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

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3
votes
7answers
183 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
64 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
145 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
85 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
45 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
49 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
67 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
36 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\\ ...
1
vote
2answers
88 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 $n\over5$ ...
0
votes
2answers
53 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?
6
votes
6answers
520 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 ...
0
votes
3answers
58 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. $$mg-m\left(\frac{g}{1+\frac{M}{2m}}\right)=\frac{mg}{1+\frac{2m}{M}}$$
0
votes
1answer
29 views

Trying to figure out a Mathematical pattern

I am given a start point, a, an end point b, and a number of values x. With that I am supposed to come up with the points between the start and end point. Below is an example ...
6
votes
5answers
738 views

How do you solve a logarithm with a non-integer base?

How would one calculate the log of a number where the base isn't an integer (in particular, an irrational number)? For example: $$0.5^x = 8 \textrm{ (where } x = -3\textrm{)}$$ $$\log_{0.5}8 = -3$$ ...
47
votes
3answers
5k views

Why do we miss 8 in 0.012345679…, 98 in 0.0001020304050607080910111213…, and so on in fractions like 1/81, 1/9801, and so on?

I've seen this happen that when you divide by a fraction using the square of any set of nines in the denominator depending on how many there are like ${1\over 99^2}={1\over 9,801}$, you get ...
1
vote
1answer
56 views

Find the value of x

$$\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)\ldots\left(1-\frac{1}{2011^2}\right)=\frac{x}{2\cdot 2012}$$ Help me solve this, obviously there is a shortcut ...
0
votes
2answers
36 views

How to find the value of $\sum_{k=1}^\infty (\frac{1}{9})^k$ using partial sums?

So I was trying to prove an infinite sum by looking at the partial sum, when I ran into a problem. Consider: $$\sum_{k=1}^n \left(\frac{1}{9}\right)^k = \frac{1}{8} 9^{-n} (9^n-1)$$ but as there are ...
0
votes
3answers
55 views

Finding out how out how much is 100%

I know 14% is 41. So how much is 100%? I know it is simple math, but... you know how it is being out of school for a few years. If at all possible, I'd like to see the equation too.
2
votes
3answers
74 views

Show that for every integer $n ≥ 1$, $1 + \frac{1}{4} +\frac{1}{9} + · · · + \frac{1}{n^2} ≤ 2 − \frac{1}{n}$

I can just think of trying to prove $\frac{1}{4} +\frac{1}{9} + · · · + \frac{1}{n^2} ≤ \frac{1}{n}$, but remains stuck.
0
votes
3answers
47 views

Trying to subtract 2 fractional

I'm trying to solve $f(x)=0$ for $x$, but I can't figure it out as I have to get both the denominators to become for instance $8x$, and then only 1 numerator has $x$ in it. How can I solve this? $$ ...
13
votes
11answers
5k views

Dividing by 2 numbers at once, what is the answer?

Let's say i have 4/1/5. or 4 divided by 1 divided by 5. Are there any rules that i am allowed to use to stop any mistakes?, for example this has 2 solutions, 4/5 , and 20. Edit: Thanks for your ...
1
vote
4answers
47 views

Rewrite fraction to calculate limit

I am practising finding limits. However, I can't seem to figure out this one. $$f(x) = \frac{x^3 + 4x - 5}{x^2-1}\text{ as $x$ goes to $1$}$$ I understand I have to rewrite the fraction somehow for ...
3
votes
5answers
236 views

How do I solve this fraction addition problem?

$4\frac{2}{9} + -9\frac{1}{2}$ yeilds result of $-5\frac{13}{18}$ but WolframAlpha says the answer is $-5\frac{5}{18}$ fixed.
1
vote
1answer
42 views

Instead of mid-point, how do i find a third of the way up the line instead.

I'm working with the program Maya, and i need to script a way to find various fractions up a line for each 3D vector. For example, lets say I have the vector (0, 0, 0), and the vector (12, 12, 12). ...
0
votes
2answers
89 views

Simplifying fractional exponents

I am very confused about the following: whenever I put in into wolfram alpha the answer it gives me is "indeterminate", is it not possible to simplify fractional exponents or something? if the ...
2
votes
3answers
53 views

Multiplying fractions to answer story problems.

My daughter had a math question about finding how far someone walked using multiplication of fractions. The distance was $1 \frac 78$ and he walked $\frac 23$ of the way. The problem wanted to ...
2
votes
4answers
75 views

How do you add two fractions?

I have a fraction I am trying to solve. I know the answer already, as Wolfram says it is $\frac{143}{300}$. The fraction is: $$\frac{5}{12} + \frac{3}{50} = \space ?$$ Please explain why and how your ...
1
vote
2answers
67 views

How do you solve this fraction?

The problem is : $ \frac{2}{3} + \frac{-1}{16} $ The answer I got was $ \frac{1}{48} $ . I believe it to be incorrect. Three does not divide into $16,$ so I cross multiplied. What am I doing wrong? ...
0
votes
1answer
36 views

Regarding +/- fractions: what are some mental tests you can apply to uncommon fraction denominators?

When adding and subtracting fractions: what if there is no uncommon factor (for example 4=2,2 and 6=2,3). Does that always mean to use the LCM? What if the LCM is too big or time consuming to ...
0
votes
1answer
74 views

Why is (n+1)/2n = 1/2 + 1/n, and not 1/2 + 1/2n?

If I factor $(n+1)/2n$ by $n$, I get $n(1+1/n)/n(2)$. Simplifying, I end up with $(1 + 1/n) / 2$. This can be rewritten as: $1/2 + (1/n)/2$, which would give me $1/2 + (1/n) \times (1/2) = 1/2 + ...
1
vote
3answers
66 views

Show that $\, 0 \leq \left \lfloor{\frac{2a}{b}}\right \rfloor - 2 \left \lfloor{\frac{a}{b}}\right \rfloor \leq 1 $

How can I prove that, for $a,b \in \mathbb{Z}$ we have $$ 0 \leq \left \lfloor{\frac{2a}{b}}\right \rfloor - 2 \left \lfloor{\frac{a}{b}}\right \rfloor \leq 1 \, ? $$ Here, $\left \lfloor\,\right ...
1
vote
2answers
97 views

Is there a faster way to add/subtract fractions then having to draw a factor tree each time?

Do you really have to draw a factor tree and work with primes every time you encounter adding or subtracting fractions? Not this way - LCM(8,15)... ...
0
votes
3answers
80 views

What is the correct way to divide a fraction?

This is a very basic question, but i'm struggling with it. Can someone explain the rules when dividing a fraction like this: $$\frac{\cos(\pi x)\sin(\pi x)}{\Large{\frac{\cos(\pi x)}{\sin(\pi x)}}}$$ ...
1
vote
2answers
47 views

Evaluating a limit as $x \to -\infty$ of a power of a rational function

Sorry for the weird title, I don't know how to put the equation on the title. $$\lim_{x\to-\infty}\left(\frac{1-x^3}{x^2+7x}\right)^5$$ Ok I divided inside the parenthesis by $x^2$, but now I am ...
0
votes
1answer
51 views

How to reduce this fraction?

I am trying to reduce the following fraction to its simplest form: $$\frac{2121212121210}{1121212121211}$$ Can someone please help me? Thanks.
0
votes
1answer
45 views

Calculate $X$ of a math problem

I am trying to learn some more math and I got stuck on this: $$\frac{0.2}{X} = 140$$ How do I calculate $X$? EDIT Sorry I meant to calculate $$\frac{28}{X} = 140$$ So that $X = 0.2$, but how do I ...