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

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1
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1answer
29 views

When graphing both X, and Y are fractions

In my instructions, I am told to place the point on the coordinate system. My X, and Y value are $$(\frac 52, \frac 72)$$ at this point I am a little lost. Would I flip it, and multiply it like so? ...
0
votes
0answers
28 views

simplifying fractions

I have the following equation: $$ \omega_m(s) = \frac{K_{\omega} \frac{K_m}{\tau_m s + 1}}{1 + K_\omega K_p \times \frac{K_m}{\tau_m s + 1}} V_r(s) $$ and I have been trying to bring in the following ...
0
votes
1answer
13 views

Calculate weight based on body fat percentage

This is the YMCA method for determining body fat percentage for a female based on weight and waist size: $${-76.76+(4.5A)-(0.082B)\over B}=C$$ Where: A = Waist size in inches, B = Weight in lbs, C = ...
0
votes
1answer
26 views

Can someone explain to me how this simplification of a fraction works?

Can someone explain to me why is the answer $30b^{3}/4(a+b)$ considering that on the previous line we multiply $[5b][a+b]/{[4][6b^2]}$. It's as if we multiply the numerator of the first term with the ...
1
vote
1answer
34 views

Is $\frac{x}{2}$ an algebraic fraction? If yes, isn't it improper? Then how to turn it proper?

According to Wikipedia on algebraic fractions, $\frac{x}{2}$ seems an algebraic fraction. Then by definition, as the degree of the numerator $1$ ($x^1$) is larger than the degree of the denominator ...
2
votes
2answers
48 views

multiplication and addition fractions

Try to visualize process of multiplication fraction addition is obvious, need to split each part to the same size - "reduce to a common denominator" for example $$\frac23 +\frac24 = ...
-2
votes
1answer
16 views

Relative width of one image wrt another [closed]

Suppose I have an image: 120: Original Width 70: Original Height I have another image: ...
0
votes
1answer
26 views

Defining priority of operations in limits with stacking fractions

I need to evaluate the following limit : $$\lim\limits_{x \to \infty} \frac{\ln(x^2+1)}{x^2}$$ Using L'Hospital rule, I get this result (which I'm pretty sure is good) $$\lim\limits_{x \to ...
1
vote
1answer
62 views

Fraction involving Surds

Fraction involving Surds. Can anyone please show me the working out? $$ \frac{(\sqrt{6}-1)}{\sqrt{3}} + \frac{(\sqrt{6}+2)}{2\sqrt{3}} $$ I did this and it was incorrect: $$ ...
0
votes
1answer
33 views

Clarification about percentage calculus

Why if we want to know what percentage of 16 is 4 we do 4/16 and not 16/4 ? 4/16 gives you the answer, because it's ...
1
vote
4answers
85 views

Among the following, which is closest to $\sqrt{0.016}$?

Among the following, which is closest in value to $\sqrt{0.016}$? A. $0.4$ B. $0.04$ C. $0.2$ D. $0.02$ E. $0.13$ My Approach: $(\frac{16}{1000})^\frac{1}{2} = (\frac{4}{250})^\frac{1}{2} = ...
1
vote
1answer
30 views

Division by rational (decimal) number meaning

When I say, that I exchanged 42 CZK into 1,5 euro. Why do I get the rate for one euro by dividing? 1) How do you explain this division in words. Like when you say when doing integer division, that ...
0
votes
2answers
81 views

Complex proof - Not sure where to go from here. (homework)

Knowing $2\pi r =\dfrac{h}{m \left(\sqrt{\frac{e^2}{mr}}\right)}$, How do I prove $r = \dfrac{h^2}{((2\pi)^2m e^2)}$? I started by dividing both sides by $2\pi$ to get $r = ...
0
votes
1answer
25 views

Algebra Fraction Problem - Variable

I honestly can't figure out how to get this answer, I feel like a complete idiot. I've taken up to Calc 2, so I'm not an idiot just been a while. I have the problem.. $$(n-1)^2 - \frac ...
7
votes
1answer
81 views

Find all $a,b,c\in\mathbb{Z}_{\neq0}$ with $\frac ab+\frac bc=\frac ca$

As the title implies, I'm looking for triples $(a,b,c)$, where $a,b,c$ are nonzero integers, with $$\frac ab+\frac bc=\frac ca$$ I checked the cases $-100<a,b,c<100$ where $a,b,c\neq 0$ (using ...
3
votes
5answers
235 views

Probability and the “out of” thing"

