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

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2answers
72 views

Monotonicity of a fraction

If I have a fraction $f(x) = \dfrac{n(x)}{d(x)}$, where $n(x)$ increases monotonically and $d(x)$ decreases monotonically; as functions of $x$. Can I be sure that $f(x)$ increases monotonically as a ...
5
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1answer
164 views

finite field to rational fraction

Suppose I have a number $n\in\mathbb F_p$, i.e. an element of the finite field obtained by arithmetic modulo some (odd) prime $p$. I'm looking for a way to find a simple description of $n$ as a ...
3
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1answer
78 views

Given two ratios $\frac{p_i}{q_i}$, what is $\frac{p_1+p_2}{q_1+q_2}$ in their terms

I am ashamed to say that I cannot figure this one out: I am given two ratios $\dfrac{p_i}{q_i}$ where $i=1$, $2$. (We just know the ratios and not the numbers $p_i, q_i$. What I mean by this is ...
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1answer
132 views

Inventory of Clocks and Frequency of Chimes

How do you determine the hours for which the clocks chime?
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9answers
2k views

Are all integers fractions?

In a college class I was asked this question on a quiz in regards to sets: All integers are fractions. T/F. I answered False because if an integer is written in fraction notation it is then ...
2
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1answer
73 views

Which numbers will remain if I keep removing the second third of the remaining interval?

Inspired by this Google Code Jam problem - Vanishing Numbers There is a pool of numbers which are arbitrary decimal fractions from the interval (0, 1). In the first round of the game the middle ...
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3answers
11k views

Most efficient method for converting flat rate interest to APR.

A while ago, a rather sneaky car salesman tried to sell me a car financing deal, advertising an 'incredibly low' annual interest rate of 1.5%. What he later revealed that this was the 'flat rate' ...
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3answers
149 views

How does $({{n/e})^n} / ({({n/{2e}})^n})$ simplify to $2^n$ (MIT OpenCourseware 6.006)

As stated in the title, how is the following simplification performed? $$\frac{\left(\frac{n}{e}\right)^n}{\left(\frac{n}{2e}\right)^n}=2^n$$ This was shown by a student in this Recitation video ...
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4answers
794 views

How do I rewrite -100+1/2 as the mixed number -99 1/2?

This has been bugging me for some time now, so I ask you to try to help me realize what is going on here. I just can't get my brain around this. I have a proper fraction and a negative integer. The ...
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1answer
74 views

Problems with basic algebra

I'm studying for an exam in a digital communications course I'm taking, and the solution to one question has me totally lost. While finding the Inverse Fourier Transform of a function, there's one ...
2
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3answers
2k views

Simplification of fraction with factorials

I'm stuck on a simplification, used to prove $C(n - 1, r - 1) + C(n - 1, r) = C(n, r)$ Could somebody clarify the step(s) from: $\frac{(n - 1)!}{(r - 1)!(n - r)!} + \frac{(n - 1)!}{r!(n - r - 1)!}$ ...
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1answer
56 views

How is this complex fraction getting cleared using this method?

Can someone please explain how multiplying these two fractions together is clearing the complex fraction? I know that by multiplying these two fractions clears the complex fraction, I just can't ...
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2answers
55 views

Simplifying $\frac{1}{x} + \frac{5+x}{x+1} - \frac{7x^2 + 3}{(x+2)^2}$

I'm having trouble simplifying this expression: $$\frac{1}{x} + \frac{5+x}{(x+1)} - \frac{7x^2 + 3}{(x+2)^2}$$ Would you first do the addition or subtraction? What's the steps to solve this? The ...
3
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2answers
874 views

How to solve this? (adding polynomial fractions)

I'm having trouble solving this expression: $$\frac{(x - 1)(7x + 6)}{(x - 1)(x + 1)^2 }-\frac{ 7}{ (x + 1)}$$ What's the steps to solve this? I know you expand $(x + 1)^2$ to $(x + 1)(x + 1)$, ...
1
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1answer
62 views

General solution for x of C = 100/(1+aX) + 100/(1+bX) … + 100/(1+zX)

Please can someone help me find a general solution for X $C = \frac{100}{(1+aX)} + \frac{100}{(1+bX)} ... + \frac{100}{(1+zX)}$ UPDATE Its not ideal but if we make C = 350 would this help?
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2answers
139 views

how to add/subtract than multiply fractions?

Q). 1 + 9/2 x -5/7 Q). 1 - y^2 x 9/4 just guide me how to solve this question Edit: From the title of the question I would infer that he/she meant $ 1 + \frac92 \times \frac{-5}{7}$ $ 1 - y ^2 ...
2
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2answers
75 views

Problem with slopes.

