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

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0
votes
1answer
16 views

fraction simplication, resolution with one variable

I'm having some problems to understand a simplification and I know the correct answer but I'd like to understand why my method is wrong or what rule I'm breaking. I have an equation like the ...
3
votes
4answers
98 views

Express the following product as a single fraction: $(1+\frac{1}{3})(1+\frac{1}{9})(1+\frac{1}{81})\cdots$

I'm having difficulty with this problem: What i did was: I rewrote the $1$ as $\frac{3}{3}$ here is what i rewrote the whole product as: $$\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{3}{3}+\...
1
vote
1answer
144 views

Subtracting or Multiplying Fractions 3/4-1/2

This is the given scenario to help visualize the problem at hand. A bird feeder is filled with 3/4 of a full bag of seeds. The birds ate 1/2 of what was in the bird feeder. What fraction of a full ...
0
votes
2answers
22 views

Inequality relationship when additing a constant to the denominators

When $\frac{a}{b}>\frac{c}{d}$ where $a, b, c,$ and $d$ are positive real numbers, is $\frac{a}{b+1}>\frac{c}{d+1}$ true?
1
vote
1answer
105 views

Reasoning and Explanation for $2/3-1/2$

Denise says that $2/3-1/2 = 1/3$ and gives the reasoning indicated in Figure (below) to support her answer. Is Denise right? If not, what is wrong with her reasoning and how could you help her ...
0
votes
1answer
30 views

Adding fractions with variables and using common denominator? Rather basic math, but here I am..

So I have these fractions I need to merge together and shorten: $$\frac{1}{2a+8} + \frac{4}{a^2-16} + \frac{4}{a-4}$$ I understand that I need to make the denominators the same so that I can merge ...
2
votes
1answer
41 views

Simplify the fraction with radicals

I want to simplify this fraction $$ \frac{\sqrt{6} + \sqrt{10} + \sqrt{15} + 2}{\sqrt{6} - \sqrt{10} + \sqrt{15} - 2} $$ I've tried to group up the denominator members like $ (\sqrt{6} + \sqrt{15}) -...
0
votes
1answer
23 views

Simplify complex fraction

This is a really low level question. I'm trying to simplify $$f(x) = \frac{36x^{-2} -3x^{-1} -18}{12x^{-2} -25x^{-1} +12}$$ After factoring, removing negative exponents, and flipping the second ...
0
votes
1answer
11 views

Removing additive factors from the denominator of a fraction

Suppose I have a variable $x_L$ defined as follows: $$ x_L=\frac{r_1e^{-t_0s}}{s + r_2 + r_3}, $$ Is there a way for me to rearrange this fraction to get something in this form $$ x_L = [\...
1
vote
1answer
60 views

Rationalise the denominator and simplify $\frac {3\sqrt 2-4}{3\sqrt2+4}$

Does someone have an idea how to work $\dfrac {3 \sqrt 2 - 4} {3 \sqrt 2 + 4}$ by rationalising the denominator method and simplifying?
2
votes
1answer
39 views

Inequality for an alternating sum of binomial coefficients times a fraction

I need to show that $$\sum_{n=0}^x(-1)^n {x\choose n}\left(\frac{1}{n+l-1}-\frac{1}{n+l}\right) >0,$$ for any $l>0$. I tried to prove this, but I didn't get anywhere. Apparently the above ...
0
votes
1answer
24 views

Simplify the fraction

I want to simplify this fraction $ \frac {1+a+a^2+...+a^n}{1+a^{-1}+a^{-2}+...+a^{-n}} $ where, $ a \in {\mathbb R^*} $ and $ n \in {\mathbb N^*} $ I think is some kind of formula here
2
votes
2answers
101 views

What is the name for the mathematical property involving addition or subtraction of fractions over a common denominator?

For any number $x$ where $x\in\Bbb R$ and where $x\ne0$, what is the mathematical property which states that: $${1-x^2\over x} = {1\over x} - {x^2\over x}$$
0
votes
1answer
36 views

Simplifying this expression, trigonometry

I have been having trouble understanding how $$6-6\cos\left(\frac{\pi}{4}\right) = 3\sqrt{2}.$$ My main problem is the conversion of the two separate terms into one.
0
votes
2answers
27 views

Derivatives of a fraction function

An example of a fraction function is: $$y= \frac{-8x}{(x^2 + 3)^2}$$ The quotient rule says that if the function one wishes to differentiate, $f(x)$, can be written as: $$h(x) = \frac{f(x)}{g(x)}$$ ...
2
votes
1answer
23 views

Summation and Patterns Question

I have a really urgent question. Today i was looking at this Pattern (Using fractions) : $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+\frac{1}{7*9}+...$=? The pattern is $\frac{n}{2n+1}$. I was ...
0
votes
1answer
57 views

Simplifying a fraction with radicals

Simplify the following fraction as much as possible $$\def\A{\sqrt{15}}\def\B{\sqrt{35}} \frac{(8+2\A)^{3/2}+(8-2\A)^{3/2}}{(12+2\B)^{3/2}-(12-2\B)^{3/2}} $$ This problem is just driving me insane....
1
vote
2answers
109 views

How to compare fractions without finding common denominators?

