Questions on fractions, numbers of the form $p/q$ where $p$ and $q$ are integers, and $q$ is not zero.

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0
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1answer
21 views

Comparing Fractions that contain epsilon

Given $\epsilon$ a constant s.t. $0<\epsilon<1$, and $n,p$ positive integers, $n >= 2p$, is the following true: $\frac{(1+\epsilon)n}{(2+\epsilon)p} \geq \lceil\frac{n}{2p}\rceil$
1
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3answers
27 views

Simplifying fraction with square root as denominator

I'm trying to find the integral of: $$\dfrac {2\sqrt{x} - 3x + x^2}{\sqrt{x}}$$ but I first need to simplify it so I tried dividing by the $\sqrt{x}$ for each of the numbers on the top like so: ...
0
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1answer
35 views

What's the difference between “continued fractions” and “compound fractions”?

What should we call a fraction which includes another fraction in its numerator or denominator, like $${ab\over {c \over d}}$$?
1
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1answer
38 views

Why does $ \frac {a}{b}$ of $c$ means $ \frac {a}{b} \cdot c$ [closed]

Why does it multiply when the preposition "of" appears?
0
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0answers
21 views

Adding a natural number to a normalized fraction

I am currently writing yet another rational number class where the fraction should always be normalized. When adding a natural number to a normalized fraction, it possible to get a non-normalized ...
4
votes
4answers
99 views

why do equations work and how do they relate to each other?

Ok, so I understand that an equation is something like 15 = 15 , and that the only criteria as far as I can tell for it being an equation is that both sides are equal to each other. I have a few ...
0
votes
2answers
23 views

Fractions from least to greatest

What is the fastest way to find the least common denominator of all the fractions without losing too much time? 7/9 , 1/4, 14/15, 2/3, 1/2 Thanks.
2
votes
0answers
60 views

All those unit fractions add to 1?

Consider $$S(n)=\{x \mid x=(a_1 ,a_2,a_3 \cdots a_n) \text{ where } \sum_{r=1}^{n}\frac{1}{a_r} =1 \}$$ Now let $|S(n)|$ denote the cardinaly (order) of set $S(n)$. Thus: $S(1)= \{(1)\} \implies ...
2
votes
2answers
44 views

Cannot find length of repeating block in decimal expansion for $\frac{17}{78}$

I am trying to find the length of of the repeating block of digits in the decimal expansion of $\frac{17}{78}$. On similar problems, that has not been an issue. Take for instance $\frac{17}{380}$. My ...
0
votes
2answers
48 views

Convergence of a series ${}\qquad{}$

Does this series converge? $$\sum_{x=2}^n \left(\frac{1}{x}\right)^{\left(\frac{1}{x}\right)}$$ I tried hard but stil had problems... Could someone help me?
0
votes
1answer
19 views

Solving for $x$ [not homework]

How do I bring the remaining $x$ to the LHS? $\pm x=\frac{(2-x)\sqrt{|q_2|} } {\sqrt{|q_1|}}$ to get $x=\frac{2 \sqrt{|q_2|}}{\sqrt{|q_2|} \pm \sqrt{|q_1|}}$ I'm just not sure about the ...
3
votes
3answers
49 views

confusion related to elementary operation on numbers

Let's take for example an fraction: $\dfrac{1+4}{2-4}$ and another fraction $\dfrac{1*4}{2*4}$. In the second fraction we can cancel 4 from both numenator and denominator but on the first we cannot ...
2
votes
2answers
84 views

Can fractions be relatively prime?

Two numbers are relatively prime if they do not share any factors, other than 1. Is it possible for fractions to be relatively prime? To reword this, do fractions even have factors?
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votes
2answers
62 views

Negative mixed fractions

I'm comfortable with fractions like $\frac{-3}{8}$ being the same as $\frac{3}{-8}$ (though I'd think the latter anachronistic and would in any case probably prefer to write either of those two as ...
0
votes
2answers
45 views

Fractional Exponents powers

I am having problems understanding how to answer questions containing fractional exponents to a given power ie $(2x^{1/2})^6$, i do not understand how to go about answering the question. I know this ...
0
votes
2answers
59 views

How to transform $2,(9)$ to form $\frac{a}{b}$

How to transform $2,(9)$ to form $\frac{a}{b}$. My attemp: $$x=2,(9)/\cdot 10$$ $$10x=29,(9)$$ $$10x-x=29,(9)-2(9)$$ $$9x=27$$ $$x=3$$ but do not know if I have done the exact. Please help me
1
vote
1answer
35 views

My small theory…

It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:- a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and ...
2
votes
2answers
50 views

Solving a fractional quadratic equation problem by completing the square

I have the following problem to solve using the method of completing the square. $$2x^2-3x-1 = 0$$ Here is where I've gotten to so far on this problem. $$2x^2-3x = 1$$ $$x^2-\frac{3}{2}x = ...
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votes
2answers
55 views

Rigorous proof for the following [closed]

Please give a rigorous proof: For all $A, B$ $$(1/A)(1/B)=1/(AB).$$
1
vote
1answer
47 views

How did my book simplify this?

