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

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0
votes
2answers
28 views

Solve using Proportions/Multiplication?

How do I solve this using proportions and multiplication? How much is $\dfrac 1{200}$ of $50$ percent? I know that the answer is $0.25$, however, how would I solve that using proportions and ...
6
votes
2answers
81 views

Finding the derivative $f(x)=\sqrt{x^2 -9}$,

I need to find the slope at a=5, using the definition for the function $f(x)=\sqrt{x^2 -9}$, $$f'(x) = \lim_{\Delta x \to 0} {f(x+\Delta x)\over \Delta x}$$ The answer book says the slope is ...
1
vote
2answers
73 views

Finding derivative $f(x)={2\over x^3}$

I have to find the derivative and the slope at $a=6$ The function is $f(x)={2\over x^3}$ I have to find the answer using the formula, $$f'(x)= \lim_{\Delta x \to 0} {f(x+ \Delta x) - f(x) \over ...
1
vote
2answers
44 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 ...
2
votes
3answers
98 views

Is a prime to the power of a fraction always irrational?

Let $p$ be a prime number and let $x$ be a faction, i.e. $x \in \mathbb{Q} - \mathbb{N}$. It seems to be the case that $p^x$ is always irrational. How do I prove this?
1
vote
3answers
95 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 ...
1
vote
2answers
164 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 ...
0
votes
1answer
34 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 ...
0
votes
1answer
61 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. ...
0
votes
1answer
39 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 ...
1
vote
3answers
82 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 ...
0
votes
3answers
55 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 ...
63
votes
14answers
4k 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 ...
-1
votes
3answers
67 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 ...
13
votes
2answers
194 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 ...
5
votes
6answers
176 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. ...
0
votes
2answers
94 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 $\dfrac{9-4\sqrt2}{4}$.
0
votes
1answer
33 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 ...
1
vote
3answers
129 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 ...
1
vote
1answer
46 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 ...
0
votes
3answers
47 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
votes
2answers
259 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 ...
1
vote
1answer
47 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 ...
1
vote
3answers
45 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 ...
5
votes
4answers
349 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 ...
15
votes
1answer
252 views

Closed-form of infinite continued fraction involving factorials

Is there a closed form of this: $$ 1!+\dfrac{1}{2!+\dfrac{1}{3!+\dfrac{1}{4!+\ldots}}} $$
1
vote
1answer
62 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 ...
12
votes
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 ...
0
votes
1answer
26 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 ...
3
votes
7answers
182 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 ...
0
votes
1answer
30 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?
1
vote
2answers
62 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 ...
0
votes
1answer
30 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.
0
votes
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
votes
4answers
129 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 ...
-1
votes
1answer
83 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 ...
0
votes
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: ...
1
vote
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?
0
votes
0answers
14 views

What can we say about the function $f(x)$ in this case?

Alright, I'm little bit confused about what's happening here to the function $f(x)$, i thought that the formula of $f(x)$, have nothing to do with its behavior or domain. there are two or many ...
0
votes
2answers
18 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
56 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 ...
1
vote
1answer
50 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 ...
0
votes
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, ...
0
votes
1answer
20 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 ...
1
vote
3answers
75 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 ...
1
vote
2answers
39 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 ...
5
votes
5answers
108 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 ...
0
votes
1answer
44 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 ...
0
votes
2answers
46 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.
1
vote
2answers
65 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. ...