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

learn more… | top users | synonyms

3
votes
2answers
105 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?
5
votes
2answers
207 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
115 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
87 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 ...
7
votes
2answers
214 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
135 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?
1
vote
0answers
58 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
52 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
149 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
31 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 ...
15
votes
2answers
601 views

What is the max of $n$ such that $\sum_{i=1}^n\frac{1}{a_i}=1$ where $2\le a_1\lt a_2\lt\cdots\lt a_n\le 99$?

What is the max of $n$ such that $$\sum_{i=1}^n\frac{1}{a_i}=1$$ where $a_{i}\ (i=1,2,\cdots,n)$ are integers which satisfy $2\le a_1\lt a_2\lt\cdots\lt a_n\le 99$ ? Also, I need how to prove that ...
1
vote
1answer
430 views

Compute operations with fractions using calculator

I have a CASIO fx-350MS, and I need to make fraction computations, like $\frac{7}{2} \cdot \frac{4}{5}$ for an exam where I have to compute a lot matrix multiplications (programmable calculators ...
-1
votes
1answer
35 views

How to create a series of fractions, such that each subsequence slice is smaller than the previous?

I need to develop a grading system for a course. The first assignment is evaluated based on only one criteria, a. The second assignment based on the first criteria, a, plus one new criteria, b, the ...
2
votes
2answers
96 views

Assuming there exist infinite prime twins does $\prod_i (1+\frac{1}{p_i})$ diverge?

Assume there are an infinite amount of prime twins. Let $p_i$ be the smallest of the $i$ th prime twin. Does that imply that $\prod_i (1+\frac{1}{p_i})$ diverges ?
3
votes
4answers
207 views

Can't simplify this fraction: $ \frac{1+x^6}{1+x^2}$

I've been having trouble simplifying this fraction : $$ \frac{1+x^6}{1+x^2} $$ Can anyone explain step by step on how to solve this? Thank you.
5
votes
2answers
140 views

REVISTED$^2$: Fraction Existence Proof

Question 1: I'm asked to prove that there exists an $n\in\mathbb{N}$ such that $$\frac{1}{n+1}\leq\frac{a}{b}<\frac{1}{n},$$ where $0<\frac{a}{b}<1$. Here $\frac{a}{b}$ is a fraction in ...
2
votes
2answers
87 views

When is the class of a fraction, the set of multiples of the fraction?

Let $D$ be an integral domain and $F=\mathrm{Frac}(D)$ be the field of fractions of $D$. We will look at $F$ as a set of equivalence classes from the equivalence relation $\sim$ on $D\times ...
1
vote
1answer
105 views

change values by a percentage factor

I have a problem in that i have a camera with a zoom range values between 1,000 and 30,000. The problem is i am accessing these values through a slider bar with values starting 250 to 750. How can i ...
0
votes
3answers
89 views

Ratio problem to find the woman weekly salary

A woman spend $5/8$ of her weekly salary on rent, and $1/3$ of the remainder on food, leaving $40 available for other expenses. What is the woman's weekly salary ? I have tried , i am really confused ...
4
votes
1answer
183 views

Algebraic structure of a set of Egyptian fractions of a positive rational?

It is said that every positive rational number can be represented by infinitely many Egyptian fractions (defined as the sum of distinct unit fractions). I am struggling to understand in a formal way, ...
1
vote
2answers
267 views

Bar Notation Problem

everyone! I came across a problem in math that dealt with bar notation. Does anyone know how, for instance, 1.234(with a bar notation over the 34) is expressed as a fraction? I know already how ...
4
votes
2answers
93 views

Why does my intuition for “order of divergence” for algebraic fractions fail?

I come across this identity once in a while but I actually never grasped it: $$\frac{2}{1-x^2}=\frac{(1-x)+(1+x)}{(1+x)(1-x)}=\frac{1}{1+x}+\frac{1}{1-x}$$ I'm surprised by it because I would ...
9
votes
0answers
253 views

To how many decimals is $\sum_ {k=1}^\infty \frac{k}{\sqrt{k!}} = \frac{49850839\,\pi}{29567947}$ correct?