I currently have a slope that looks like this: $\frac{-5}{10}$ However, I need to bring it down to it's lowest terms, so I divided the numerator and denominator by -5 and I got: $\frac{1}{-2}$ ...
2
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3answers
8k views

How can I convert this negative fraction to a positive one?

This question may be very simple, but I get confused on things like it. If I have a fraction like this: $-\frac{x}{-2}$ How can I convert this negative fraction to a positive one? It does not ...
1
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2answers
2k views

Problem with getting variable by itself in fraction.

I have a problem that looks something like this: The difference of the quotient of a number and $-2$ from $12$ is $15$. So I started off like this: $12-\displaystyle\frac{x}{-2}=15$ Then I ...
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1answer
90 views

What fraction of smarties are brown?

If I have 26 smarties and 2 of them are brown, what fraction is that?
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2answers
2k views

What's the largest possible repeating decimal that can be created from a fraction (if n <= 9,999 & d <= 9,999)

What's the largest possible repeating decimal that can be created from a fraction if: The numerator has to be less than or equal to 9,999 The denominator has be less than or equal to 9,999? I know ...
3
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2answers
2k views

What are some effective ways in teaching fractions to 5th graders who are behind (special needs)

I am teaching a group of 8 kids on fractions and I did not realize how difficult this can be. These kids were selected by their teachers for needing additional outside help. I really need some advice, ...
6
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6answers
348 views

How to show that $\frac{x^2}{x-1}$ simplifies to $x + \frac{1}{x-1} +1$

How does $\frac{x^2}{(x-1)}$ simplify to $x + \frac{1}{x-1} +1$? The second expression would be much easier to work with, but I cant figure out how to get there. Thanks
6
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1answer
598 views

Check my proof of an algebraic statement about fractions

I tried to prove the part c) of "Problem 42" from the book "Algebra" by Gelfand. Fractions $\frac{a}{b}$ and $\frac{c}{d}$ are called neighbor fractions if their difference $\frac{cb-ad}{db}$ has ...
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1answer
85 views

How to chose a rational with a non-repeating fractional part in an arbitrary base?

How can I choose an $x\in[a,b)\subseteq[0,1)$, where $a,b\in\mathbb{Q}$, such that $x$ has a non-repeating fractional part in some chosen base? For example, say I'm looking at ...
4
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2answers
371 views

How to prove that construction of Farey sequence by mediant is coverage?

Farey sequence of order $n+1$ ($F_{n+1}$) can be construct by adding mediant value (${a+c \over b+d}$) into $F_{n}$, where ${a \over b}$ and ${c \over d}$ are consecutive term in $F_{n}$, and $b+d = ...
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3answers
107 views

In a fraction between integers, what denominators produce a periodic result?

I'm trying to remember something that a math teacher told me many years ago about fractions. If I remember correctly he said that, in a fraction between integers, when the denominator is a multiple of ...
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2answers
105 views

Is the index in an nth root allowed to be fractional?

We have nth roots that can be rewritten as fractional powers: $$\sqrt[n] x = x^\frac 1 n$$ I was looking around on Wikipedia and some other online material, but I couldn't find any definitive set of ...
3
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3answers
189 views

Finding the minimum of $\frac pq + \frac rs$ for distinct integers $p, q, r, s$ from $\{1,2,3,4,5,\ldots,16,17\}$

Here is the question: Four distinct integers $p$, $q$, $r$ and $s$ are chosen from the set $\{1, 2, 3, 4, 5, \ldots, 16, 17\}$. The minimum possible value of $\frac pq + \frac rs$ can be written ...
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6answers
1k views

How to simplify $\frac{4 + 2\sqrt6}{\sqrt{5 + 2\sqrt{6}}}$?

I was tackling through an olympiad practice book when I saw one of these problems: If $x = 5 + 2\sqrt6$, evaluate $\Large{x \ - \ 1 \over\sqrt{x}}$? The answer written is $2\sqrt2$, but I ...
8
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4answers
198 views

What is the 'physical' explanation of a division by a fraction?

For example, dividing by 2, means we cut something in two. But dividing by 0.5, can only be explained with multiplying something by 2. So, is there a "physical" explanation of dividing by 0.5? Is it ...
2
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1answer
57 views

Need an explanation of a particular expression transformation

Please, I need an explanation of the one transformation. I have the equation set and its solution. $$ \begin{cases} \frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 3\\\\ \frac{y}{x} + \frac{z}{y} + ...
3
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2answers
943 views

How do I get the integer part of a number by using basic arithmetic?

