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

learn more… | top users | synonyms

-1
votes
1answer
26 views

Bob and Jim's Coins [on hold]

Bob had 52 more coins that Jim after Jim gave 1/5 of his coins to him. If they had 260 coins total, how many coins did Bob have at first?
5
votes
7answers
120 views

What happens when you add $x$ to $\frac{1}{3}x$?

I am dealing with an equation that requires me to add $x$ to $\frac{1}{3}x$: $x + \frac{1}{3}x$ = ?? I know this might be simple to any of you on this site, because you are all asking questions with ...
2
votes
5answers
84 views

When is $\sqrt{x/y^2}$ equal to $\sqrt{x}/y$?

The solution to the quadratics is given by $r = -\dfrac{b}{2a}\pm\sqrt{\dfrac{b^2-4ac}{4a^2}}$, which is shortened to $r = -\dfrac{b}{2a}\pm\dfrac{\sqrt{b^2-4ac}}{2a}$, but I'm wondering how if this ...
3
votes
3answers
6k views

Detecting that a fraction is a repeating decimal

Given any fraction where both the numerator (N) and denominator (D) are both positive and are both whole numbers. Without manually dividing N by D, is it possible to pre-determine if the resulting ...
1
vote
3answers
42 views

A fraction problem [on hold]

$$a = x + \frac1x \\b =y + \frac1y \\ c = xy +\frac1{xy} $$ Express $c$ in terms of $a$ and $b$
2
votes
2answers
36 views

Property of fractions

Given two fractions $\frac{h}{k}$ and $\frac{h^{'}}{k^{'}}$ both in reduced form. I am unable to find a case when $\frac{h+h^{'}}{k+k^{'}}$ does not lie in the interval $\big[ \frac{h}{k},\frac{h^{'}}{...
0
votes
1answer
25 views

simple integration artimethic error

I am trying to integrate a polynomial but I couldn't get the correct answer somehow. I feel like I'm making a mistake when evaluating the integral. $$\pi\int_{-1}^1{1-2x^2+x^4}dx=[{x-{2x^3\over3}+{x^...
2
votes
3answers
76 views

Can fractions actually be converted to decimals?

I was working on a spreadsheet in Excel (I'm a plebe, I know), and I came across a fraction that actually equated to 33.3% of a total number. While looking at it, and looking at the number that went ...
0
votes
1answer
25 views

Working out cost based on time spent - simple math [closed]

I did a task, and my hourly rate is $£25$ , I spent a total of $36$ minutes on it, how can I work out the total amount of time spent on the task? My attempt: I can do this for simple sums such as ...
0
votes
1answer
44 views

Help with some algebra

Can anybody explain to me how they went from this $$y − y_1 = \frac{y_2 − y_1}{x_2 − x_1} (x − x_1)$$ to this. $$(y_1 − y_2 )·x − (x_1 − x_2)·y − (y_1 − y_2 )·x_1 + (x_1 − x_2)·y_1 = 0$$ Its ...
3
votes
2answers
101 views

Evaluate $1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{…}}}}$ when you see $15$ fraction lines

Evaluate $1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{\ddots}}}}$ when you see $15$ fraction lines. I have solved this problem but using a quater calculating I come from down to up 15 times and ...
-1
votes
2answers
59 views

Find the integer closest to $ a - b$ [closed]

Let $$a = \frac{1^{2}}{1} + \frac{2^{2}}{3} + \frac{3^{2}}{5} + \ldots + \frac{1001^{2}}{2001}.$$ Let $$b = \frac{1^{2}}{3} + \frac{2^{2}}{5} + \frac{3^{2}}{7} + \ldots + \frac{1001^{2}}{2003}.$$ ...
0
votes
1answer
37 views

How to solve: $\ \lim_{n \to +\infty} \frac{n^n + \frac {1}{n}}{(n + \frac {1}{n})^n} \ t^n $

How can I solve: $$\ \lim_{n \to +\infty} \frac{n^n + \frac {1}{n}}{(n + \frac {1}{n})^n} \ t^n $$ tis a whole number. Thank you very much! Please tell me your ...
4
votes
5answers
459 views

What is the fastest method to find which of $\frac {3\sqrt {3}-4}{7-2\sqrt {3}} $ and $\frac {3\sqrt {3}-8}{1-2\sqrt {3}} $ is bigger manually?

What is the fastest method to find which number is bigger manually? $\frac {3\sqrt {3}-4}{7-2\sqrt {3}} $ or $\frac {3\sqrt {3}-8}{1-2\sqrt {3}} $
0
votes
1answer
38 views

Pre-Algebra Fractional Exponent Question

Why does $t^{\frac{3}{2}} \cdot t^{\frac{1}{2}} = t^2$? What I tried to do was multiply the exponents together $\frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}$ so my final answer was $t^{\frac{3}{4}}$ ...
0
votes
1answer
55 views

Proof of $\frac{q_n}{q_{n-1}} = [a_n,a_{n-1},a_{n-2},…,a_2,a_1]$?

