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

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2answers
64 views

Fractions with Hours and Days

So the question is: The number of hours left in a day on Mars was $\frac{1}{4}$ on the number of hours that had already passed. How many hours were left in the day? Day on Mars: $40$ hours. I did ...
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3answers
111 views

Can $1\over 1$, $1\over 2$, $1\over 3$, $1\over 4$, etc. be calculated by the added fractions below?

About $1\over 1$, $1\over 2$, $1\over 3$, and $1\over 4$, can $1\over 4$ also be written as $1\over 5^1$+$1\over 5^2$+$1\over 5^3$+$1\over 5^4$+...=$1\over 5$+$1\over 25$+$1\over 125$+$1\over ...
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2answers
264 views

Understanding the concepts of division and fractions

$\require{cancel}$ I'm having some issues regarding division so I will start by asking how this concept was developed throughout the ages: What was the first civilization to introduce the idea of ...
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1answer
38 views

How to calculate a whole amount with fractions?

A contractor first completes $7/16$ of a building. Then he completes $1/4$ of it. And finally completes $2/5$th of the remainder of the building. If there is $36$ days left to finish the construction ...
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1answer
182 views

How to calculate a distance with different fraction ratios?

This is the math question for my sixth grader son. The answer is $136$ meters but could not figure it out. Can someone please explain how to solve it. Thank you. Adam first walks $3/8$th of a road. ...
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1answer
46 views

Maple, simplyfing ODEs questions

I'm a novice using Maple 16. I'm using it mostly to check my DE homework solutions. And it happens a lot that I get stuff like in the picture. I mean (if I'm not missing anything important) that ...
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3answers
94 views

Which one is less than others?

Which one is less than others? $\frac{3}{5} , \frac{2}{3} , \frac{6}{13} , \frac{23}{38}$ Yes the answer is $\frac{6}{13}$ but the real question is this: I've a 12 years old brother and he just ...
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3answers
83 views

Given that $yz:zx:xy = 1:2:3$ and $\tfrac{x}{yz}: \tfrac{y}{zx} = 1:k$, find $k$

Given that $yz:zx:xy = 1:2:3$ and $\dfrac{x}{yz}: \dfrac{y}{zx} = 1:k.$ Find $k$. I understand that $ k = \frac{y^2}{x^2}, y = 1,$ and $x = 2$. Therefore $k = \frac{1}{4}$. This also brings me ...
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15answers
6k views

Why rationalize the denominator?

In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$. An answer on this site says that "there ...
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3answers
71 views

How to show that show that $\frac{v+u}{1+ uv/c^2}=c$ when $u=c$?

I am trying to show that $\dfrac{v+u}{1+\dfrac{uv}{c^2}}=c$ when $u=c$. Context It's needed for a physics proof that I'm working on. This is the formula for relative velocity, $u$ represents the ...
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2answers
225 views

Why do I get $0.098765432098765432…$ when I divide $8$ by $81$?

I got this remarkable thing when I divided $16$ by $162$, or, in a simplified version, $8$ by $81$. It's $0.098765432098765432\cdots$, or more commonly known as $0.\overline{098765432}$, with all the ...
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6answers
202 views

How $\frac{1}{\sqrt{2}}$ can be equal to $\frac{\sqrt{2}}{2}$?

How $\frac{1}{\sqrt{2}}$ can be equal to $\frac{\sqrt{2}}{2}$? I got answer $\frac{1}{\sqrt{2}}$, but the real answer is $\frac{\sqrt{2}}{2}$. Anyway, calculator for both answers return same numbers. ...
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2answers
126 views

How to simplify this expression with radicals? $3\sqrt2 - \sqrt{32} + \sqrt{\frac{80}{16}}$

I don't understand how I could calculate this: $3\sqrt2 - \sqrt{32} + \sqrt{\dfrac{80}{16}}$ My answer is $-\sqrt2 + \sqrt5$, but the real answer should be $\dfrac{9-4\sqrt2}{4}$.
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1answer
61 views

How to differentiate for critical points with variable in denominator

sorry for posting a particular problem, this is maybe more of an algebra problem than a calculus problem, but it does involve differentiating so I thought I would state the problem as one. I am ...
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3answers
133 views

How to solve following limit

I've been struggeling a bit with the following limit: $\lim\limits_{x \to 0} \frac{a- \sqrt{a^2 - x^2}}{x^2}$ The solution is: If a < 0 then -$\infty$ . If a > 0 then $\frac{1}{2a}$ But I don't ...
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1answer
48 views

Are some infinite fractions in one counting system non-infinite in another?

