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

learn more… | top users | synonyms

0
votes
0answers
38 views

Transformation of fractions

I have a problem with a certain transformation of a fraction. This is part of a reudctio ad absurdum to show that there are infinit prim numbers. $\mathrm{P} = \prod_{i=1}^{n} p_i$ as the amount of ...
3
votes
1answer
38 views

Is the fraction of the irrational exponentiations of two coprime integers by a rational an irrational?

Consider two strictly positive integer coprimes $n, m\in\mathbb{N^*}$ and a rational $r=\frac{p}{q}\in\mathbb{Q}$. Consider furthermore that the three number statifies the following condition: ...
1
vote
3answers
44 views

Reducing a fraction, divisibility and indeterminate symbol

Quick question about validity, just to make sure. When I have a fraction in a form: $$\frac{3a + 3b}{a+b}$$ and I extract the common factor 3 out to get: $$\frac{3(a+b)}{a+b} \;=\; 3\frac{a+b}{a+b}$$ ...
1
vote
2answers
57 views

Calculating percentage to compensate for percent discount.

Missing something very basic here and cannot pin point it. We need to charge a client \$100 for a product. Let's say our payment processor charges us 10% on every transaction. We make this ...
0
votes
6answers
285 views

Why Not Define $0/0$ To Be $0$?

For every number $x$, $x\times 0=0$, hence $\dfrac{0}{0}$ can be any number! So $\dfrac{0}{0}$ "is knows as indeterminate" [1]. But what if we define it to be $0$? I already have an answer, but ...
0
votes
2answers
55 views

Is the product of two numbers both less than one less than one

I'm bad at mathematics, and I wanted to know something. Say there are two numbers $a$ and $b$ where $a, b \in \Bbb R$ $-1 < a < 1$ and $-1 < b < 1$ Is it necessary that $a \times b < ...
1
vote
1answer
95 views

Simplifying square root with fraction

I'm not sure about this equality $$4(-3+\sqrt {15})/4)^2 = (9-6 \sqrt{15} +15)/4$$ Hope some one can enlighten me. I will be facing more of such fractions, please guide me on how to solve/simplify ...
1
vote
0answers
21 views

Rational exponentiation?

Consider the following operation: $\left(\frac{a}{b}\right)^\frac{n}{m}$ where $a, n\in\mathbb{Z}$ and $b, m\in\mathbb{N^*}$. My question is: when the result is a rational number, how (formula or ...
0
votes
1answer
29 views

If $\sum_{k=1}^{p-1}\frac{1}{k}=\frac ba$ where $\frac ba$ is an irreducible fraction, then $b$ can be divided by $p^2$?

Question : Is the following true for any prime number $p\ge 5$ ? If $\sum_{k=1}^{p-1}\frac{1}{k}=\frac ba$ where $\frac ba$ is an irreducible fraction, then $b$ can be divided by $p^2$. ...
5
votes
1answer
131 views

$\frac{\prod_{i=1}^n (1+x_i)-1}{\prod_{i=1}^n (1+x_i/\delta)-1} \stackrel{\text{?}}{\le} \frac{(1+x_n)^n-1}{(1+x_n/\delta)^n-1} $ .

Let $x_1 \le x_2 \le \cdots \le x_n$. Let $\delta>1$ be some positive real numbers. I assume that $0\le x_i <1$, for $i=1,\ldots,n$ and $x_n >0$. Does the following expression hold? $$ ...
0
votes
1answer
80 views

Fractional-Recursive Sequence

Here from the fraction set we have a really hard question to be answered...suppose that a sequence is defined as a(n) = a(n-1) - 1/a(n-1), where a(0) is given. ...you already know what I'm asking you ...
0
votes
1answer
40 views

How to work out these fractions?

$\dfrac{-x^4 + 4x^2 + 6}{x}$ $\dfrac{7x^8 - 5x^5 + 9x^3 + x^2}{x}$ I have no idea how to do this. I was first thinking of doing $-x$ or collecting up the $x's$ but I'm not sure as I haven't dealt ...
0
votes
1answer
52 views

Calculating a Fraction's Reciprocal

Is there any way or equation that allows me to calculate the reciprocal of any fraction? I mean if i have 5/6 and i need it's reciprocal by using a formula or an equation to calculate it. Is there or ...
0
votes
1answer
45 views

Embarrassingly-basic fraction question

I'm trying to do a calculation at work to figure out what the average # of pages a visitor is viewing. I am given: 47,000 visits 12% of visits do not bounce (that is, 12% navigate the site at least ...
1
vote
4answers
110 views

How to compute $\frac{t}{t+1}$ to the form $1-\frac{1}{t+1}$?

How to compute $\frac{t}{t+1}$ to the form $1-\frac{1}{t+1}$? What else? Well. Well can you use long division?
11
votes
2answers
298 views

Is $\sum_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}=\frac{m^2-1}{3}$ true for $m\in\mathbb N$?

