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
47 views

solve ratio word problem without algebra

Four gallons of yellow paint plus two gallons of red paint make orange paint. I assume this makes six gallons. So the ratio is 4:2, or 2:1. Question: how many gallons of yellow paint, and how many ...
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3answers
50 views

How do I compute the individual terms of a polynomial to the power of -1?

If my polynomial $p$ is: $x+1$, obviously $p^{-1} = \frac{1}{x+1}$. Is it possible for me to split $\frac{1}{x+1}$ into a sum of two terms? In other words, is there an algorithm to write $p^{-1}$ as ...
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2answers
43 views

Simplifying algebraic fractions.

I cannot simplify the following expression. Please need help. $\large \frac{3}{x+1}-\frac{1}{x+3}+\frac{3}{1-x}-\frac{1}{3-x}$ Thanks in advance. Regards !
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0answers
48 views

Name of rational numbers of the form $p/q$ with $p,q$ prime

For the life of me, I cannot think of whether there is a name for fractions of the form $\frac{p}{q}$, where $p,q$ are both prime. Fractions such as $\frac{4}{5}$ are sometimes said to be in "reduced ...
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1answer
19 views

Magnitude relation of fractions for four real numbers with a condition

I would like to know if the following proposition holds or not. For all $a, b, c, d$ such that $a, b, c, d$ are positive real numbers, IF $a < b$ and $a - c > b - d \geq 0$ THEN $\frac{c}{a} ...
1
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2answers
54 views

Formula help with this equation

I don't know what the answer to this formula is, can someone please help me. I've tried lots of things but getting no where. If $x=\dfrac56+\dfrac{15}{18}-\dfrac{10}{12}$, then $(x-1)3=$ ?
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1answer
51 views

Linear Equation Problem

Evaluating the expression below: $\displaystyle \frac{2(6-x)}{3} = \frac{9(x+5)}{6} + \frac{1}{3}$ The answer is $-\frac{23}{13}$ but to obtain this answer what specific method do you use?
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0answers
73 views

If I have $\lfloor\frac{E}{K}\rfloor =\lfloor \frac{E}{K + m}\rfloor$, what is the upper limit of 'm' in terms of 'E' and 'k'

Given that E, K, m > 0, then is there a way to find out value of m in terms of E and ...
1
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2answers
70 views

Converting fractions / decimals to percentages

Can someone show me the methodology on how to convert 1.2794 to a percentage form? If I multiply it by 100, I get 127.94%, which is the correct answer. I'm not really sure 'why' I multiplied it by ...
0
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1answer
47 views

formula to apportion cost of transport among three people in a liftshare

I share lifts with Sed and Awk to work every day. We tally journeys owed on a spreadsheet. A week might look like this: ...
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2answers
35 views

Help with solving this fraction

Solve for $h$: $$125=\pi \left (\dfrac{5}{\sqrt[3]{\pi}} \right )^2h$$ This is from an optimization problem, in which the volume is the constraint of $125$. I've done everything in the ...
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4answers
53 views

Recognizing the proper polynomial factorization to solve an indeterminate limit

I had to solve the $\lim_{x \to 3} \frac{x^3-3x^2-x+3}{x^2-x-6}$ that is indeed an indeterminate form ($\frac{0}{0}$). The approach I adopted was to factor the polinomials so that I can deviate from ...
0
votes
1answer
80 views

period of recurring decimals

The period of a recurring decimal fraction $1/d$ is equal to the multiplicative order of $10$ mod $d$. For fractions with even period, the digits sum to 9 i.e. $1/7 = 0.(142857)...$ $$142\\ 857\\ ...
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2answers
51 views

Fraction Cross Multiply

Students first learning about fractions are often taught to "cross-multiply" when dealing with fraction with non-like denominators, however, in Mathematica, with the function ...
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3answers
38 views

mixed numbers subtraction vertically

In the following subtraction we are subtracting $2$ mixed numbers vertically. I know how it works except the last step. $$ 7 \frac{1}{3} - 4 \frac{1}{2} = 3 + \frac{-1}{6} = 2 + \frac{5}{6} = 2 ...
0
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1answer
192 views

How to solve this fraction within minute? (or trick)

I want to solve this question within minute but bcz of fraction it take more than a minute. does any one know a trick to solve this type question.plz share thanks
1
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1answer
195 views

How to calculate decimals of the fractional number 1/49?