I'm curious whether some infinite periodic fractions in one counting system (e.g. decimal - 10/3 = 3.33333...) turn out to be non-infinite in another system and vice - versa. Please excuse me if my ...
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3answers
94 views

Split a whole number into fractions, find which of thoses fractions another belongs in

I want to split a number into $n$ parts and then take another number (which is less than or equal to the first number) and see which of the fractions the other number belongs to. For example, split ...
2
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2answers
263 views

Determine if $\frac{k-1}{k}+\frac{1}{k(k+1)}=\frac{k}{k+1}$ holds

How to prove if the following equality holds? $$\frac{k-1}{k}+\frac{1}{k(k+1)}=\frac{k}{k+1}$$ Maybe finding a common denominator would work, but I have no idea how to do it in this example. I see ...
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1answer
77 views

What is the chances of a duplicate in this equation

I'm not very good at math; However I have a scenario where I'm trying to find the chance of duplicate for randomly generated data. In a nuttshell I have a "bag" with 62 different items, lets say a ...
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3answers
53 views

How to find the value of $a$ and $b$ from this limit problem with or without L'Hopital's formula?

Consider the limit: $$\lim_{x\to4} \frac{x^2+ax+b}{x-4} =14$$ Question: How can I find the values of $a$ and $b$? Attempt: My first thought is, we need to use L'Hopital's rule to make sure ...
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4answers
392 views

Find the fraction where the decimal expansion is infinite?

Find the fraction with integers for the numerator and denominator, where the decimal expansion is $0.11235.....$ The numerator and denominator must be less than $100$. Find the fraction. I ...
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1answer
269 views

Closed-form of infinite continued fraction involving factorials

Is there a closed form of this: $$ 1!+\dfrac{1}{2!+\dfrac{1}{3!+\dfrac{1}{4!+\ldots}}} $$
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1answer
77 views

Can two integer divisions be unified above one whole fraction line?

Is there a way to combine two integer divisions (i.e. division with the result rounded down to the nearest integer) into a single division operation? What I mean is that, when working with with real ...
13
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4answers
1k views

Is Cantor's diagonal argument dependent on the base used?

Applying Cantor's diagonal argument to irrational numbers represented in binary, one and only one irrational number can be generated that is not on the list. Wikipedia image: But if you change ...
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1answer
27 views

Help clarifying fraction and percentage question.

I have the following problem: Convert the mixed number $18 \frac 25 \%$ to an improper fraction, then, use the definition of percent to convert to fractional notation. If I follow the steps of ...
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7answers
194 views

Why Is $y^{-1}$ = $\frac{1}{y^1}$?

Basically, I'm asking 'Is there any place where I can access a compendium of formal mathematical proofs'? I need to know what processes mathematicians went through to declare $(-1)(-1)=1$ and so on. I ...
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1answer
32 views

Relating an expression to two similar ones

Is it possible to express $C$ solely in terms of $A$ and $B$, where $$A = \dfrac{m}{x+z}, B = \dfrac{n}{y+z}, C=\dfrac{m+n}{x+y+z}$$ and $m,n,x,y,z>0 \ ?$ If not, how close can I get?
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2answers
72 views

Hard problem with fractions

I can't solve the following problem. A person is $x$ years old. Find his age if the following is true. In a group of $x$ people each one started taking pictures of each of the others. At some point ...
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1answer
33 views

Basic solving for fractions

Can someone help me with this? I am a beginner to physics and in a question i need no isolate a constant to solve for another one. A/B=C/D solve for D step by step please.
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2answers
43 views

How to re-write one fraction as two others.

I have the two following fractions. $$ \dfrac{A}{Bx^{\alpha+1}}$$ and $$ \dfrac{C}{Dx^{\alpha+\beta}}$$ The form i want $$ \dfrac{E}{Fx^{\alpha+\beta+1}}$$ I was thinking to do partial fractions or ...
2
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4answers
287 views

How to extract fraction from a floating point number

I'm making some tests with float type (floating point number) with programming and in some of my tests I need to extract the fraction that originates the float value. Let $ x $ be a floating point ...
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1answer
101 views

How is it possible that when you divide 1 by 9,899, you get two-digit Fibonacci numbers also being carried, etc.? [duplicate]

When I divided $1$ by $9,899$, I got two-digit Fibonacci numbers also being carried: $0.0001010203050813213455904636\dots$ When I divided $1$ by $89$, I got one-digit Fibonacci numbers at the ...
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0answers
108 views

How is it possible that you get two digit numbers multiplied by three at the beginning if you divide 1 by 97, etc.? [duplicate]

I divided $1$ by $97$ and I got this: $0.0103092783\dots$; I got two digit numbers being multiplied by three at the beginning. I divided $1$ by $997$ and I got a similar thing: ...
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3answers
113 views

What is $\frac{9}{3} - \frac{1}{2}$?

