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

learn more… | top users | synonyms

3
votes
1answer
95 views

How can I do this? $\int\frac{dx}{x^4+1}$ [duplicate]

I tried to integrate this: $\displaystyle\int \dfrac{dx}{x^4+1}$ I tried to do it with the partial fractions method (after factoring the denominator), but the process is really large, and I got a lot ...
1
vote
4answers
166 views

Can a fraction be simplified like this?

Ridiculously embarrassing question, but can $\frac{x^2-x}{x^2-25}$ be simplified to simply $\frac{1-x}{1-25}$? Full thought process here is that this is essentially $\frac{x*x-x}{x*x-25}$ so the $x$s ...
5
votes
4answers
536 views

What is the non-trivial, general solution of these equal ratios? [closed]

Provide non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ $a=?, b=?, c=?$ The solution should be general.
0
votes
1answer
39 views

Comparing Fractional Numbers

Does a formula exist for comparing two fractional numbers, without resolving to using anything other than integers and fractions? (Thus not real numbers). In other words: given $\dfrac{a}{b}$ and ...
26
votes
14answers
6k views

Logic behind dividing negative numbers

I've learnt in school that a positive number, when divided by a negative number, and vice-versa, will give us a negative number as a result.On the other hand, a negative number divided by a negative ...
0
votes
1answer
30 views

Spending fraction of salary

I have this question and kind of confused... Mary spent $1/4 $ of her salary in for rent and $1/4$ more than rent for car payment. Which of the following could be the fraction of her savings if ...
4
votes
3answers
104 views

Ratios as Fractions

I’m having trouble understanding how fractions relate to ratios. A ratio like 3:5 isn’t directly related to the fraction 3/5, is it? I see how that ratio could be expressed in terms of the two ...
2
votes
4answers
57 views

Simplify $\frac{x}{c} - \frac{x}{c-d}$

There's a long time that I don't solve questions like this one. I'm having problems to simplify this one: $$\frac{x}{c} - \frac{x}{c-d}$$
2
votes
1answer
88 views

Is there a mathematical concept of fractions using transfinite numbers as numerators and denominators?

http://de.wikipedia.org/wiki/Cantors_erstes_Diagonalargument (German) http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument (English) While looking at Cantors method of proof, which he used to ...
0
votes
1answer
49 views

how to tell a fraction in denominator or numerator should be substituted with its integer equivalent

Suppose we have equations as follows (A, C and B are all integers and $\gcd$=greatest common divisor). $$R_1 = \frac{A\times C}{B} \hspace{2cm} R_2 = ...
5
votes
3answers
517 views

Recognizing the sequence 1/16, 1/8, 3/16, 1/4, 5/16, …

What is the missing number? $$\frac{1}{16}, \frac{1}{8}, \frac{3}{16}, \frac{1}{4}, \frac{5}{16}, \ \ \ [?]$$ $$A. \frac{5}{4}\quad B. \frac{3}{4}\quad C. \frac{5}{8}\quad D. \frac{3}{8}$$ ...
3
votes
4answers
116 views

Deeply confused about $\sqrt[5]{a^5}=(a^5)^{1/5}$

So is this correct? $\sqrt[5]{a^5} = \left(a^5\right)^{\frac{1}{5}}$ I need proof why $\left(a^5\right)^\frac{1}{5}$ can or cannot just be $a^\frac{5}{5}$ or just $a$? I think of that rule of ...
0
votes
2answers
82 views

How does $\sqrt {\frac{{4 + \sqrt {15} }}{8}} = \frac{{\sqrt {8 + 2\sqrt {15} } }}{4}$

I have the follow answering to a question from my textbook: $\sqrt {\frac{{4 + \sqrt {15} }}{8}}$ However my textbook simplifies it to: $\frac{{\sqrt {8 + 2\sqrt {15} } }}{4}$ I've checked and my ...
0
votes
5answers
50 views

imaginary number evaluation

Question Let $z_1 = 1 + i$, $z_2 = 2 - i$, evaluate $$\left | \frac{z_1}{z_2} \right |$$ I have this question! Its to evaluate the fraction ! what I did is the following ...
3
votes
4answers
102 views

Why does $\dfrac{8}{\frac{8\sqrt{145}}{145}} = \sqrt{145}$?