This is the question: Use reasoning other than finding common denominators, cross-multiplying, or converting to decimals to compare each pair of fractions listed below. Which is greater? Give ...
1
vote
1answer
61 views

What is the value of $x$ which satisfies: $\frac{17}{85}+\frac{19}{95}+\frac{21}{105}+\frac{23}{115}+\frac{25}{125}+\frac{x}{135}=1$

What is the value of $x$ which satisfies: $\frac{17}{85}+\frac{19}{95}+\frac{21}{105}+\frac{23}{115}+\frac{25}{125}+\frac{x}{135}=1$ I thought $x=27$ because the numerator seems to have a pattern of ...
1
vote
6answers
82 views

How to prove $\frac{1}{n} > \frac{1}{n+1}$?

I understand this fact is very simple, but how would I go about it from a fundamental perspective only know that $n$ is less than $n+1$?
3
votes
2answers
201 views

Inequality - GM, AM, HM and SM means

I've got stuck at this problem : Prove that for any $a > 0$ and any $b > 0$ the following inequality is true: $$ {3} {\left(\frac{a^3}{b^3} + \frac{b^3}{a^3}\right)} \geq \frac{a}{b} +\...
-3
votes
1answer
43 views

How do I work out ${10\sqrt 30}\over{ 5\sqrt5}$ $?$ [closed]

I am told the answer is $10\sqrt 6$ but I keep getting $2\sqrt 6$. How do I get $10\sqrt6$ as the answer$?$
1
vote
5answers
173 views

Is there a formula to approximate $\pi$ in the form of $\dfrac{p}{q}$?

Is there a formula which helps in approximation of $\pi$ as $\dfrac{p}{q}$ where $p,q \in \mathbb{Z}$? I got this site though : [http://qin.laya.com/tech_projects_approxpi.html ] which shows the ...
0
votes
2answers
44 views

SAT question… confused

At a certain university, 1/4 of the applicants failed to meet the minimum standards and were rejected immediately. Of those who met the standards, 2/5 were accepted. If 1200 applicants were accepted, ...
1
vote
2answers
37 views

creating a fraction or decimal using only addition or subtraction

how do i create a decimal or a fraction by only using addition or subtract? I have the numbers 1 and 2, and I want to end up with .5 -- have been stuck on this for quite a bit! I cannot just do 1/2, I ...
0
votes
1answer
30 views

Simplifying Rational Expressions

Simplify the following rational expression: $5/(x+3) - 7x/(x-1)$ I came across this question in my homework and because it is a fraction, I decided that I needed to establish a common denominator of:...
-1
votes
2answers
105 views

Convert fraction into decimal [closed]

Trying to help my daughter with a question for her maths that has got me stuck...wish I was better at maths! Convert the fraction 27/50 into decimal Could someone please help me with this question.
0
votes
4answers
56 views

How Do I Simplify $1 - \frac{1}{2^{m-1}} + \frac{1}{2^{m}}$

Someone help. Somehow my textbook says that it simplifies to $1 - \frac{2}{2^{m}} + \frac{1}{2^{m}}$ I don't see this at all.
0
votes
2answers
39 views

What is the probability of getting heads or a 4?

When a coin is flipped and a die is thrown, what is the probability of getting a heads or a 4 ? What I've tried: P(Getting Heads) = $\frac12$ P(Getting a 4) = $\frac16$ Thus, P(Getting Heads or 4) ...
0
votes
1answer
6 views

Integral solutions to expression given below.

Given expression $xy=2^23^45^7(x+y)$ What are its integral solutions? I tried to solve it by converting it to $\frac{1}{2^2}\frac{1}{3^4}\frac{1}{5^7}=\frac{1}{x}+\frac{1}{y}$ But thereafter it got a ...
0
votes
3answers
17 views

proving that given fraction is irreducible.

Prove that for every natural number n, fraction $\frac{21n+4}{14n+3}$ is irreducible. I deduced that if we can prove that numerator and denominator have 1 as their GCD, we can get the result, but I ...
1
vote
2answers
62 views

Candy Box Dilemma

There was a box of candy on the table. Ali ate half the candy. Miranda came along and took two-thirds of it. Jane decided she wanted some, so she took three-fourths of the remaining candy. Micayla ...
0
votes
1answer
31 views

Steps to simplify specific fraction

What are the steps to simplify the first fraction to the second? $$\frac{\frac{3-(3+h)}{3(3 + h)}} {h} \implies \frac{-1}{3(3 + h)}$$ I assume the first step would be to re-write it like so: $$\...
-2
votes
2answers
50 views

How to solve this exercise with ratio? [closed]

There is some kind of exercise: We know that $ \frac{u}{m} = 2.5$ and $\frac{m}{b} = 5$. I need to find out what is u/b equal?
1
vote
3answers
98 views

Evaluate $\frac{3}{4}$ to the power of $-3$

I have gotten to the next stage where you write it as $\frac{1}{\left(\frac 34\right)}$ to the power of $3$, now I am stuck I've got it now, thanks everyone.
0
votes
0answers
8 views

What are all of the possible fractional forms an offspring's genetic makeup?

