Questions on fractions, numbers of the form $p/q$ where $p$ and $q$ are integers, and $q$ is not zero.

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1
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0answers
24 views

exponential integration with fractional powers

I am trying to solve the following integral $$\int_{-\infty}^a \frac{\beta_1 \beta_2}{y^2(c-y)^2} e^{-\beta_1/(c-y)} e^{-\beta_2/y} \, dy$$ where $a<0$, $c>0$, $\beta_1>0$, $\beta_2>0$ I ...
2
votes
3answers
55 views

Why does $\sqrt{x} / y =\sqrt{x/y/y}$?

Sorry for the awkward title, hard to to sum a mathematical problem with words alone. Having said that, I recently learned that the root of any value, $x$, and then that over value $y$, is identical ...
-4
votes
2answers
41 views

Find out students [on hold]

As a part of learning journey program 73 pupils traveled on two buses, one air conditioned and one non air conditioned to the Singapore Discovery center. Three fifth of the pupils on the air ...
-4
votes
1answer
44 views

How much laundry is done? [on hold]

On Saturday morning, Bambi washed 3/5 of 50 clothes in the laundry bag. In the afternoon, she washed 4/5 of the clothes. How many clothes did Bambi washed?
1
vote
1answer
20 views

Function that maps a rational number to its numerator and denominator

Question: Is there a simple way to represent a function $f:\mathbb Q\to \mathbb Z^2$ that maps a rational number in lowest terms $r=\frac ab$ to the ordered pair of its numerator and denominator ...
0
votes
4answers
129 views

What does Pi equal to [duplicate]

What is the approximation of pi in a fraction form. I am very curious to know what it is. I have been seeing pi almost everywhere.
0
votes
1answer
27 views

Show that $\frac c {1+c} \le \frac a {1+a} + \frac b {1+b}$ , for $c \le a+b$ and $a,b,c \ge 0$

Show that $\frac c {1+c} \le \frac a {1+a} + \frac b {1+b}$ , for $c \le a+b$ and $a,b,c \ge 0$ So need to show $\frac c {1+c} \le \frac {a+b+2ab} {1+a+b+ab}$ We have $\frac c {1+c} \le \frac {a+b} ...
82
votes
12answers
10k views

Can you be 1/12th Cherokee?

I was watching an old Daily Show clip and someone self-identified as "one twelfth Cherokee". It sounded peculiar, as people usually state they're "1/16th", or generally $1/2^n, n \in \mathbb{N}$. ...
1
vote
3answers
70 views

How do I solve this, first I have to factor $ 2x\over x-1$ + $ 3x +1\over x-1$ - $ 1 + 9x + 2x^2\over x^2-1$?

I am doing calculus exercises but I'm in trouble with this $$\frac{ 2x}{x-1} + \frac{3x +1}{ x-1} - \frac{1 + 9x + 2x^2}{x^2-1}$$ the solution is The only advance that I have done is factor $ ...
0
votes
1answer
35 views

Integral exponential and fraction of powers

I am trying to solve the following integral $$ \int_0^y \frac{x^{m-1}}{(1+x)^{m+k}} \exp\left(-\frac{m}{\gamma} x \right) dx. $$ I tried to look into different books such as Gradshteyn and Prudnikov ...
0
votes
1answer
28 views

power of a fraction

I am having trouble understanding where the numbers are coming from in this question. John and Melissa wonder about the potential increase in the value of their house. Assuming a 6% appreciation per ...
4
votes
5answers
98 views

$-\frac76=-\frac {4n}{3}$ struggling on solving this equation

I was wondering how to do this equation step by step. I forgot how to but it would be awesome if someone could help me out $$-\frac76=-\frac {4n}{3}$$
0
votes
2answers
26 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
59 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
56 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
27 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 ...
1
vote
2answers
63 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
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3answers
90 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
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1answer
84 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
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1answer
25 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
38 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
38 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
73 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
52 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 ...
56
votes
14answers
3k 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
59 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
170 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
158 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
80 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
17 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
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3answers
125 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
45 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
33 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 ...
0
votes
2answers
227 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
40 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 ...
0
votes
3answers
32 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
299 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 ...
14
votes
1answer
226 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
41 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
981 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
18 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
177 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
58 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
28 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
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2answers
41 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
55 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
34 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
105 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
110 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?