I can't seem to work out why this is true: $$\frac{8}{\dfrac{8\sqrt{145}}{145}} = \sqrt{145}$$ Could someone break it down for me?
1
vote
5answers
43 views

Decompose a fraction in a sum of two

Let's say that I have this fraction: $$ \frac{2x}{x^2+4x+3}$$ I would like to decompose in two fraction: $$ \frac{A}{x+3} + \frac{B}{x+1}$$ Which is the procedure for that? :)
0
votes
3answers
437 views

Dividing line segments with ratios vs. fractions [closed]

I know that $2:3$ is actually $\frac {2}{3}$. So when you split a line segment by a ratio, you would add $2$ and $3$ to get a fraction of $\frac {2}{5}$ that will be used to solve the problem. I ...
2
votes
2answers
57 views

A property of proportions: if $a/b=c/d$, then $(ma+nb)/(pa+qb)$ is equal to $ (mc+nd)/(pc+qd)$

If $\large\frac{a}{b}=\frac{c}{d}$ how we can obtain $\displaystyle{\frac{ma+nb}{pa+qb}=\frac{mc+nd}{pc+qd}}$? I can get $\large\frac{ma}{qb}=\frac{mc}{qd}$ and $\large\frac{nb}{pa}=\frac{nd}{pc}$ , ...
4
votes
7answers
840 views

When the numerator of a fraction is increased by 4, the fraction increases by 2/3…

When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$. What is the denominator of the fraction? I tried, Let the numerator of the fraction be $x$ and the denominator ...
3
votes
3answers
129 views

How does $-\sqrt {\frac{{2 - \sqrt 2 }}{{2 + \sqrt 2 }}} $ simplify to $1 - \sqrt 2 $?

I've the answer for a question in my textbook to be: $-\sqrt {\frac{{2 - \sqrt 2 }}{{2 + \sqrt 2 }}} $ which i've then simplifed to: $-\sqrt {3 - 2\sqrt 2 } $ However my textbook states $-\sqrt ...
0
votes
1answer
59 views

Using all types of fractions

Is their a website that teaches you everything you need to know about fractions, just fractions. I ask this because I do calculus...and I suck at fractions. I hate them so much. I have no idea how to ...
0
votes
0answers
14 views

proving a fraction with 2 parameters to be small

Hi I have a fraction as below $$\frac{1.623x^4+0.434x^4\sum_iy_iz_i^2+(0.014x^2+0.0027)\sum_iy_iz_i^4}{1.645x^2+(0.083-0.329x^2+0.435x^4)\sum_iy_iz_i^2+0.014\sum_iy_iz_i^4}$$ where $x\in[0, 0.5]$, ...
1
vote
2answers
84 views

Definition of Rational/ Irrational Numbers reguarding denominators

The definition of a Irrational number is "Irrational numbers don't include integers OR fractions. However, irrational numbers can have a decimal value that continues forever WITHOUT a pattern." So ...
0
votes
0answers
50 views

L'Hospital's rule for higher derivatives

Let $u,v \in C^\infty(\mathbb{R})$, where $u(0) = 0$ and $v(0) = 0$ and $v'(0) \not= 0$. Then, one can define a function $f \in C^\infty(\mathbb{R}\setminus\{0\})$ by $f := u/v$. L'Hospital allows ...
1
vote
3answers
31 views

Fraction exponents in division

if I have $\frac{a^{6/5}}{b^{1/5}}$, I know you subtract exponents when dividing so $6/5 - 1/5$ is $5/5$, so since that's just one, is this equal to $a/b$?
4
votes
2answers
39 views

Non-negative fractions summing to $1$

Let $ d_1,\ldots, d_n \ge 2 $ be pairwise relatively prime. Are there any $ c_1,\ldots,c_n \in \mathbb{Z}_{\ge 0} $ with $ c_i \le d_i-1 $ for all $ i=1,\ldots,n $, such that $\displaystyle ...
2
votes
3answers
111 views

can fractions be done on a regular caculator?

I am wondering if I can use me standard calculator to solve fraction problems which include: adding, subtracting, multiplying, and dividing fractions, or do I need to buy a scientific calculator to ...
0
votes
5answers
57 views

Fraction with negative exponent fraction.

Q: $$\left(\frac{27 a^6 b^{-3}}{c^{-2}}\right)^{-2/3}$$ A: $$\frac{b^2}{9 a^4 c^{4/3}}$$ How in the world are they getting that?
0
votes
1answer
26 views

Solving function in difference quotien equation

I have the problem Find the difference quotient $\frac{f(2 + h) - f(2)}{h}$ for $f(x) = \frac{1}{x^2}$. The answer they gave is $\frac{-(4 + h)}{4(2 + h)^2}$ So far I've done: $$\frac{[1/(2 + h)^2 ...
1
vote
2answers
62 views

How do you simplify an algebraic expression?

Please explain how to simplify an expression that is similar to this one $\displaystyle\frac{a+3}{6}+\frac{a-4}{4}+\frac{a+2}{-3}$
3
votes
2answers
76 views

Absolute value on the top of a fraction

What is the answer to a question similar to this one, where the absolute value bars are only around the numerator of the fraction? $$\frac{|2+4(2)|}{5-10}$$ Would the fraction be equal to ...
2
votes
2answers
36 views

Fraction With Scientific Notation As A Percentage

I have this fraction $\frac{3.09\times 10^{-9}}{0.02\times 10^{-9}}$ and I need to convert it to a percentage. What I do know is that the $10^{-9}$ cancels out and we are left with $\frac{309}2$, but ...
0
votes
1answer
42 views

cancell common factors

p³ - PQ² --------- Divided by (P+Q)² Apparently the answer is P(P-Q) --------- Divided by P+Q But how? - What I was thinking P-P (P-Q), (P+Q) ------------------ Divided by (P+Q) which is P-P ...
1
vote
2answers
40 views

How to solve this algebraic fraction?

