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

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2answers
27 views

Which rules are used to make function like one in Laplace Transformations table?

I have function like this: $$\frac{s^2+3s+3}{(2s^2+7s+7)} $$ It needs to be brought to the level of Laplace Transformations from table, like these two: $$\frac{a}{(s-b)^2 + a^2} $$ ...
1
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2answers
27 views

Fractions (Dividing… Maybe?)

The question... (With mixed fractions) (3)3/4 is bigger than (1)19/21 How many times bigger? I assume you divide the first fraction by the second but I cant seem to do it, could someone maybe answer ...
0
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1answer
37 views

Is there a better way of simplifying fractions?

The way I teach my students to simplify fractions is to first write the numerator and denominator as a product of prime numbers, and then cancel. For instance: $$\frac{15}{20} = \frac{3 \times 5}{2 ...
2
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0answers
37 views

Pull constant out of a summation of fractions

General problem $$ \sum_{i=1}^n \frac{a_i + x}{b_i + x} = 0 $$ Is it possible for solve for $x$? Some context I've hit a road block in my derivation... At this point, I need to pull the model ...
1
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1answer
19 views

(Straight line) Gradient for (-4, 0) (0, 2.5)

So I changed the question the textbook gave me to (-4,0) (0, 5/2). The question asked me what is the gradient for the X and Y.I was doing the question without a calculator and the answer I got was ...
0
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2answers
23 views

Cancellation fractions; why this is not equal to this?

I'm very bad with math, i will go right to the question: Why i can't make this cancellation? (or why this is False, I tested this in symbolab and gave false)... $$\frac{3^{-m}\cdot ...
0
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1answer
28 views

Square Root of Rational Number $\frac{A}{B}$

Here's the question: Let $x=\frac{A}{B}$ be a positive rational number in lowers terms (i.e., $A, B\in\mathbb{N}$ and $hcf(A,B)=1$). Prove that $\sqrt{x}$ is rational if and only if $A$ and $B$ are ...
1
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0answers
31 views

How to make continued fractions of any number?

I recently found an continued fraction representation of $\pi$, and I wondered how can I make an continued fraction that converges into a number? The MAIN question is: how do you make a continued ...
0
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1answer
22 views

Numerical analysis: what is the error term for the rule…?

The question goes: derive the error term for the rule $phi$ to approximate the third derivative of f(a). I have attached a screenshot I understand how to take the Taylor series in the hint, but the ...
1
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1answer
35 views

Is there a positive integer n such that the fraction $(9n+5)/(10n+3)$ is not in the lowest term?

Is there a positive integer n such that the fraction $(9n+5)/(10n+3)$ is not in the lowest term? Please explain. I found $n=2$ be a solution. Is it correct?
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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
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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: ...
0
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1answer
29 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
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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
453 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
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4answers
51 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
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3answers
35 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
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3answers
35 views

fraction division understanding

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
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2answers
78 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
83 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 ...
0
votes
3answers
67 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
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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 ...
1
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1answer
30 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
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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
27 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
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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
2answers
51 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 = ...
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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
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1answer
27 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
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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: $$ ...
0
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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
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4answers
89 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
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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 = ...
0
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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 ...
7
votes
1answer
82 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
237 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 ...
3
votes
2answers
94 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
68 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
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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
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2answers
39 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 ...
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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
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0answers
41 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 ...