Question : Is the following true for any $m\in\mathbb N$? $$\begin{align}\sum_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}=\frac{m^2-1}{3}\qquad(\star)\end{align}$$ Motivation : I reached ...
0
votes
2answers
24 views

Total Time Expression Question

How do I do this question? Thanks!
0
votes
1answer
102 views

What are the big ideas needed to develop conceptual understanding of fractions?

In order to be able to perform arithmetic on fractions, students need to understand what fractions are and how they operate. Just teaching rules (e.g. "to add fractions you must have common ...
2
votes
1answer
44 views

Dividing rational expressions

How come I am able to divide the following: $$\frac{2}{2} = 1$$ Yet I am not allowed to divide the $2x$'s in the following: $$x^2 + \frac{2x}{2x} = x^2 + 1$$ Why can't I divide the $2x$ in ...
2
votes
1answer
38 views

special addition on fractions.

I would like to define a function $\oplus$ on $\mathbb Q$ ($\oplus:\mathbb Q^2\mapsto \mathbb Q$), such that (for all $a,b,c$): (commutativity) $a\oplus b=b\oplus a$ (associativity) $(a\oplus ...
0
votes
2answers
37 views

Percentage of Amounts

I'm studying and I'm not that sure how to answer this question. Is $97.1%$ $=$ $650,000,000$? I was going to find $2.9%$ of $650,000,000$ however this would be wrong as I would finding our the ...
1
vote
2answers
8k views

How do you simplify radical expressions with fractions in them [closed]

I need to know for algebra 2 homework ex. Radical 5/32
0
votes
3answers
79 views

Grade calculation

My teacher said that $\frac{1}{3}$rd of the final grade will be based on Exam 1, $\frac{1}{12}$th each based on Exam 2-5, and $\frac{1}{3}$rd again based on Exam 6, how will my teacher calculate my ...
2
votes
2answers
35 views

How to identify whether a fractional part of a number contains more that 2 digits.

EX. I want to accept numbers which have maximum of 2 digits after decimal points. i, e, 10.23 should be allowed and 10.233 should not be allowed. What mathematical operations can be done to ...
0
votes
3answers
76 views

How are fractions involving three numbers simplified.

This is something thats been bugging me since my high school. Is A/B/C = A/BC or AC/B
5
votes
2answers
700 views

Is 9/1 an improper fraction?

My son took a test in school. The teacher told them that they did not need to simplify improper fractions in their answers. On one question, for example, the answer of 28/3 was marked as correct. ...
0
votes
1answer
52 views

Unknown terms of the proportion

please help me solving this problem. The question is, find the unknown terms of the proportion $$\frac 23 = \frac x{12} = \frac y{15}.$$
4
votes
1answer
77 views

$\left\lfloor\left(\sum_{k=n}^{\infty}\frac 1{k^3}\right)^{-1}\right\rfloor=2n(n-1)$ is true for any $n\in\mathbb N$?

Question : Is the following true for any $n\in\mathbb N$? $$\left\lfloor\left(\sum_{k=n}^{\infty}\frac 1{k^3}\right)^{-1}\right\rfloor=2n(n-1).$$ Note that $\lfloor x\rfloor$ is the largest integer ...
0
votes
2answers
50 views

Simplifying Multiple Summations for worst case analysis

I'm figuring out a worst case analysis on a function. After converting it to a set of summations, and changing the sigma notations into summation formuale I ended up with: ...
0
votes
0answers
21 views

Calculating summary with variable multiplication factor

I have a formula of thermal conductance heat transfer rate. Here it is: $$ Q = \lambda{S (T_1 - T_2) \over L} \Delta t $$ For my calculations I have got some constant values available $$ Q = 0.58{1 ...
4
votes
1answer
85 views

Correctness of proof of division in ceiling function

My professor asked me to present a proof to my fellow students tomorrow that $$\left\lceil\frac{n}{2^k}\right\rceil = \left\lceil\frac{\left\lceil\frac{n}{2^{k-1}}\right\rceil}{2}\right\rceil$$ I ...
1
vote
1answer
137 views

$\sum_{k_1+k_2+\cdots+k_N=n,\ k_i\ge0\in\mathbb Z}\frac1{\prod_{j=1}^{N}\{(N-1)k_j+1\}}\le 1$ is true for any $n,N\in\mathbb N$?

Is the following true for any $n,N\in\mathbb N$? $$\sum_{k_1+k_2+\cdots+k_N=n,\ k_i\ge0\in\mathbb Z}\frac1{\prod_{j=1}^{N}\{(N-1)k_j+1\}}\le 1$$ Motivation : I've known the $N=3$ case. ...
0
votes
3answers
69 views

simplify fraction with radical in numerator, first steps?