How did my book go from: $\frac{4}{5}=\frac{x}{30}$ to $\frac{4}{1}=\frac{x}{6}$ I understand that I could have cross multiplied it in the first place but what I don't understand is why my book ...
1
vote
1answer
73 views

Why a decimal fraction is not expressing exactly what a rational number is in base 2?

I am currently using rational numbers to express currency and math operations with currency, while dealing with rational numbers has provided a great convenience in over coming the limitations of ...
0
votes
1answer
21 views

Simplifying a fraction.

The answer of a "solve for x" equation equaled to -10/-19, and the website on which I am practicing says it needs to be simplified, but I have no idea how. Help?
2
votes
1answer
32 views

Confusing sum of fractions

Question is to find the sum of: $$(\frac{1}{2^2-1})+(\frac{1}{4^2-1})+(\frac{1}{6^2-1})+(\frac{1}{20^2-1})$$ I know that $a^2-b^2=(a+b)(a-b)$, and that with this I can find the LCM to be 1995, ...
8
votes
3answers
640 views

Numbers whose self and reciprocal are finitely decimally expressable that are close to one?

How would I go about finding numbers x such that x and 1/x are finitely decimally reciprocal and are also close to 1? I'm not entirely certain how to phrase this question, but take for example 2. 2 ...
1
vote
2answers
42 views

How to solve $\dfrac{7x}{8}+4-\dfrac{2x}{3}=4x-3$?

$$\frac{7x}{8}+4-\frac{2x}{3}=4x-3$$ I do not understand how to simplify this. Could anyone here help me, please? Thanks.
2
votes
2answers
164 views

Question in fraction (not simple )

I have a question and its answer but I don't know how can i solve $$\frac {37}{13} = 2+ \frac {1}{x+\frac{1}{5+\frac{1}{y}}} $$ the answer $ x =1, y=2$ Could any one explain how to solve this ?? ...
0
votes
2answers
33 views

How to solve fraction which is divided by decimal fraction [closed]

$$\dfrac{\;\;\;\frac{5}{12}\;\;\;}{\frac{0.25}{0.5}}=?$$ I need to solve this. I'm a beginner in math and I got a exam tomorrow...
0
votes
2answers
69 views

Mixed repeating decimals

How can be proven that a fraction having at the denominator a multiple of both 2 and 3 is transformed to a mixed repeating decimal number? I thought to bring the denominator to the form of ...
1
vote
0answers
21 views

MultiEquations (with fractions)

Can you please help me solve these equations i don't understand how to solve them with fractions. 1=n-2/15 151/20 =2a+1 3/4 -3/5 -2 1/5k = - 26/25
0
votes
2answers
36 views

How to simplify this fraction?

Can anyone show me how to simplify this fraction: $$ \frac{(k + 1)((k + 1)+1)(2(k + 1)+1)}{6}\;\;. $$ What can be factored out and so forth? Thanks.
3
votes
2answers
127 views

When can't $dy/dx$ be used as a ratio/fraction?

By searching this question, I found this: Can I ever go wrong if I keep thinking of derivatives as ratios? However, the answers don't have what I'm looking for! (Edit: Meaning, a counterexample. ...
0
votes
1answer
38 views

Reducing an inquality with fractions

can you help me reduce the following inequality (i need to get a relation between x and y -- express x in terms of y) $\frac{n}{2x} < \frac{n}{(4+\epsilon)y}+1$ I would like to show somehow that ...
1
vote
3answers
79 views

If you add the same constant to the numerator and denominator, what is the relation between the new fraction and the original fraction?

If I add a constant $\varepsilon < 1$ to the numerator and denominator of a fraction, is the new fraction always greater than the original? That is, do I have $$ \frac{a}{b} \leq ...
2
votes
1answer
67 views

$\sqrt[\large m]{(x+y)}\over \sqrt[\large k]{(x+y)}$ $=\sqrt[\large m-k]{(x+y)} $?