Consider: $$\sum_ {k=1}^\infty \frac{k}{\sqrt{k!}} = \frac{49850839\,\pi}{29567947}$$ This is, as far as I'm able to check with my software, correct to at least 167 decimals. If anyone has the ...
0
votes
1answer
171 views

Finding percentage which is less

The number that is 50% greater than $60$ is what percentage less than the number that is 20% less than $150$ ? My try : I considered a number is 50% of $130$ which is greater than the $60$ and 20% ...
39
votes
1answer
865 views

Why does this ratio of sums of square roots equal $1+\sqrt2+\sqrt{4+2\sqrt2}=\cot\frac\pi{16}$ for any natural number $n$?

Why is the following function $f(n)$ constant for any natural number $n$? $$f(n)=\frac{\sum_{k=1}^{n^2+2n}\sqrt{\sqrt{2n+2}+{\sqrt{n+1+\sqrt ...
1
vote
0answers
85 views

Turn a number $x$ into a fraction with a denominator with no more than $k$ digits

Is there a function for turning any number $x$ into a fraction with a denominator that has a maximum of $k$ digits? (I'm sure there is, since Excel has one built in, I just can't figure out what it ...
22
votes
1answer
644 views

Simplify $\left({\sum_{k=1}^{2499}\sqrt{10+{\sqrt{50+\sqrt{k}}}}}\right)\left({\sum_{k=1}^{2499}\sqrt{10-{\sqrt{50+\sqrt{k}}}}}\right)^{-1}$

Simplify $$\frac{\displaystyle\sum_{k=1}^{2499}\sqrt{10+{\sqrt{50+\sqrt{k}}}}}{\displaystyle\sum_{k=1}^{2499}\sqrt{10-{\sqrt{50+\sqrt{k}}}}}$$ I don't have any good idea. I need your help.
3
votes
2answers
106 views

Question involving approximation, taylor series and proving

Question: Consider the approximation $$\ln(2)\approx 2\left ( \frac{1}{3}+\frac{1}{3\times 3^{3}}+\frac{1}{5\times 3^{5}} \right )$$ Prove that the error in this approximation is less than ...
1
vote
4answers
122 views

Simplifying compound fraction: $\frac{3}{\sqrt{5}/5}$

I'm trying to simplify the following: $$\frac{3}{\ \frac{\sqrt{5}}{5} \ }.$$ I know it is a very simple question but I am stuck. I followed through some instructions on Wolfram which suggests that I ...
-2
votes
4answers
138 views

Canceling in fractions sometimes gives a wrong result

When the same factor appears in the numerator and denominator, it can be canceled out: $$\frac{4a}{4a} = 1$$ However, in this more complicated fraction this does not work: $$\frac{4ac-b^2}{4a} \neq ...
0
votes
2answers
2k views

Numbers that cannot be expressed as fractions

What are Numbers that cannot be expressed as Fractions called?
1
vote
2answers
169 views

How to solve a ratio question

Studying for the GRE. In the GRE guide, it says that If the ratio is $2x:5y$, and this equals the ratio $3:4$, what is the ratio of $x:y$? I tried cross multiplying but I don't get the answer. ...
2
votes
0answers
97 views

Trigonometric functions of rational fractions of pi

Consider rational numbers $\frac{m}{n}$ and $\frac{m'}{n'}$, where $0<\frac{m}{n}, \frac{m'}{n'} <1$. Then $$\sin^2 (\tfrac{m}{n} \pi) = 2 \sin^2 (\tfrac{m'}{n'} \pi)$$ When $\frac{m}{n} = ...
0
votes
1answer
468 views

Ceiling to Floor Function Conversion Proof

I am working on a proof to convert a ceiling of a fraction to a floor of a fraction. I found this: \begin{aligned} q=\left\lceil \frac{n}{m} \right\rceil \;&\Leftrightarrow\; \frac{n}{m} \leq q ...
3
votes
2answers
89 views

How do we know $p/q$ can be expressed as a terminating fraction in base $B$ only if prime factors of $q$ are prime factors of $B$?

On cs.stackexchange I asked a math question: How to demonstrate only 4 numbers between two integers are multiples of .01 and also writable as binary. Yuval Filmus answered with a explanation ...
0
votes
2answers
624 views

Ratio - Basic Question

If ratio of A:B = 1:2 if it is doubled , should it be not 2:4 i see many problems where they are simply multiplying numerator by 2 please can some one explain
0
votes
4answers
96 views

breaking up fractions

I have these two fractions ${11 \over 31 }+{-11 \over 61}$ Adding them gives $330 \over 1891$ But how do I go back to the two fractions, once I've added them? I can get the denominators just by ...
1
vote
3answers
300 views

Reverse percentages

My mothers recently started doing a distance learning course. And is struggling with her mathematical questions. I'm trying to explain to my mother how to answer the following question. Despite my ...
1
vote
2answers
104 views

Fractional overlap of 1/2 and 1/3

Given a subset of the natural number sequence (positive integers starting from 1) we could say that $\frac12$ of the numbers in the set are divisible by 2. e.g if the set were ${[1,2,3,4,5,6,7]}$ we ...
18
votes
11answers
3k views

Why is $\frac{1}{\frac{1}{X}}=X$?