I need to compute $\frac{9}{3} - \frac{1}{2}$. I got an answer of $\frac{8}{6}$ but that is incorrect. $\frac{5}{2}$ is the correct answer. How is this possible?
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2answers
23 views

Determine rational expression

Can somebody help me with the following word problems: Problem #1 Russel's combine can clear a field in 24 tractor hours. Jerome's combine can clear the same field in 30 hours. If they work ...
2
votes
1answer
69 views

Rewriting to quintic equation

Consider the force $F_\Omega$: $$ F_\Omega= \Omega^2\left(x -\frac{\beta\left(x+\alpha R\right)R^3}{\left(\left(x+\alpha R\right)^2\right)^{3/2}} -\frac{\alpha\left(x-\beta ...
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1answer
67 views

$(-3)^{3/2} \neq (-3)^{6/4}$

$(-3)^{\frac{3}{2}}=-3\sqrt{3}i$ $(-3)^{\frac{6}{4}}=\sqrt{27}$ (not the same thing). What's the deal? It's interesting because people work with fractional exponents all the time and I've never ...
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1answer
28 views

Question on three algebraic expressions

Assume that $a < b$ , and both are natural numbers (like 2 or 4). Is $a/b$ * $a/b$ more, less or equal to $a/b$ ? Is $a/b$ / $a/b$ more, less or equal to $a/b$ ? Is $ab/a$ - $ab/b$ more, less, ...
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1answer
22 views

Algebra - fraction problem

"The cooler in a car contains $8$ litres. The coolant fluid contains $\dfrac3{10}$ of glycol and rest is water. To increase the glycol content to $\dfrac35$ you drop some of the coolant fluid and fill ...
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3answers
82 views

easier way to decompose fraction into partial fraction

It is a question in a test, and I couldn't manage to complete it. Given a complex fraction $\frac{1}{(z-1)^3(z+1)^3}$, we know that it can be decompose into ...
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2answers
40 views

Algebra problem with fractions

"In a musical class, the students either played piano or violin as head instrument. By a concert, the students got to choose whether they would do a solo or pair-performance. A piano player can only ...
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5answers
109 views

Calculating the value of $\frac{a-d}{b-c}$

If $\frac{a-b}{c-d}=2$ and $\frac{a-c}{b-d} = 3$ then determine the value of: $$\frac{a-d}{b-c}$$ Where $a,b,c,d$ are real numbers. Can someone please help me with this and give me a hint? I tried ...
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1answer
50 views

Calculate discount needed in order to achieve required profit margin. (algebra with fractions)

This problem seems to require algebra with fractions. This is basic high school (or even middle school?) stuff, but embarrassingly, I seem to have forgot it. Background I own a small business and ...
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2answers
78 views

Writing the sum of two rational functions as a single rational function.

Write as a single fraction: $$\frac{2x}{x-1} - \frac{x}{x+1}$$ Please can somebody talk me through this question as I don't understand how to get a common denominator. Thank you.
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2answers
90 views

limits question with radicals, rationalizing

Find the limit value Here's what I did (Above) I think I can rationalize the numerator to solve it, but I'm having trouble rationalizing numerator, when I'm usually rationalizing the denominator. ...
2
votes
2answers
42 views

Can ratios really be manipulated as fractions?

In high-school Maths, we were taught that it was possible to manipulate ratios as fractions. For example, $$ 1 : 7 = 3 : x \\ \frac{1}{7} = \frac{3}{x} \\ \frac{x}{7} = 3\\ x = 3 \times 7\\ x = 21\\ ...
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2answers
157 views

Is there an operator for adding the numerator and denominator of a fraction separately?

Numbers in the Farey sequence are expressed as fractions e.g $F_5$: $0\over1$ $1\over5$ $1\over4$ $1\over3$ $2\over5$ $1\over2$ $3\over5$ $2\over3$ $3\over4$ $4\over5$ $1\over1$ All of the $n\over5$ ...
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2answers
54 views

What is the property that allow the transformation $\frac{16a^3}{8ac}=\frac{16}8\cdot\frac{a^3}a\cdot\frac1c$?

In a monomial division like this: $$\frac{16a^3}{8ac}=\frac{16}8\cdot\frac{a^3}a\cdot\frac1c$$ Why I can do this $\dfrac1c$? Where this 1 come from?
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6answers
940 views

The steps of simplifying a fraction?

So I'm in an Adult Education class for my GED and I'm trying hard to study on my Math which is the only subject I have trouble with. I only have "barely" a 6th grade education to Math so I'm having a ...
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3answers
61 views

Basic algebra/fractions: derivation

How do I do this derivation step? I don't understand why there is equality. The derivation is from my textbook. $$mg-m\left(\frac{g}{1+\frac{M}{2m}}\right)=\frac{mg}{1+\frac{2m}{M}}$$