I have quite an odd question: I am not able to fully understand the concept of "out of". If I roll a dice once, from a total of $6$ possible outcomes, I'll get 1. Why does that mean a fraction ...
0
votes
0answers
40 views

Receiving different answers

Ok, so im following a tutorial on how to calculate a limit numerically and when the tutor plug'd in the number $(-1.1)$ into the equation $\frac{(t^6 -1)} {(t^3 + 1)}$ HE gets −2.331 as the ...
3
votes
2answers
90 views

Fraction Sum Series

This question was asked in (selection) IMO for 8th graders. $1/2 + 1/6 + 1/12+ 1/20 + 1/30 + 1/42 +1/56 + 1/72 + 1/90 + 1/110 +1/132$ I have noticed that it can be written as $1/(1*2) + 1/(2*3) ...
1
vote
2answers
67 views

Where did my simplification go wrong? Sum and difference formula simplification

I'm struggling with the following: We are to use the sum and difference formulas to find the exact value of the expression. The problem is simplification has been tough. As a last resort I decided to ...
0
votes
1answer
18 views

simple multiplication question: multiplying radial fractions

I'm having a bit of brain block right now. In order to multiply any fractions you simply reduce to lowest form, then multiply num., then denom. When I tried with fractions in radian form it didn't ...
0
votes
2answers
38 views

A reduction of $10\%$…

A reduction of $10\%$ in the price of sugar would enable a man to buy $2\,\rm{kg}$ of sugar more for Rs. $125$. Find the reduced price per kg. My attempt: Let the initial price of sugar be Rs. $x$ ...
0
votes
0answers
25 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 ...
-3
votes
1answer
22 views

Fraction walk through [closed]

$$0.824 = \frac{n/20\cdot 1}{n/20\cdot 1+(1-n/20)\cdot 0.5}$$ Source. Please answer this question with step by step. Thank you so much
1
vote
0answers
37 views

quotient of two differentiable functions is differentiable

I have two functions $k(t)$ and $l(t)$ in a certain closed interval $[a,b]$ both functions are continuous and differentiable in the interval. In addition we have: Both functions are increasing with ...
1
vote
4answers
58 views

Find the limit of fraction involving logarithms

I am looking for a way to prove the following limit for integer $x$s: $$\lim_{x\to\infty}{\frac{\log(x+2)-\log(x+1)}{\log(x+2)-\log(x)}}=\frac{1}{2}$$ I could find the result by using a computer ...
1
vote
0answers
24 views

Stern-Brocot Tree and sum of coefficients of continued fraction

Suppose we are given a continued fraction $$\frac{p}{q}=a_{1}+\frac{1}{a_{2}+\frac{1}{a_{3}+\frac{1}{a_{4}+\cdots}}}$$ I am trying to find an expression, possibly asymptotic, for the sum of the ...
3
votes
3answers
58 views

Basic algebra problem: $ \frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x^2}-\frac{1}{y^2}} $

Basic algebra problem I can't seem to figure out: $$ \frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x^2}-\frac{1}{y^2}} $$ $x,y \in \mathbb{R}, x^2 \neq y^2, xy\neq0$. Now I know the result is: ...
2
votes
3answers
57 views

Why Doesn't $2^{1/n}= 1/(2^n)$

Take $2^{1/n}$. Since $1/n$ can be simplified as $n^{-1}$, the original term can become $2^{n^{-1}}$. The exponents can then be multiplied to result in $2^{-n}$ which is $1/(2^n)$. However it is ...
0
votes
4answers
40 views

Simple Fraction needing explanation

$$\frac{x}{x^{-1/2}} = x^{3/2}$$ How? I don't see what is going on here. What rule is being used to achieve this amount?
3
votes
1answer
61 views

Repeating decimal notation of 1/53 on WolframAlpha vs notation on Wikipedia

WolframAlpha shows for 1/53 $0.0\overline{1886792452830}$ as the repeating decimal. Why is it not $0.\overline{0188679245283}$ instead? For example, Wikipedia shows for 1/81 ...
1
vote
0answers
41 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
3answers
34 views

How do you solve B and C for $\frac{s-1}{s+1} \frac{s}{s^2+1} = \frac{A}{s+1} + \frac{Bs+C}{s^2+1}$?

How do you solve B and C for $\frac{s-1}{s+1} \frac{s}{s^2+1} = \frac{A}{s+1} + \frac{Bs+C}{s^2+1}$ ? $A = \left.\frac{s^2-s}{s^2+1} \right\vert_{s=-1} = \frac{1-(-1)}{1+1}=1$
20
votes
9answers
2k views

How to find irrational numbers between rationals. (And is my method correct?)