Can someone help me understand in basic terms why $$\frac{1}{\frac{1}{X}} = X$$ And my book says that "to simplify the reciprocal of a fraction, invert the fraction"...I don't get this because isn't ...
0
votes
2answers
149 views

removing the remainder of a fraction

I would like to remove the remainder from a fraction if possible. I want a function $$f(x,y) = x/y - remainder$$ for example $$f(3,2) = 1$$ $$f(7,2) = 3$$ $$f(12,5) = 2$$ It seems so simple but ...
4
votes
3answers
404 views

Why are only fractions with denominator 2 and 5 non-repeating?

Given a rational number $\frac{n}{d}$, I understand that in the base $10$ number system, the number can be represented as a non-repeating decimal number if and only if $d$ has only prime factors of ...
1
vote
4answers
107 views

question about partial fractions why $\frac{6x^2+19x+15}{(x-1)(x-2)^2}=\frac{A}{(x-1)}+\frac{B}{(x-2)}+\frac{C}{(x-2)^2}$

can anyone tell me why $$\frac{6x^2+19x+15}{(x-1)(x-2)^2}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{(x-2)^2}$$ I don't undestand the $\frac{C}{(x-2)^2}$ and also what is wrong according to basic math ...
4
votes
2answers
132 views

Proof for $\displaystyle\sum_{k=1}^n k^a$ equaling a sum of fractions

I know $\displaystyle\sum_{k=1}^n k^2$ equals $n/6+n^2/2+n^3/3$, but... why? And I also know that $\displaystyle\sum_{k=1}^n k^3$ equals $n^2/4+n^3/2+n^4/4$, but... is there a pattern so I can easily ...
2
votes
2answers
54 views

which parameters always make this rational equation evenly divisible?

Hi guys I have the following equation: $$x = \dfrac{a + b \times c - b}{c}$$ This is what I know about each variable: $$a \ge 64$$ $$b \ge 0$$ $$8 \le c \le a$$ My questions is there a concise way ...
-1
votes
1answer
35 views

$\frac{-4z^{-1}}{(1-\frac{1}{4}z^{-1})(1-4z^{-1})} = \frac{16}{15}\frac{1}{(1-\frac{1}{4}z^{-1})}-\frac{16}{15}\frac{1}{(1-4z^{-1})}$

Can anyone help me clarify how this rewriting is done? $$\frac{-4z^{-1}}{(1-\frac{1}{4}z^{-1})(1-4z^{-1})} = \frac{16}{15}\frac{1}{(1-\frac{1}{4}z^{-1})}-\frac{16}{15}\frac{1}{(1-4z^{-1})}$$
0
votes
1answer
37 views

How to show that $\frac{1}{(1-\frac{1}{4}z^{-1})(1-\frac{1}{4}z)} = \frac{-4z^{-1}}{(1-\frac{1}{4}z^-1)(1-4z^{-1})}$

Can anyone help me clarify what rule is used in this rewriting of this fraction? $$\frac{1}{\left(1-\dfrac{1}{4}z^{-1}\right)\left(1-\dfrac{1}{4}z\right)} = ...
2
votes
1answer
158 views

Tetration and its inverse to various exponents

I've recently seen in my studies tetration, or the next operation in the addition, multiplication, exponentation... series. I've also heard much discussion about how to extend this operation to ...
1
vote
2answers
188 views

Solving Simple Mixed Fraction problem?

How do you wrap your head around mixed fraction, does anyone knows how to figure out, can someone give me an example how it can be solved?
5
votes
1answer
397 views

Is it possible to rationalize a denominator containing two cube roots?

The fraction in question is $$-\frac{12}{\sqrt[3]{12\sqrt{849} + 108} - \sqrt[3]{12\sqrt{849} - 108}}$$ And was reached in calculating the solution to $x^4 - x - 1 = 0$. I've tried all the standard ...