Is it always true that: $\sqrt[\large m]{(x+y)}\over \sqrt[\large k]{(x+y)}$ $=\sqrt[\large m-k]{(x+y)} $ where $m,k \in \mathbb N$ ? I tried it with a few numbers and it seems to work every time.
0
votes
4answers
23 views

How to make sense of fractions concretely

I can solve fractions abstractly, for example, $\frac{5}{2}$ divided by $\frac{3}{2}$, you can flip $\frac{3}{2}$ so that $\frac{5}{2}$ multiplied by $\frac{2}{3}$. Specifically, math makes sense ...
0
votes
1answer
42 views

fraction as index number?

given these inputs x = 4, S = [1 2 3 4 5 6 7 8 9 10], and n = 10 ...
7
votes
1answer
437 views

Does it make sense to multiply slopes?

Multiplying fractions is a regular occurance. If those fractions are considered slopes, does it make any sense? For example, if these fractions are slopes,$\frac{9}{8} \times \frac{49}{48},$ does the ...
1
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3answers
51 views

How have they done the algebra here?

Proof by induction \begin{align}&4-\frac{k+2}{2^{k-1}}+(k+1)\left(\frac12\right)^k\\ =&4-\frac{2(k+2)}{2^k}+\frac{k+1}{2^k} \\ =&4-\frac{(k+1)+2}{2^{(k+1)-1}} \end{align} Original image ...
1
vote
1answer
47 views

Calculating the average of multiples and divisions

Imagine a number line that contains every value that is greater then (but not inclusive of) 0. The center of the line is 1. On the right side of the center(1), obviously, are all the whole and ...
-1
votes
1answer
31 views

What is the formula's are used to convert to meters/second?

What are the formula's to convert the following per hour intervals into meters per second (using meters/s from light speed): Kilometer Mile (US) Mile (Nautical) Feet The result should be decimal ...
0
votes
1answer
26 views

Addition on an Elliptic Curve and Modular Arithmetic involving fractions

I'm having a bit of an issue with addition on elliptic curves. For example, I've been given the curve $Y^2 = X^3 + 2X + 1$, working modulo 3. Now, say I want to add the point $(1,2)$ with itself. To ...
0
votes
2answers
33 views

Fractions with 3 diffferent variables

Calculate the values of $a$, $b$ and $c$ if: $$\frac{5}{13} = \frac{1}{a+\frac{1}{b+\frac{2}{c}}}$$ Can anyone give me a hint and not the answer? Thanks.
0
votes
0answers
14 views

Identity for fractional summation

I would like to know if there's an identity to represent the following summation $\sum_{i=0}^{n}\frac{x_i}{y_i}$ Where x and y are non integer values. The result of this is being calculated using ...
0
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2answers
37 views

Subtracting 2 fractions with variables in the denominator that have different exponents.

Sorry for the relatively elementary question, but I am having trouble remembering exactly how to do this type of problem. I am looking to simplify this: $$ \frac{3}{4t^{1/4}} - \frac{1}{2t^{3/4}} $$ ...
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votes
1answer
28 views

How do I use the partial fractions technique in this case?

How do I use the partial fractions technique in this case? $$\frac{(x - 1)}{(x^2 - x + 1)(x + 1)}$$
6
votes
1answer
129 views

Find all natural numbers such that $\sum_{k=1}^{n} \frac{n^k}{k!}$ is an integer

Find all natural numbers such that $\sum_{k=1}^{n} \frac{n^k}{k!}$ is an integer. I've tried to bring all fractions under commmon denominator and it didn't helped me much. With guessing I find out ...
3
votes
3answers
119 views

How do I integrate $\frac{1}{x^6+1}$

My technique so far was substitution with the intent of getting to a sum of three fractions with squares in their denominators. $t = x^2 \\ \frac{1}{x^6 + 1} = \frac{1}{t^3+1} = ...
1
vote
3answers
41 views

Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b,c > 0 $?

Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b> 0$ and $c\geq 0$ ? Is there a general proof for that relation ?
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votes
1answer
118 views

How to multiply, divide, add and subtract fractions

I've spent hours on this and I keep getting mixed answers. I need to know the rules for multipling, dividing, adding, subtracting equations involving fractions. I google search but the information is ...
0
votes
0answers
23 views

Calculating an average value based on separate subsamples from the same sample

I have a question coming from biological research. We routinely have to quantify on microscopic images certain values characteristic of a piece of tissue – for example the percentage of cells that are ...