$(\sqrt x−2)/(x−4)$ Looking to simplify a fraction with radical in the numerator.
3
votes
1answer
141 views

About two 'negative' continued fractions whose sum equals $1$

Letting $a_1,a_2,\cdots,a_r$ be integers which are larger than or equal to $2$, let us define $$[a_1,a_2,\cdots,a_r]=\frac{1}{a_1-\frac{1}{a_2-\frac{1}{\ddots-\frac{1}{a_r}}}}$$ (Note that the ...
1
vote
1answer
83 views

Any 'odd unit fraction' whose denominator is not $1$ can be represented as the sum of three different 'odd unit fractions'?

Let us call a fraction whose denominator is odd 'odd fraction'. Also, let us call an odd fraction whose numerator is 1 'odd unit fraction'. Then, here is my question. Question : Is the following ...
0
votes
3answers
67 views

Fractions and roots

I have this problem: $$\frac{\sqrt{18}+\sqrt{98}+\sqrt{50}+4}{2\sqrt{2}}$$ I'm able to get to this part by myself: $$\frac{15\sqrt{2}+2}{2\sqrt{2}}$$ But that's when I get stuck. The book says ...
12
votes
3answers
198 views

Any 'odd fraction' can be represented as the finite sum of different 'odd unit fractions'?

Let us call a fraction whose denominator is odd 'odd fraction'. Also, let us call an odd fraction whose numerator is $1$ 'odd unit fraction'. Then, here is my question. Question : Is the ...
0
votes
4answers
41 views

Reducing a fraction with exponents

How do I reduce $$ \frac{(k+1)^2}{k^2} $$ to simplest terms? My algebra is really rusty... Thanks!
2
votes
1answer
118 views

About the set of all the solutions $\mathbf x=(x_1,x_2,\cdots,x_m)$ to $\sum_{j=1}^m\frac{1}{x_j}=\frac1n$

Let $m,n$ be natural numbers, and let $S_{m,n}$ be the set of all the natural number solutions $\mathbf x=(x_1,x_2,\cdots,x_m)$ to the following equation : $$\sum_{j=1}^m\frac{1}{x_j}=\frac1n.$$ ...
3
votes
2answers
95 views

Calc 101 Question on simplifying a fraction

$$\lim_{h \to 0} \left(\frac 1h -\dfrac{1}{h^2+h} \right).$$ What do I do about the denominators?
4
votes
2answers
146 views

Fraction raised to integer power

if I have $(p/q)^n$ where $p,q,n$ are integers and $p/q$ is a... I don't know what you call it. Not a whole number, but something like 15/7 where you can't reduce it any more and it's non-integer. Can ...
0
votes
3answers
79 views

How to solve for x if it is on the top of the fraction?

so you have the equation: $$0.0850= \frac{x}{0.125} $$ How do you solve for x?
2
votes
1answer
78 views

Percentage of an amount?

I'm totally confused, we were doing a question in class and there are two answers but I'm not sure why one works and the other one doesn't. For example; there are 6000 pandas now and over 10 years ...
6
votes
1answer
130 views

How to best understand Euclid's definition of equal ratios? How does it relate to Dedekind cuts?

This is something I've been wondering about. When I think of "ratios" $x/y$ and $z/w$ as being "equal", with $x$, $y$, $z$, and $w$ being real numbers, this means the results of dividing the real ...
1
vote
1answer
56 views

What is a “constant fraction” of a total?

What is it mean to say that some quantity is a "constant fraction" of another quantity?
0
votes
0answers
12 views

If $d/dx_t ({\dot y}_t/y_t) > 0$ and $dy_t/dx_t < 0$ what can I then say about the sign of $d{\dot y}_t/dx_t$?

Assume that the rate of change in $y_t$ over time is ${{{{\dot y}_t}} \over {{y_t}}} = {x_t}$, where $x_t >0$. The derivative of this expression with respect to $x_t$ will be positive (well, it ...
1
vote
0answers
53 views

Does there exist an operation which partitions any fraction into the sum of the minimum number of unit fractions?

Motivation : I've been interested in finding an operation which partitions a fraction into unit fractions. The following is one of the operations which I've found. Let's start a rational number $q_0$ ...
0
votes
2answers
49 views

Simplifying two fractions on top of a third fraction

How would I go about simplifying this fraction: $$\frac{\frac{1}{x} - \frac{1}{a}}{x - a}$$ I've looked at similar questions such as this one but still can't seem to figure this one out. Any help ...
1
vote
4answers
128 views

Pre calculus fraction simplify question

Simplify: $$\frac{\frac{16x^4}{81} - y^4}{\frac{2x}{3} + y}$$ Wolfram alpha confirms the answer from the answer sheet: Wolframalpha answer
2
votes
1answer
28 views

Proportion Problem

I came across a problem about proportion as follow: There are 5 girls for every 12 boys, if the total number of children is 5200, how many are boys and girls? I tried following solution but the ...