I have a question from an A-level revision book: Find an irrational number which lies between $\frac34$ and $\frac78$. What is the correct method for doing this? Here is my method: Square ...
3
votes
1answer
41 views

Simple formula for the $n$-ary version of $(x,y) \mapsto \frac{x+y}{1-xy}$

Let $x * y = \frac{x + y}{1 - xy}$. I want a single formula for $x_1 * x_2 * \ldots * x_n$, for all natural $n$. In order to generate plausible candidates, let's see what happens at small values of ...
-1
votes
2answers
43 views

World Problem Math Algebra Fraction

The denominator of a fraction in simplest form is greater than the numerator by $3$. If $7$ is added to the numerator, and $5$ added to the denominator, then the fraction itself is increased by ...
0
votes
1answer
42 views

Partial fraction integration with unclear roots

Let's look at a simple example like $\frac{1}{x^3+2x+1}$ here. We know that the denominator has a real root between $0$ and $-1$ (could go closer, but that's not the point). By the concept of slope of ...
0
votes
2answers
43 views

Partial fraction in two variable problem

How to write partial fraction of $$\frac{12m-n-3mn+7}{5m-2n-2mn+5}$$ I just write first and second denominator: $5-2n$ and $m+1$.
0
votes
1answer
37 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)= ...
3
votes
3answers
59 views

How to articulate where the extra 1 came in this easy question

"Albert owns 5/9ths of the stock in the North West Chocolate Company. His sister, Rena, owns half as much stock as Albert. What part of stock is owned by NEITHER Albert nor Rena?" The answer is ...
-1
votes
1answer
62 views

The name of the sum $\sum_{i=0}^n \frac{1}{m-i}$

Sorry for the vague question name, since I am looking for the name of the series. Also this might not be a "series" by the strict definition of a series.. anyways here it is: Choose some $m$ and $n$ ...
2
votes
1answer
38 views

Is it correct? Prove that any fraction can be reduced

I want to know if my prove is correct. My goal is proving: Hypothesis: $a,b \in \mathbb Z$ and $a,b \notin \{-1, 0, 1\}$. Thesis: for all $ a, b$, exist $a',b'\in \mathbb Z$ that verify ...
2
votes
1answer
22 views

About a largest integral value of this sum of reciprocal numbers.

In a test , I was asked to solve the following question : If $a_1,a_2,a_3, \cdots ,a_n$ are $n$ distinct odd natural numbers and not divisible by any prime number greater than equal to $7$ . Then the ...
2
votes
3answers
60 views

Solve fractions multiplication

I believe this is a very simple one, but I simply can't figure it out. How to solve? $$\frac12\cdot\frac34\cdot\frac56\cdots\frac{17}{18}\cdot\frac{19}{20}$$
3
votes
2answers
70 views

Laurent expansion of $\frac{1}{z^2}$

I need to find a Laurent expansion of $\frac{1}{z^2}$ with centre in $z_0 = 1$ and $P(1, 2014, 2015)$. If it was $\frac{1}{z}$, I'd rewrite the fraction like this: $$ \frac{1}{(z-1) +1 } $$ But ...
1
vote
4answers
80 views

How do I show that $-\frac{1}{e^x + 1} + 1 = \frac{e^x}{e^x + 1}$?

The expression is $$-\frac{1}{e^x + 1} + 1 = \frac{e^x}{e^x + 1}$$ I would like help to get from the left side to the right side.
-1
votes
2answers
49 views

If the chance of an event was $1/128$ and increased by $20\%$, what is the new chance?

So I have something that has a 1/128 chance of occurring, let's say. Suddenly, the chances of that thing happening are increased by 20%. How is that fraction written? Would you multiply 1/128 by ...
3
votes
3answers
48 views

How to properly set up partial fractions for repeated denominator factors

I was just trying to solve a problem that had the following item which I needed to split into separate generating functions: $$\frac{x}{(1-2x)^2(1-5x)}$$ I had assumed I needed to split it into: ...
0
votes
1answer
26 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? ...
3
votes
1answer
32 views

Unit Fraction Addition

My teacher challenged us: "Can you express the fraction $55\over 108$ as the sum of two unit fractions$?$" I figured out that ${1\over 54} + {1\over 2} = {56\over 108}$ but I could not figure out a ...
5
votes
1answer
41 views

Multiplication of algebraic fraction not giving desired result

I am having a try at solving this: that supposed to return: but I get stuck at: which can be written as