I find this tricky one. How to calculate the first 50 digits/decimals of the fractional number 1/49? Two of my calculators and MatLab gives different answers so I'm curious, how this is calculated ...
8
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1answer
385 views

IMO 1979 problem

The question is $$\text{If }\, p, \ q\in \mathbb{N}, \;1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}=\frac{p}{q}.\qquad \text{Prove that } 1979\mid p.$$ So my solution went like ...
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2answers
71 views

A little explanation of square root in a fraction

I was on KhanAcademy when I ran into a problem involving a sine of a triangle, this was the solution: $$\frac{9}{3\sqrt{13}}$$ (9 being the length of the opposite and $3\sqrt{13}$ being the length ...
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4answers
128 views

change $0.684 210 526 3$ into a fraction

I am a non-mathematician who quit with math after middle school. Now I face a practical problem which I cannot solve. Suppose I want to turn $0.684 210 526 3$ into a fraction, how would I do that ...
0
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1answer
69 views

Can someone explain how this linear equation was solved [proof provided]

Can someone please explain to me the steps taken in the proof provided to solve the linear equation? [1]: http://i.imgur.com/2N52occ.jpg "Proof" What I don't understand is how he removed the ...
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1answer
53 views

A problem with rounding

Short version of the question: when rounded variable is used to calculate another variable, should I use rounded or unrounded value? Longer version: say I have two calculations: a / b = c and c + d = ...
4
votes
3answers
144 views

Proving that $\frac{3}{2} \sum_{k=1}^{\infty} \frac{4}{k^3+k^2} = \pi^2-6$

I'm trying to prove that: $$\frac{3}{2} \sum_{k=1}^{\infty} \frac{4}{k^3+k^2} = \pi^2-6$$ I've tried looking at the partial sums, but no luck there. I just have no idea where to begin. Knowing that ...
0
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1answer
63 views

Graphs of functions with fractional powers: $x^{p/q}$

How does changing the value of $\dfrac{p}{q}$ affect the drawing of the graph (domain/range/shape, etc.) How do you calculate asymptotes? Below is a question dealing with this type of function. ...
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1answer
36 views

help with simple order of operations in fractions?

first time poster here, so please be kind. :) I am working on an issue that I can't see past. I've got a worksheet with a multiple choice set of answers, but i KNOW they are all wrong! But maybe I ...
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2answers
54 views

manipulation of subtraction

I am trying to solve an induction problem and got stuck at this part. $$ 1 - \frac{n+2}{(n+2)!} + \frac{n+1}{(n+2)!} = 1 - \frac{(n+2) - (n+1)}{(n+2)!} $$ Shouldn't it be $$ 1 - \frac{n+2}{(n+2)!} ...
2
votes
2answers
87 views

The floor of a product of fractions

Evaluate: $ \displaystyle \Bigg \lfloor \prod_{n=0}^{248} \frac{33+8n}{29+8n} \Bigg \rfloor= \Bigg \lfloor \frac{33}{29} \times \frac{41}{37} \times \frac{49}{45} \times\ ...\ \times ...
2
votes
3answers
136 views

Rules for cancelling fractions with exponents

I have an expression that I need to simplify, I know the answer (wolframalpha) but I'm not sure of the rule that gets me there. $\dfrac{(\alpha) X_1^{\alpha -1} X_2^{1-\alpha}}{(1-\alpha)X_1^\alpha ...
1
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3answers
48 views

Irreducibility of gcd/lcm or lcm/gcd

Consider two irreducible fractions: $r_{1} = \frac{p_{1}}{q_{1}}$ $r_{2} = \frac{p_{2}}{q_{2}}$ Are these two fractions: $r_{3} = \frac{\text{gcd}\left(p_{1}, p_{2}\right)}{\text{lcm}\left(q_{1}, ...
14
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4answers
307 views

Show the identity $\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}=-\frac{a-b}{a+b}\cdot\frac{b-c}{b+c}\cdot\frac{c-a}{c+a}$

I was solving an exercise, so I realized that the one easiest way to do it is using a "weird", but nice identity below. I've tried to found out it on internet but I've founded nothingness, and I ...
1
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1answer
118 views

Evaluate the expression

Evaluate the expression $$\frac{1^2}{1^2-10+50}+\frac{2^2}{2^2-20+50}+\cdots+\frac{80^2}{80^2-80+50}$$ What should I do after that ? $\sum\frac{n^2}{n^2-10n+50}$ I'm not seeing anything to find ...
0
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5answers
93 views

largest fraction less than 1 [duplicate]

What is the mathematically rigorous way to answer the question: "what is the largest fraction less than 1"? (or to explain why it cannot be answered in the manner worded).
0
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2answers
22 views

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
votes
4answers
173 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: ...
0
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2answers
57 views

How to simplify this fraction

It's embarrassing, but I need help solving this one... Need some refresher course for algebra. $$ \frac y{y+\sqrt y} $$
1
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3answers
94 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 ...
1
vote
6answers
111 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.
1
vote
3answers
128 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 ...
0
votes
2answers
55 views

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

What is the formula of converting fraction into addition of fractions? $$\frac{4-s}{(s-3)(s-2)(s+1)}=\frac 1 4 \frac 1 {s-3} - \frac 2 3 \frac 1 {s-2} +\frac 5 {12} \frac 1 {s+1}$$
0
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4answers
61 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}\\ =& ...
0
votes
4answers
104 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 ...
0
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1answer
22 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 ...
0
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4answers
70 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!
0
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4answers
97 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 ...
0
votes
1answer
62 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 ...
0
votes
1answer
140 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 ...
5
votes
3answers
1k 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
72 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?
1
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2answers
42 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 ...
1
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1answer
51 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 ...