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

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Help Reducing simple fraction

This has got to be easy, but for some reason I just don't see it, probably because it's late. Solution key to a quiz we took online says that: $\frac{A^2 + A + AB}{(A + B)(A + B + 1)}$ can get ...
3
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4answers
221 views

Simplify this complex algebraic fraction

I'm stumped on this problem, I need to know how this answer was arrived at but my text book doesn't show this. $$\frac{\frac{1}{x+y}}{\frac{x}{y}}$$ The text book says the answer is this: ...
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2answers
70 views

How to simplify this fraction

It's embarrassing, but I need help solving this one... Need some refresher course for algebra. $$ \frac y{y+\sqrt y} $$
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3answers
129 views

Mixed number fractions vs regular fractions? $3\frac{1}{6}-1\frac{11}{12}$

I just passed Calculus 2 in college with an A and I'm rather embarrassed that I'm asking this question. My wife is taking an intermediate Algebra course in college and they gave her the below ...
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7answers
165 views

Why is $1 / x^y = x ^ {-y}$

I've known this rule for a long time, but I never got to understand why is that and how it works, could anyone explain to me how it is done? Any help is appreciated.
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4answers
183 views

How to work out this easy fraction?

I need help working out this fraction, I know it seems quite easy but I'm a bit stuck. The question is: $$\frac{5/2}{5/9}$$ My attempt was changing the denominators by multiplying by $2$ to make ...
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2answers
60 views

What is the formula of converting fraction into addition of fractions?

What is the formula of converting fraction into addition of fractions? $$\frac{4-s}{(s-3)(s-2)(s+1)}=\frac 1 4 \frac 1 {s-3} - \frac 2 3 \frac 1 {s-2} +\frac 5 {12} \frac 1 {s+1}$$
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4answers
67 views

Short expression $\frac{x^2-y^2}{x(x-y)}+\frac{x^2-y^2}{x(x+y)}$

I tried to short this expression: $$\frac{x^2-y^2}{x(x-y)}+\frac{x^2-y^2}{x(x+y)}$$ The result should be $2$ but I get: \begin{align} &\frac{x^2-y^2}{x^2-xy}+\frac{x^2-y^2}{x^2+xy}\\ =& ...
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4answers
119 views

Fraction Problem

The product of two fractions is 1/9. The larger fraction divided by the smaller fraction is 4. What is the sum of the two fractions? $\frac{a}{b}\frac{c}{d}=\frac{1}{9}$ I will assume that ...
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1answer
27 views

Scaling fractions

I have a set of values between $0$ and $1$ inclusive and I want to scale them so that they are all between $0.5$ and $1$ inclusive. What function can I use to do this? \begin{align} f(0) &\to ...
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4answers
73 views

Partial Fraction Decomposition.

The intial fraction is: $\dfrac{3x^3-x+4}{x^3+2x^2+6x}$ How should to make the decomposition for the denominator? Thanks!
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4answers
118 views

Why does $ \frac {\frac {1}{\sqrt{x}}}{x} = \frac {\sqrt{x}}{x^2} $?

A homework question recently asked for me to simplify: $\frac{1}{\sqrt{7}} \div {7}$ It's easy to see that this becomes $\frac{1}{7\sqrt{7}}$ But according to wolfram alpha this is also equal to ...
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1answer
81 views

simplify cube root of a fraction

I asking this question here to just check the work and that I have simplified it correctly. Given the formula $\Large \sqrt[3]{\frac{12m^4n^8}{5p^4}}$ We need to rationalize the denominator by ...
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1answer
853 views

Dividing an amount proportionately among unequal amounts

I have \$100000. I want to divide the amount proportionately to 300 employees. I want the money divided inversely from the top down. So, the top earner get \$0 and the lowest paid employee(s) get the ...
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4answers
8k views

What's the algebraic property where you can flip the fractions in an equation?

Earlier in algebra, we spent over 20 minutes trying to figure out $$ \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_e} \,\,\,\, \text{solve for }R_2 $$ when the teacher said "What you start out with is ...
2
votes
2answers
79 views

For how many integers $a$ is $\frac{2^{10} \cdot 3 ^8 \cdot 5^6}{a^4}$ an integer?

In Mathleague $11316$ Target #$4$, the question is: For how many integers $a$ is $$\frac{2^{10} \cdot 3 ^8 \cdot 5^6}{a^4}$$ an integer?
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2answers
187 views

Finding modular of a fraction

Im really into cryptography and to find the private key of a message I need to use modular arithmetic. I understand how modular arithmetic using a clock with whole numbers. But I get really stuck when ...
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1answer
126 views

GRE - Percentage Question

A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the ...
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2answers
286 views

Algebraic Manipulation question - trying to get alternate form

I'm currently working on algebraic manipulation, changing algebraic fractions into a chosen alternate form but I've hit a brick wall. I'm trying to get: $$\frac{2(3^x - 2^x)}{3^{x+1} - 2^{x+1}}$$ ...
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3answers
58 views

Proof of rational division…

I know that this how it's done but i used to know a simple proof which i have forgotten...so please if you know let me know.. $$\frac{\frac{a}{b}}{\frac{c}{d}} =\frac ab \frac dc.$$ When you ...
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3answers
71 views

Rationalizing a denominator.

The question instructs to rationalize the denominator in the following fraction: My solution is as follows: The book's solution is which is exactly the numerator in my solution. Can someone ...
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1answer
89 views

Algebraic Fractions, no I'm not kidding..

I know most of the people on this forum/site are very advanced, and I'm just sitting here wondering how in the world you do this equation, or "simplify" it. I know how to do equations like these when ...
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3answers
35 views

Equation with fractions

If $P=\frac{h}{1-h}$ then $h$ is equal to? Answer is: $\frac{P}{1+P}$ I understand that $\frac{P}{1+P}$ is the right answer for when I replace $\frac{P}{1+P}$ for h the answer solves the equation, but ...
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2answers
34 views

Fractions and invitations

Diane sent out 25 invitations to her birthday party. If 1/6 of the invitations were for her family, about how many invitations were for her family? Please show your work and explain.
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2answers
61 views

Simple algebra question - separating fractions

How does the following come about? I'm completely lost. Can anyone help me fill in the steps in between? $$ \frac{s+2}{s(s+1)} = \frac{2}{s} - \frac{1}{s+1} $$ I figured that $$ \frac{s+2}{s(s+1)} ...
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2answers
58 views

How to derive duration of unemployment?

The average monthly flow out of unemployment pool of $7.0$ million people each month is $3.1$ million. Put another way, the proportion of unemployed leaving unemployment equals $\frac{3.1}{7.0}$ or ...
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0answers
82 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
89 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: ...
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3answers
66 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: $$\frac{3(a+b)}{a+b} \;=\; 3\frac{a+b}{a+b}$$ ...
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2answers
108 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 ...
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8answers
450 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 ...
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2answers
66 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
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1answer
126 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 ...
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0answers
27 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 ...
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1answer
34 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 $p^2$. ...
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1answer
147 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
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1answer
130 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 $a_{n} = a_{n-1} - \dfrac 1{a_{n-1}}$, where $a_0$ is given. ...you already know what ...
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1answer
43 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
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1answer
59 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
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1answer
69 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 ...
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4answers
115 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?
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4answers
814 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 ...
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2answers
30 views

Total Time Expression Question

How do I do this question? Thanks!
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1answer
219 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
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1answer
54 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
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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 ...
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2answers
43 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 ...
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3answers
100 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
52 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
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3answers
103 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