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

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1
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5answers
504 views

Un-Simplifying a fraction, i.e. computing partial fraction decomposition

$\frac{3x^2+17x}{x^3+3x^2+-6x-8}$ I need to find the value of C in the form of $\frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{x+4}$ which is based on the fraction give at the top. I can get so far to do ...
1
vote
1answer
10 views

Explaining the non-application of the multiplication law of logarithms, when logs are in the denominators.

I have an A' Levels student who had to solve the following problem: $ log_2 x + log_4 x = 2$ This was to be solved using the Change of base rule, and then substitution, as follows: $ \frac{1}{log_x ...
0
votes
1answer
25 views

Is there a value for $a$ other than a factor or a multiple of $c$ in $\frac{a}{b}=\frac{c}{d}$

Suppose $a,b,c,d$ to be whatever quantities whatsoever that satisfy the proportion $\frac{a}{b}=\frac{c}{d}$. Is there a value for $a$ other than a factor or a multiple of $c$. Or, is there a value ...
0
votes
0answers
18 views

GCD and fraction problem

If x/y = 1/a + 1/b + 1/c and GCD of a , b and c is 9 then find a) minimum of x and y which do not cause x/y repeating decimal b) the best of x and y that cause x/y nearly to 3/10 many ...
0
votes
2answers
41 views

Does there exist $a,b,c,d$ such that $\frac{a+b+c+d}{4}$ is an integer?

Let $a,b,c,d$ be defined as such: $$\{a,b,c,d\} \geq 1,\\ a\neq b\neq c\neq d,\\ a \not\in \{bx,cx,dx\},\\ b \not\in \{ax,cx,dx\},\\ c \not\in \{ax,bx,dx\},\\ d \not\in \{ax,bx,cx\},\\ \{a,b,c,d\} ...
3
votes
1answer
60 views

When is $(12x+5)/(12y+2)$ not in lowest terms?

I am struggling to solve this problem and would appreciate any help: When is $\frac{12x+5}{12y+2}$ NOT in lowest terms? (x,y are nonnegative integers) I have found that it is not in lowest terms for ...
4
votes
3answers
64 views

Proving $\lim _{x\to \infty }\left(\frac{\sqrt{x+1}-\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-3}}\right) = \frac35$

$$\lim _{x\to \infty }\left(\frac{\sqrt{x+1}-\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-3}}\right)$$ Can someone help me to solve it? result of online calculator: 3/5
4
votes
2answers
367 views

Equivalent of adding to a denominator?

Given the inequality $\frac{n}{m} \ge \frac{1}{2}$, I want to add $1$ to both $n$ and $m$: $$\frac{n+1}{m+1}.$$ What would be the equivalent operation on the RHS of the equation? Adding $1$ to $n$ ...
1
vote
2answers
100 views

How is $\frac{1-x}{x^2-1}=\frac{1}{x+1}$?

When integrating $\int \frac{1-x}{x^2-1} dx$ Maple rewrote it as $-\int\frac{1}{x+1}dx$ How is $\frac{1-x}{x^2-1}=\frac{1}{x+1}$?
0
votes
1answer
53 views

Shorten $\frac{n}{n^\frac{1}{2}}$?

I have a short question to solve my problem. Can I simplify $\frac{n}{n^\frac{1}{2}}$ ? Thanks already for answers.
0
votes
1answer
25 views

Rearranging equation

I'm reading a textbook in which an equation is rearranged and I'm failing to see how they've done it. I've tried writing it down step by step in my notebook but can't come up with the right answer. ...
0
votes
1answer
86 views

Fractions vs Decimal numbers

I want to know if there is any difference between Fractions and Decimal numbers, are Decimal numbers just Fractions that are written in a different way according to a predefined rule: using "a group ...
0
votes
1answer
40 views

Fractional Exponents and Fractions

When dealing with fractional exponents like in the question below, how do you combine them so the two "n's" in the first fraction become one? ((how do i combine $4/3$ with $1/3$)) The aim is to end ...
2
votes
5answers
45 views

need help on this fraction equation $2/5 = 2/3 - r/5$

$$\frac{2}{5} = \frac{2}{3} - \frac{r}{5}$$ I'm trying to find $r$. Can anyone give me a step by step?
1
vote
1answer
39 views

What is the smallest fraction produced by a sum of fractions with bounded denominator?

For $x$ a sum of fractions: $$ x = \sum_{i=1}^{N}\frac{a_i}{b_i} $$ for all $a_i, b_i \in \mathbb{Z}$ with $ 0 < b_i \leq D$ and $N$ are non-zero positive integers, I know that the denominator of ...
0
votes
1answer
31 views

Why do the denominators of two fractions with numerators $1$ add up to a third fraction that have the special things below?

I found out that the denominators of two fractions with numerators $1$ add up to a third fraction that has the sum in the numerator and the product in the denominator. For example, ${1\over ...
1
vote
2answers
26 views

How do I solve this equation?

I have an equation, where I need to find n, that I need help solving. I already cheated a little bit by using a CAS (Maple) to solve the equation, so i know what the result should be, but I need to ...
23
votes
8answers
2k views

How to make sense of fractions?

Can anybody explain what a fraction is in a way that makes sense. I will tell you what I find so confusing: A fraction is just a number, but this number is written as a division problem between two ...
0
votes
2answers
46 views

variables to the power of a fraction

I have this question for advanced math, I can't seem to get my head around. $$\frac{x^{5/2}}{(x^{1/3})^4}$$
6
votes
1answer
290 views

Will 0.99999999 eventually become equal to 1?

I am currently learning about fractions, and there is something that I am finding it hard to make sense of. When a fraction it added to the right of the decimal point, the number becomes slightly ...
0
votes
2answers
32 views

what is the default order and direction of operation?

I have a division like this 16/8/4/2 what is the default way to do calculations when the bracket is not specified . Method 1 : Is it correct to go from right to left like [16/ (8 / { 4 / ...
5
votes
2answers
126 views

How do I simplify this expression about factorization?

I am trying to simplify this $$\frac{9x^2 - x^4} {x^2 - 6x +9}$$ The solution is $$\frac{-x^2(x +3)}{x-3} = \frac{-x^3 - 3x^2}{x-3} $$ I have done $$\frac{x^2(9-x^2)}{(x-3)(x-3)} = ...
1
vote
0answers
40 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
64 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 ...
6
votes
3answers
238 views

Why is $\frac{\sqrt{x+1}-1}{x}$ equal to $\frac{1}{\sqrt{x+1}+1}$?

I'm working with the expression $$\frac{\sqrt{x+1} - 1}{x}.$$ According to Wolfram Alpha "alternate form" section (http://www.wolframalpha.com/input/?i=%28%28x%2B1%29%5E1%2F2-1%29%2Fx) it is equal to ...
1
vote
1answer
22 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
168 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
28 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} ...
86
votes
12answers
11k 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
78 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
43 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
32 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
101 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
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
70 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
65 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
38 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
2answers
73 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
93 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
1answer
110 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
27 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
44 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
78 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
53 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 ...
58
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
63 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
181 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
171 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
87 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 $\dfrac{9-4\sqrt2}{4}$.