I am wondering what fractions are considered to be "impossible" and "possible" for describing the genetic composition of an offspring. This is what I mean: Example: Say one parent is 1/2 Polish, ...
1
vote
2answers
34 views

choosing N object from set of M>N maximizing overall ratio value/weight

I have a set of M objects each with a certain value and weight. From this set I want to take out N objects ($N<M$ of course) and maximize the ratio: total value of the N objects / total weight of ...
1
vote
1answer
54 views

Dividing Fractions as Recipricol Multiplication

How do you know the order of operations when dividing by fractions? Recently I've been messing up problems involving dividing fractions. The division is written as fractions over fractions and not as ...
1
vote
2answers
46 views

Algebra II: Basic Adding fractions question

Disclaimer: I'm new to adding fractions this way. Does anyone understand how the author justifies the circled equation?
1
vote
5answers
127 views

Is there a name for the rule $a \div (b \times c) = a \div b \div c$?

Edit, because I should have looked it up before I posted the question: Is there a name for the rule $a \div (b \div c) = a \div b \times c$ ? I ran across this in Liping Ma's book, Knowing and ...
2
votes
1answer
48 views

How to express $15.3\dot{9}$ in fractional form

In the number $15.3\dot{9}$, $9$ is repeated forever. If the number is rational then it can be expressed as a fraction (i suppose it is rational since it's an exercise for me to find it's rational ...
2
votes
1answer
38 views

rationalize the denominator

Is there any theorem saying that in below fraction we can't rationalize the denominator $\frac{2}{\pi}$ I couldn't find any way and I don't think there is but I was wondering if this actually proved? ...
0
votes
2answers
37 views

Derivative of $f(x)= {\sqrt{x^2-1}\over x}$

I have the function following: $$f(x)= {\sqrt{x^2-1}\over x}$$ And here is what I did: $$f(x)= {\sqrt{x^2-1}\over x}$$ $$ = {{(x^2-1)^{1 \over 2}} \over x}$$ $$f'(x) = { x \cdot {1 \over 2} (x^2-1)...
3
votes
0answers
24 views

Prove that $\left\{\frac{a}{2^b}: a \in\mathbb{Z}, b \in\mathbb{Z}_{\geq 0}\right\}$ is dense in $\mathbb{R}$. [duplicate]

What am I looking for exactly? The hint I was given: show that we can find such a fraction between any two given real numbers.
2
votes
0answers
46 views

How to do this ratios problem without algebra?

Dinesh had some fiction and nonfiction books. The number of fiction was $4/9$ of the total number of books. After he had donated $80$ fiction books and $25$ nonfiction books, there were $20\%$ as many ...
0
votes
2answers
41 views

Distributive Propery with Fractions

I have several problems in this format and I don't know where to start. I understand the distributive property until I get to some fractions. The directions say write each fraction as a sum or ...
0
votes
3answers
29 views

Adding fractions (to find an equal) without known denominator

The question is "Find $v$": $$\frac {1}{20}=\frac {1}{30}+\frac {1}{v}$$ I have no idea what I'm really doing so if someone could explain in a somewhat easy-to-understand way I'd really appreciate ...
1
vote
0answers
106 views

three fractions between π and 22/7

three fractions between π and 22/7 π=355/113 =3.14159 22/7=3.1428 using a/b 355/113<22/7 then a+b/c+d 1) 355+22/113+7 =377/120~ 3.14166 2) 377+22/12+7 =399/127~3.14173 3) 399+22/127+7 =421/134~3....
-2
votes
2answers
49 views

How to solve the following equation: $\frac{3}{x} - \frac{x-3}{2x+10} + \frac{8}{3x+15} = \frac{4}{3}$? [closed]

I'm facing difficulties in solving the following equation - would someone mind giving me a hint? $$\frac{3}{x} - \frac{x-3}{2x+10} + \frac{8}{3x+15} = \frac{4}{3}$$ Thanks in advance!
3
votes
1answer
87 views

$\left[\frac n1\right]+ \left[\frac n2\right] + \cdots+\left[\frac nn\right]+\left[\sqrt n\right]$ is even [duplicate]

Let $n$ be any natural number. Prove that $\left[\dfrac n1\right]+ \left[\dfrac n2\right] + \left[\dfrac n3\right]+\cdots+\left[\dfrac nn\right]+\left[\sqrt n\right]$ is even. I tried this by ...