Could someone please help me with solving this algebraic fraction. I tried it a few times and I got the wrong answer all of the times. My brother also tried, who had recently finished Matric and he is ...
0
votes
3answers
83 views

Splitting the numerator

Can someone explain how we can get the second fraction by splitting the numerator? $$\frac{x^3}{x^2+x+1}=x-1+\frac{1}{x^2+x+1}$$ I can get the LHS from the RHS but not the other way around. What ...
0
votes
2answers
32 views

I don't understand the expected result from an equation. [closed]

I came across this a while ago in my studies and let it pass however exams are closing in so I better figure it out. I am not sure why in the second equation 458 is the answer.
0
votes
1answer
144 views

Deradicalization of denominators

Task: Develop a fraction equivalent to $$ 1\over{\sum\limits_{i=0}^{n-1}c_in^{i/n}} $$ in which the denominator is rational.
0
votes
4answers
29 views

Rank odds without converting

Brazil are currently playing Mexico, and at the start of the game Brazil were 2/5 to win. As it's the 38th minute and still 0-0, their odds have changed to 8/15. Now, if I'm not wrong that represents ...
1
vote
3answers
66 views

Basic algebra, isolating the variable

So I have the equation $$\tan30=\frac{4.9t-\frac{10}{t}}{\frac{8.77}{t}}$$ And I want to find t, but my algebra has failed me. This is my working so far. ...
0
votes
1answer
65 views

Rearranging algebraic formula when subject is on both sides

I have run into some difficulty with a question on making a variable the subject of an equation where the variable is on both sides. I am really struggling to find a method for making "a" the ...
0
votes
5answers
92 views

Guys, hard limit, please help.

Here is the limit I'm struggling with: $$\lim_{x\to0}\cfrac{x\tan x-x\sin x}{x\sin^2x/\cos x}.$$ Worked so hard to find it, but couldn't.
0
votes
1answer
199 views

Is three halves a fraction?

Is three halves (3/2) a fraction? I understand there may be a more accurate name for this kind of number (improper fraction?) which would be interesting to know. But that isn't what I'm after me, I ...
4
votes
3answers
1k views

Can you give me a visual representation on 1/6 of 4/5 to get 4/30?

I'm trying to understand fractions more by using a visual representation, and I having a hard time making a visual representation of the 1/6 of 4/5 and getting a visual understandable representation ...
0
votes
1answer
61 views

Why is the word “of” equivalent to multiplying in fraction word problems?

I know this is a very easy problem, but I'm having a hard time getting my head around this concept, consider this example from a book. *Jerry bought a pie and ate 1⁄5 of it. Then his wife Doreen ate ...
3
votes
5answers
117 views

How do I prove $\frac{ \sqrt{x+h}-\sqrt{x} }{ h}=\frac{1}{\sqrt{x+h}+\sqrt{x}}$?

$$\frac{ \sqrt{x+h}-\sqrt{x} }{ h}=\frac{1}{\sqrt{x+h}+\sqrt{x}}$$ I know I just asked a question and I did figure out how that one worked but I'm not sure how I would go about this one.
0
votes
1answer
22 views

Comparing Fractions that contain epsilon

Given $\epsilon$ a constant s.t. $0<\epsilon<1$, and $n,p$ positive integers, $n >= 2p$, is the following true: $\frac{(1+\epsilon)n}{(2+\epsilon)p} \geq \lceil\frac{n}{2p}\rceil$
1
vote
3answers
35 views

Simplifying fraction with square root as denominator

I'm trying to find the integral of: $$\dfrac {2\sqrt{x} - 3x + x^2}{\sqrt{x}}$$ but I first need to simplify it so I tried dividing by the $\sqrt{x}$ for each of the numbers on the top like so: ...
0
votes
1answer
44 views

What's the difference between “continued fractions” and “compound fractions”?

What should we call a fraction which includes another fraction in its numerator or denominator, like $${ab\over {c \over d}}$$?
1
vote
1answer
38 views

Why does $ \frac {a}{b}$ of $c$ means $ \frac {a}{b} \cdot c$ [closed]

Why does it multiply when the preposition "of" appears?
0
votes
0answers
40 views

Adding a natural number to a normalized fraction

I am currently writing yet another rational number class where the fraction should always be normalized. When adding a natural number to a normalized fraction, it possible to get a non-normalized ...