac{X}{Y})}+\frac{C}{(\dfrac{X}{Z}-1)}$$where I am required to ...
0
votes
2answers
27 views
Simplification of a complicated fraction
I am going over a physics text and I have difficulty to see how one can go from
$$2A = (1+ \frac{\alpha}{ik})(1+\frac{ik}{\alpha})\frac{Fe^{ika}e^{-\alpha a}}{2} + (1- \frac{\alpha}{ik})(1-\frac{ik}{...
0
votes
1answer
24 views
How to break long expressions into multiple lines?
Say I want to write a long radical expression like this
$\sqrt{a + b - c + d - e + f - g + h - i + j…}$
on paper or blackboard. It cannot fit in one line. How should I break it into two lines?
...
-1
votes
2answers
107 views
Help me simplify $\left(\frac{a^2-ab}{a^2b+b^3}-\frac{2a^2}{b^3-ab^2+a^2b-a^3}\right)\cdot\left(1-\frac{b-1}{a}-\frac{b}{a^2}\right)$ [closed]
Supposedly solution is $\frac{a+1}{ab}$, but both problem and solution could be erroneously defined because a book I retyped problem from has a few misprints here and there.
There's no need to post ...
0
votes
0answers
31 views
What's with Fractional Subtraction as an action on a number
This a simple (sort of stupid) arithmetic based question that may require just the littlest bit of work.
Consider $\cfrac {x}{a}$
I know that division is the number of times I'll have to remove a ...
1
vote
1answer
59 views
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{cos(x)^{sin(x)}}{(cosx)^{sin(x)}+(sinx)^{cos(x)}}dx$
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{cos(x)^{sin(x)}}{(cosx)^{sin(x)}+(sinx)^{cos(x)}}dx$. EDIT: By changing the variable, $x\rightarrow \frac{\pi}{2}-x$, $\int_{0}^{\frac{\pi}{2}}\frac{cos(x)^{...
1
vote
2answers
74 views
Calculate the integral $\int \frac{2-3x}{2+3x} \sqrt{\frac{1+x}{1-x}}dx$ [duplicate]
I have to calculate the integral $\int \frac{2-3x}{2+3x} \sqrt{\frac{1+x}{1-x}}dx$. I tried the following substitutions: $x \rightarrow \frac{1+t}{1-t}, x \rightarrow \frac{1-t}{1+t}, x \rightarrow \...
0
votes
1answer
34 views
asinh from fraction
If I have $$
\mathrm{asinh}\left(\frac{x}{2.8\cdot10^{-10}}\right) = 15
$$
How can I calculate $x$?
Should I use $\mathrm{asinh} \, x = \ln(x+\sqrt{x^2+1})$
Or something else?
2
votes
3answers
51 views
Stumped by a pretty basic fraction division
I'm self-studying through Stroud & Booths's amazing "Engineering Mathematics", 7th Edition, and am still on the "Arithmetic" section. Even though I've gone through the whole chapter and a lot of ...
0
votes
1answer
28 views
Rationalising the denominator problem
I need help rationalising this
$$\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1) }$$
I'm so stuck with this problem!
0
votes
1answer
121 views
Estimation of fractional expression
We define
$$\displaystyle f(x,y)=\frac{1}{x^{2y}-\frac{1}{4^y}}+\frac{1}{(1-x)^{2y}-\frac{1}{4^y}} \text{ for } (x,y) \in \left[0,\frac{1}{2}\right) \times \left(\frac{1}{2},1\right]$$.
A study ...
0
votes
3answers
50 views
Understanding Square Root rules to understand an equation [closed]
So this is an equation from one of the solutions in my textbook that I am trying to understand as part of solving a cholesky-factorization problem:
$$\sqrt{18-(\frac{a}{\sqrt2})^2} = \sqrt{\frac{36-a^...
1
vote
1answer
37 views
why componendo and dividendo is failing in this question
If a positive fraction numerator and denominator is increased by 2 the fraction increases by $\frac{1}{24}$ find the difference between the numerator and denominator, given the sum of Numerator+...
0
votes
1answer
19 views
Difference between rationals in a certain set is at least a certain amount
Define $A = \{\frac{p}{q} \in \mathbb{Q} \mid q \in \mathbb{N}, q < n, gcd(p,q) = 1\}$. I am trying to prove that the difference of any 2 distinct elements of this set is greater than $\frac{1}{n}$....
0
votes
1answer
46 views
Adding to the denominator of two fractions
Say I am working with one fraction larger than another and only in the domain of positive fractions.For example, let's say I have $\frac{20}{20}$ and $\frac{50}{80}$. Clearly $\frac{20}{20}$ is the ...