Proof of continued fractions axiom. Let $c=[a_0,a_1,a_2,\dots,a_n,\dots] = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \ddots}}$ be a continued fraction which could be finite or infinite. By $\frac{p_n}{...
-1
votes
1answer
35 views

when the sum of some fractions equal to 1. [duplicate]

$r$ is a number such that $r=p^a$. If the sum of some fractions equal to $1$ and one of the denominators is divisible by $r$ then there is another denominators that is exactly divisible $r$. It seems ...
2
votes
1answer
34 views

when the sum of some fractions be $1$

prove if we want that the sum of some fractions be $1$ and the denominators of one of them is $d$ then another denominators should divisible by $d$ or $d$ should be divisible to another denominators. ...
0
votes
3answers
92 views

Very Basic Math question?

How can I prove that $$\frac{r}{(1-x)^2} + \frac{rx}{x(1-x)} = \frac{r}{x(1-x)^2}$$ I have tried to prove that , but I could not , can someone help me please ? Thanks
0
votes
2answers
35 views

Please help me understand this simple fraction

I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this Now as I'm trying to find further exercices, I keep stumbling upon ...
8
votes
2answers
105 views

Does $\frac{x-2}{3x-6}$ really equal $\frac{1}{3}$?

In my maths lesson today we were simplifying fractions by factorising. One question was something like this: $\frac{x-2}{3x-6}$, which I simplified as $\frac{x-2}{3x-6}=\frac{x-2}{3(x-2)}=\frac{1}{3}$....
3
votes
3answers
62 views

multiplication and addition fractions

Try to visualize process of multiplication fraction addition is obvious, need to split each part to the same size - "reduce to a common denominator" for example $$\frac23 +\frac24 = \frac{8}{12}...
1
vote
4answers
38 views

fraction division understanding

Want to visualize rule division of fraction. For example 1) 2 2 4 _ * _ = _ 2 3 6 in this case we "split" each piece of cake in numerator to the ...
1
vote
1answer
94 views

For which $a,b\in \mathbb{N},$ is $\frac{\sqrt{2}+\sqrt{a}}{\sqrt{3}+\sqrt{b}}$ is a rational number.

I found the following problem on a Olympiad question paper: For which $a,b\in \mathbb{N},$ is $$\frac{\sqrt{2}+\sqrt{a}}{\sqrt{3}+\sqrt{b}}$$ a rational number. I am unable to solve it. Any help ...
2
votes
2answers
90 views

How to remove parentheses from $x/(y-z)$

To remove parentheses from $x(y-z)$ I reword it to $xy-xz$. How do I remove parenthesis from $x/(y-z)$?
1
vote
1answer
65 views

Estimation of fraction of integrals

(edited for more clarity) For a given function $f$, which is continuous, and $a < b$ real numbers, I need to make an estimation of the type $ \Bigg| \frac{\int_a^b f(t) (-t)dt}{\int_a^b f(t)dt} \...
1
vote
4answers
46 views

How can I find the remainder for the following problem?

This is for algebra 2 honors. Of course I can long divide or use synthetic, but that would take a while. $$\frac{2x^{100}-3x+4}{x-1}$$
0
votes
1answer
16 views

Ratio and fraction, transfer of water from Container A to B.

The ratio of the capacity of Container A to the capacity of Container B was 4:1. 2/9 of Container A was filled with water. If all the water in Container A is poured into the empty Container B, what ...
-1
votes
2answers
32 views

Finding limits when given $2$ different limits.

Let $\lim\limits_{x\to -1} f(x) = 8$ and $\lim\limits_{x\to -1} g(x) =-4$. Find $\lim\limits_{x\to -1} \dfrac{f(x)}{g(x)}$. Answer Choices are: A. $-2$ B. $12$ C. $-1/2$ D. $-1$ I started out ...
2
votes
2answers
45 views

Determining a Limit when given 2 limits

Let$\lim\limits_{x\to -3} f(x) =2$ and $\lim\limits_{x\to -3} g(x) =9$ Find $\lim\limits_{x\to -3} [\frac{[f(x)]^2}{2+g(x)}]$ I believe that the answer is $4/11$ but I wanted to check with you guys ...
2
votes
1answer
38 views

Irrationality of the decimal fraction

Surfing the internet I bumped into a very interesting problem, which I tried to solve, but got no results. The problem is following: let $h_n$ be the most right non-zero digit of $n!$, for example, $...
0
votes
0answers
14 views

Why is (x-xi)^n still a linear factor (Partial Fraction Decomposition)?

