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

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2
votes
2answers
70 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 = ...
1
vote
1answer
49 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
116 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
22 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
40 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
647 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
45 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
169 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 ?? ...
-1
votes
2answers
38 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
121 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
41 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
166 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
39 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
102 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
73 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
34 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
44 views

fraction as index number?

given these inputs x = 4, S = [1 2 3 4 5 6 7 8 9 10], and n = 10 ...
8
votes
1answer
488 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
vote
3answers
53 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
69 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
83 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
32 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
35 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
23 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
votes
2answers
39 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: $$ \frac{3}{4t^{1/4}} - \frac{1}{2t^{3/4}} $$ ...
-2
votes
1answer
30 views

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

How do I use the partial fractions technique in this case? $$\frac{(x - 1)}{(x^2 - x + 1)(x + 1)}$$
7
votes
1answer
137 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
124 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
43 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 ?
-3
votes
1answer
198 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
32 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 ...
3
votes
2answers
172 views

How do you calculate how many decimal places there are before the repeating digits, given a fraction that expands to a repeating decimal?

If you have a fraction such as $$\frac{7}{26}=0.269230\overline{769230}$$ where there are a number of digits prior to the repeating section, how can you tell how many digits there will be given just ...
0
votes
2answers
35 views

Is there a formula for this?

Take a test score represented by the fraction ${a\over b}$. This test score could be curved by removing a wrong answer to get ${a\over b-1}$ or adding a correct answer to get ${a+1\over b+1}$. ...
0
votes
1answer
31 views

Find pdf of $f(x)$ such that $g(x)/f(x)$ is approximately a constant

My friend asked me a question that asks to find a pdf function $f(x)$ such that $f(x)/g(x)$ is approximately a constant, where $g(x)=\sqrt{e^{x^2}+e^x}$, and $f(x) \neq g(x)$. And the range of x is ...
0
votes
0answers
31 views

How can I simplify the following expression with exponents.

$$\frac{(t+1)^{\frac{1}{3}}-\frac{1}{3}t(t^2+1)^{-\frac{2}{3}}}{(t^2+1)^{-\frac{2}{3}}}$$ I found this problem from a book and its answer is $\frac{2t+3}{3(t+1)^{\frac{4}{3}}}$(as in the book's ...
0
votes
2answers
56 views

Simple ratio problem that I can't solve.

One fifth of criminals are hard-core criminals. The hard-core criminals commit two-thirds of the criminal acts. What is the ratio of the number of criminal acts committed by the average hard-core ...
2
votes
1answer
141 views

Existence of a simultaneous rational approximation of real numbers in (0,1)

I have a simple question the rational approximation of real vectors. Dirichlet's simultaneous approximation theorem states: Given any $d$ real numbers $\alpha_1,\ldots,\alpha_d$ and for every ...
0
votes
2answers
62 views

Rationalising the Surds

Please help me rationalise and simplify: $$ \frac{1}{\sqrt[3]{2} - 1} \ - \ \frac{2}{\sqrt{3} - 2} \ . $$ I have tried using the cube of the denominator and the square of the denominator on the ...
0
votes
4answers
129 views

How to simpify this?

How to simplify following fraction? I have tried everything, but nothing seems to work... $$-a^3 (c^2 - b^2) + b^3 (c^2 - a^2) - c^3 (b^2 - a^2)\over (c-b)(c-a)(b-a)$$
8
votes
2answers
95 views

Integrating $\int{\frac{\sqrt{1-x^2}}{(x+\sqrt{1-x^2})^2} dx}$

I am a little bit lost with integral: $$\int{\frac{\sqrt{1-x^2}}{(x+\sqrt{1-x^2})^2} dx}$$ I have already worked on in and done substitution $x = \sin(t)$: This brings me to: ...
1
vote
2answers
115 views

Dividing amount unequally in tournament winners?

Hi I am trying to write the algorithm to calculate the winning amount of the winners. My problem is as below, 1) I have open ended tournament in which participants can be in ratio of 2 (i.e 2,4,8,16 ...
1
vote
6answers
255 views

Solution of $\dfrac{a}{b}=\dfrac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$

Let $\dfrac{a}{b}=\dfrac{a'}{b'}$ , $a,b,a',b' \in \mathbb{N}$ s.t. $a$ and $b$ have no common factors. How can we show that the only solution to this equality is $a'=na$ and $b'=nb$, $n$ is a natural ...
0
votes
1answer
60 views

Integration involving $\log_2(x)$

Having a hard time going about this problem: $$\int{\frac{\ln(2)\log_2(x)}{x}}$$ I believe $\ln(2)$ would be considered a constant, so than the equation would then changed to: ...
1
vote
0answers
63 views

Prove that there exists a subset with sum >=1 such that the remaining integer sum reduces by 1

let $ n \in \mathbb{N} $ and $ \frac{1}{w_1},\ldots, \frac{1}{w_n} $ for some (not necessarily distinct) $ w_1,\ldots,w_n \in \mathbb{N} $ and $ w_1,\ldots,w_n \ge 2 $ be given. Assume that $ ...
0
votes
0answers
45 views

How to find maximum and minimum of $\frac{x+y+z}{ax+by+cz}$ where $0\leq x \leq y \leq z \leq 1$ for given positive real numbers $a,b,c$

How do I find the maximum and minimum of $$\frac{x+y+z}{ax+by+cz}$$ where $0\leq x \leq y \leq z\leq 1$ for given positive real numbers $a,b,c$? I guess those are one of $\frac{3}{a+b+c}$ or ...
0
votes
1answer
76 views

How to solve a inequality with fractions and roots in denominator and numerator

The inequality is like that: $$ \sqrt{\frac{3x+1}{2}}>1 $$ I have no idea how should i begin with it.
0
votes
2answers
185 views

Counting four-digit numbers with repeating digits

Of all the four-digit positive integers containing only digits from the set $\{2,4,6,8\}$, what fraction of them have at least one of their digits repeating? Express your answer as a fraction. ...
8
votes
1answer
156 views

$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$

I have a pretty simple straightforward question. Q) Find the value of $x$ in the following: $$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$$ Instinctively, I do the quickest thing I know how to ...
0
votes
2answers
86 views

Solve algebraically: $\lim\limits_{x \to 3} \frac{3-x}{5-\sqrt{x^2+16}}$

$$\lim\limits_{x \to 3} \frac{3-x}{5-\sqrt{x^2+16}}$$ The professor says we can't use l'hopital's rule and must solve algebraically.