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

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0
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2answers
28 views

Fractional Exponents - Is the sign discarded?

For example, 16^(3/4) Is the accepted as both -8 and 8 or just 8? I ask this because on an AS maths mark scheme it says to condone -8 Thanks
0
votes
2answers
29 views

How does this numerators and denominators relate with the fraction? [duplicate]

Suppose if we have two fractions $\frac{a}{b}$ and $\frac{c}{d}$ then how are their values related with the fraction $\frac{a+c}{b+d}$ ? I have observed this inequality: $\frac{a}{b}\le\frac{a+c}{b+d}...
0
votes
1answer
32 views

One tap fills a pool. The other one empties it. It's a word problem.

In a pool there are two taps, one for filling and one for emptying. Once, when the pool was empty they opened the filling tap for $4$ hours. Afterwards, they opened by mistake the emptying tap and ...
2
votes
3answers
30 views

Find $\frac{y}{x}$ from $3x + 3y = yt = xt + 2.5x$

I need to find the ratio of $$\frac{y}{x}$$ If given that $$3x + 3y = yt = xt + 2.5x$$ So what I tried is: $$t = \frac{3x + 3y}{y}$$ And then put it in the equation $$\frac{x(3x + 3y)}{y} + 2.5x ...
1
vote
2answers
49 views

Resolve $ \frac{120}{x+y} + \frac{60}{x-y} = 6;\,\frac{80}{x+y} + \frac{100}{x-y} = 7$

I want to resolve this system of equations: $$\begin{cases} \frac{120}{x+y} + \frac{60}{x-y} = 6 \\\frac{80}{x+y} + \frac{100}{x-y} = 7\end{cases}$$ I came to equations like $$x - \frac{10x}{x-y} + ...
3
votes
3answers
455 views

Find equation for mass in gravity

A satellite is moving in circular motion round a planet. From the physics we know that $$\Sigma F_r = ma_r = \frac{GMm}{r^2}$$ So I wanted to find the equation for $M$ knowing also that $$v = \...
4
votes
2answers
56 views

Simplifying Fractions involving negative numbers

I want to simplify $$\frac{\frac{7}{-10} \times \frac{-15}{6}}{\frac{7}{-19} + \frac{-17}{-8}}$$ I really don't understand how to do this, or even how to start? Negative numbers make it even harder ...
1
vote
4answers
53 views

What exactly goes raising a number to a fraction mean?

I apologise for asking something so fundamental, but what exactly does $$2^\frac{2}{5}$$ actually mean? I get raising a whole number to another whole number $$x^y$$ means you are multiplying x with ...
2
votes
3answers
51 views

Can someone explain why this happens? (Dividing variables with exponents)

Alright, so let's say I have $$\frac{x^{-6}}{-x^{-4}}$$ The answer is $\dfrac{1}{x^2}$, but why isn't it $\dfrac{1}{-x^2}$?
0
votes
3answers
36 views

Comparing two fractions

I saw this problem from an elementary textbook: Let $$ A = \frac{2014}{2015} + \frac{2015}{2016} $$ and $$ B = \frac{2014 + 2015}{2015 + 2016} $$ Compare $A$ and $B$. I know the answer is $A \...
0
votes
4answers
50 views

Prove a sum of fractions less than a value

I happened to see this problem from an elementary school textbook, but cannot solve it: $$ C = \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + ... + \frac{1}{15} + \frac{1}{16} + \frac{1}{17} $$ Prove $$C ...
1
vote
3answers
47 views

fraction division understanding [duplicate]

Want to visualize rule division of fraction. For example 1) 2 2 4 _ * _ = _ 2 3 6 in this case we "split" each piece of cake in numerator to the ...
1
vote
2answers
81 views

Is the ring $\mathbb{Q}$ isomorphic to $\operatorname{Frac}(\mathbb{Q}[x])$?

Is the field of rational numbers $\mathbb{Q}$ isomorphic to the fraction field $\operatorname{Frac}(\mathbb{Q}[x])$? Both are fields, I can't disprove it by some algebraic properties that hold for ...
2
votes
2answers
34 views

Square root fraction confusion

I was doing math for school and got to something that really confused me. With having the rule $\frac{2}{4} = \frac{4}{8}$ (or some simular fraction equation) in mind, I got to the following confusing ...
5
votes
2answers
102 views

If $\frac1x-\frac1y=\frac1z$, $d=\gcd(x,y,z)$ then $dxyz$ and $d(y-x)$ are squares

Let $x, y, z$ be three non negative integer such that $\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{z}$. Denote by $d$ the greatest common divisor of $x, y, z$. Prove that $dxyz$ and $d(y-x)$ are squares ...
0
votes
3answers
68 views

Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator [closed]

If $w = \frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3} $ Express the following in the simplest form (with a rational denominator) i) $w$ ii) $\frac1w$ I'm confused about (ii) question :/ pls help me.
0
votes
0answers
44 views

Express $w$ and $\frac1w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator [duplicate]

If w = $\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3} $ Express the following in the simplest form (with a rational denominator) i) w ii) $\frac {1}{w} $ It must be like this right ? w = $\frac {\sqrt2+\...
1
vote
1answer
32 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
14 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
28 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 $...
3
votes
3answers
65 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 = \frac{8}{12}...
-2
votes
1answer
18 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
29 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
65 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: $$ 2\sqrt{3}(\sqrt{6}-...
0
votes
1answer
34 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
109 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} = \...
2
votes
1answer
37 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 = \dfrac{h}{m\left(\sqrt{\...
0
votes
1answer
27 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 {(n-2)(n-1)}{...
7
votes
1answer
85 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
239 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 $1\...
3
votes
2answers
95 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/(...
1
vote
2answers
71 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
40 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. $x$ kg....
0
votes
0answers
29 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
23 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
48 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
61 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
30 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 $a_i$'...
3
votes
3answers
66 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: $\frac{xy}{y-...
2
votes
3answers
58 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
42 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
66 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 $0.\overline{...
1
vote
0answers
42 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}} = \frac{3x^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 $\frac{s-1}{s+1} \frac{s}{s^2+1} = \frac{A}{s+1} + \frac{Bs+C}{s^2+1}$ ? $A = \left.\frac{s^2-s}{s^2+1} \right\vert_{s=-1} = \frac{1-(-1)}{1+1}=1$
21
votes
9answers
3k 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 $...