When we perform a Partial Fraction Decomposition and one of the solutions of the denominator is a multiple solution (let's say quadratic), we write: $$\frac{A_{1}}{(x-x_{i})} + \frac{A_{2}}{(x-x_{i})^...
26
votes
2answers
2k views

Why is the decimal representation of $\frac17$ “cyclical”?

$\frac17 = 0.(142857)$... with the digits in the parentheses repeating. I understand that the reason it's a repeating fraction is because $7$ and $10$ are coprime. But this...cyclical nature is ...
1
vote
2answers
42 views

Irreducible fraction of a given rational

Given a rational $ r \in \mathbb Q $, how to find the irreducible fraction $ \frac a b = r $? Any direct formula based on the digits of $ r $, instead of successive approximations by increasing ...
2
votes
3answers
58 views

Find two fractions such that their sum added to their product equals $1$

This is a very interesting word problem that I came across in an old textbook of mine. So I managed to make a formula redefining the question, but other than that, the textbook gave no hints really ...
0
votes
3answers
33 views
0
votes
0answers
22 views

Simplifying MATLAB fraction to make numerator equal to 1

I have a function which returns this fraction, which is not in the needed format. $$\frac{36893488147419103232*z^2}{36893488147419103232*z^2 - 672282507639892864*z + 6656262451880127}$$ I need it to ...
1
vote
0answers
12 views

unique ringhomomorphism from the Field of fractions to another field

$R$ is a ring, $L$ a field and $K$ the fraction field constructed from $R$. For any injective ring homomorphism $f=R \rightarrow L$, there is a unique ring homomorphism $\tilde{f}:K \rightarrow L$ ...
1
vote
1answer
26 views

Partial Fraction Decomposition - Multiple Answers-Question

Now I do understand how partial fraction decomposition works and why you can do it, but there is one case that I don´t understand. And that is, the following: $$\frac{A_{1}}{(x-x_{1})} + \frac{A_{2}}{(...
1
vote
1answer
22 views

Auto loan calculator website widget

I was going to try my luck on StackOverflow, but I have a feeling my issue here is on order of operations. I'm using the loan calculation found here to build a loan calculator for a clients website. ...
0
votes
1answer
27 views

Total Percentage Change - Why does this work?

Algebraically this works, but I'm looking to understand (1) why it works and (2) if there is a simpler formula. Problem: I want to get total % change over time. Facts: Example Data - Jan 2013 - ...
3
votes
0answers
29 views

Origin/history of mixed number notation with misleading hyphen, e.g. 1-1/2

So there is a system of writing mixed numbers (that is, a combination of whole number and fraction, used instead of an “improper” fraction) used in cases where typing vulgar fractions (e.g. ½) ...
5
votes
2answers
59 views

Can fractions be written as over 1?

I know that all whole numbers can be written as the whole number divided by one. I was wondering if fractions could be written the same way, for example.. Can $1\over2$ be written as $1/2\over1$ ...
0
votes
2answers
38 views

Partial fractions - alternative result

I have the following fraction: $$ \frac{z}{(z-1)(z-2)} $$ When I try to decompose it to partial fractions, I get: $$ -\frac{1}{z-1} + \frac{2}{z-2} $$ But the result in my book is: $$ -\frac{z}{z-...
4
votes
7answers
2k views

When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$…

When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$. What is the denominator of the fraction? I tried, Let the numerator of the fraction be $x$ and the denominator ...
2
votes
1answer
21 views

Partial Fraction Decomposition with complex poles

I have a function which I'd like to perform partial fraction decomposition on, to allow easier inverse laplace transform. $$F(s) = \frac{1}{s(s^2+140s+10^4)}$$ I begin with finding the poles $$s = ...
1
vote
1answer
53 views

Is the answer key wrong? or it's me?

ok, so im reviewing for a math test and the following question is from the practice final exam. Rationalize the denominator in the example: $$\frac{\sqrt {2}}{\sqrt {x-3}}$$ after multiplying both ...
-4
votes
1answer
31 views

How would you solve this problem by multiplying by the reciprocal? [closed]

How would you solve 3/1 ÷ (1/2)/1 ? Please show all the steps clearly! I know you have to multiply by the reciprocal when dividing fractions, however you just get back to the original problem when ...
1
vote
4answers
101 views

Intuitively, why does $\dfrac{a}{c} = \dfrac{1}{\dfrac{c}{a}}$?

For intuition, I reference objects. Imagine making a dessert with: $a$ as apples and $c$ as chestnuts. Question. How and why is $\dfrac{a}{c} \qquad (3) \quad = \quad\dfrac{\color{red}{1}}{\dfrac{c}{...