While it is trivial to simply remove the fractional part of an irrational or rational number, and in programming I could just use the floor() or ...
12
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2answers
461 views

proof of $\sum\nolimits_{i = 1}^{n } {\prod\nolimits_{\substack{j = 1\\j \ne i}}^{n } {\frac{{x_i }}{{x_i - x_j }}} } = 1$

i found a equation that holds for any natural number of n and any $x_i \ne x_j$ as follows: $$\sum\limits_{i = 1}^{n } {\prod\limits_{\substack{j = 1\\j \ne i}}^{n } {\frac{{x_i }}{{x_i - x_j }}} } ...
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1answer
20 views

Laplace Transform Help

The Laplace Transform of $\frac{3}{(2s+5)^3}$ is given as $\frac{3 t^2}{16}e^{-\frac{5}{2}t}$ Can someone please walk through how this was obtained? Especially the $\frac{3}{16}$?
2
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1answer
402 views

Rounding .5 - why isn't rounding away from zero the 'right' answer?

I am familiar with the issue of 'how should one roung .5?', and I am familiar with the conventional solutions, but I don't understand why there isn't a correct answer. When you're formulating a ...
0
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1answer
113 views

Find the set of all natural number that make $(n+1)/(n+3)$ reducible

Lets assume $d$ is a natural number which makes $(n+1)/(n+3)$ reducible, then $d|n+1$ and $d|n+3$. $d|[n+3-(n+1)] = d|2$ which means $d=1$ or $d=2$. $n+1$ and $n+3$ must be divisible by $2$ so all ...
2
votes
3answers
207 views

Proving that $\frac{n+1}{2n+3}$ is irreducible

I am trying to solve the following problem: Prove that the following fractions are irreducible for any n (n is a natural number and it cannot be null). $\frac{n}{n+1}$ $\frac{n+1}{2n+3}$ ...
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0answers
82 views

How to prove that $0.\overline{9} \neq 1$? [duplicate]

Possible Duplicate: Does .99999… = 1? $\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1$ but $0.\overline{3} + 0.\overline{3} +0.\overline{3} = 0.\overline{9}$ Does that mean ...
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4answers
175 views

Infinite repeated decimals in a number

I don't now how to convert infinite periodic decimal number $$x=3,1(42)=3.1424242...$$ to a fraction $$\frac{a}{b}$$ a,b are integers. Need to find a,b THANks
2
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3answers
151 views

Could $\frac x0 = \pm\infty$? [duplicate]

Possible Duplicate: Is it wrong to tell children that 1/0 = NaN is incorrect, and should be ∞? I remember that dividing by zero is frowned upon, because it is said that there is no real ...
4
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3answers
148 views

Expressing in rationals

I have this question to express it in a specific form Express $\dfrac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$ in the form $a \sqrt{2} + b \sqrt{3} + c \sqrt{7} + d \sqrt{42}$, for some rationals ...
3
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1answer
627 views

Nested Division in the Ceiling Function

During class, we were introduced to a proof that used the ceiling function. We assumed (without proof) that: $$ \left\lceil{\frac{n}{2^i}}\right \rceil= ...
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1answer
43 views

How to represent fraction $\frac{1}{a+b\cdot \sqrt[3]{2} + c\cdot (\sqrt[3]{2})^2}$ as $a_1 + b_1 \cdot \sqrt[3]{2} + c_1 \cdot (\sqrt[3]{2})^2$?

What do I have to multiply both numerator and denominator with to get the representation is asked? $a, b, c, a_1, b_1, c_1$ are rational numbers.
6
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1answer
521 views

Faster arithmetic with finite continued fractions

I was curious about different representations of rational numbers and came across the finite continued fraction (see wp:Finite_continued_fractions ). Note: I will refer to traditional rational ...
2
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1answer
195 views

Rationalizing fractions with multiple radicals

I am having trouble rationalizing $\frac{2}{\sqrt{2-\sqrt{2}}}$ I have tried multiplying the fraction by $\sqrt{2 + \sqrt{2}}$ and got $\frac{2\sqrt{2+\sqrt{2}}}{\sqrt{2}}$ I am not sure if that is ...
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1answer
313 views

Simplifying fraction with multiple radicals

I have an answer to a problem that I am working on but I have no idea how to rationalize the denominator because I have never worked with this type of problem before. The problem is: ...
2
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3answers
3k views

How do I go about simplifying this complex radical?

I'm having a difficult time trying to simplify the radical below. When I type the radical to the left into my calculator, I arrive at the correct answer to the right. But I cannot seem to figure out ...
1
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1answer
142 views

If I add a constant $c$ to each fraction's numerator and denominator in a sequence of fractions, how is the sequence affected?

Given a sorted ascending sequence of fractions, if I add a constant $c$ to each fraction's numerator and denominator, how is the sequence affected? For example, if I have a sequence in ascending ...
0
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0answers
19 views

Question on passing from rational to exponet

it's not a question itself, but I'd like to check if am I doing this passage from rational numbers to the exponent form right: From: $\sqrt{a\sqrt{a}}$ Evaluete to: $\sqrt{a*a^{\frac{1}{2}}}$ = ...