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

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1
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2answers
49 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
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1answer
55 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 ...
0
votes
6answers
81 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
165 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
41 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
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2answers
68 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
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2answers
40 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, ...
0
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2answers
30 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
28 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 ...
-1
votes
2answers
76 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
29 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
5 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
49 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
48 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
89 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
6 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
32 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
35 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
44 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
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5answers
123 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
45 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
37 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
35 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} ...
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
43 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
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0answers
98 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 ...
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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
84 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 ...
0
votes
0answers
74 views

Simplifying a ratio to lowest form: How to tell which number to divide by both quantities of the ratio to get to lowest form in just one step?

The question is to simplify the following ratio 72 is to 48 which can be written as 72 : 48. Now if I knew the table of 24, ...
1
vote
1answer
48 views

What is the difference between a simple “fraction” and a “common fraction”?

I have read about a common fraction in this statement (written in a text book): Ratio is the simplest form of a common fraction, in which the numerator denotes the antecedent and the denominator ...
0
votes
1answer
106 views

Converting a negative decimal with fractions to binary and hex

I am asking the question even though it has been answered before because I am looking at 3 different pages with 3 different answers right now. I am wondering how to convert a negative decimal with a ...
2
votes
3answers
123 views

How would one work this out? (Fractions)

One fifth of all value lamps are already defected at the time of purchase. How many do you have to buy to ensure that you have 16 functioning lamps.? Anyone have any advice on how to layout this ...
0
votes
3answers
53 views

The result of subtracting the integer part of $x$ from $x$

I want to know what does this formula do with the integer $x$ $$\text{frac}(x) = x - \lfloor {x}\rfloor ,\ x >= 0$$ I've searched and found that this is called finding the fraction part of $x$ ...
0
votes
0answers
24 views

Variable value estimation for given product/fracture values

I have a data set (time series) with given values for certain fractions xy = x/y (where x,y are not constant over time) Thus, there are following fractions: AB = A/B CB = C/B AD = A/D CD = C/D AE = ...
0
votes
0answers
46 views

Euler Totient Function and new fraction numbers

Euler’s Totient Function can be used to calculate the count of new fraction numbers [below 1] as the divisor increases. New fractions identified are always either odd/odd, even/odd or odd/even. With ...
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votes
3answers
94 views

Find the value of $\frac{ x_1^2}{1-x_1}+\frac{x_2^2}{1-x_2}+…+\frac{x_n^2}{1-x_n}.$ [closed]

Suppose, $x_1+x_2+...+x_n=1\space (x_i\in \mathbb{R}, x_i ≠1)$ and $\frac{ x_1}{1-x_1}+\frac{x_2}{1-x_2}+...+\frac{x_n}{1-x_n}=1.$$\\$ Find the value of $\frac{ ...
0
votes
3answers
30 views

Comparison of two values

I have to figure out the relation between the quantity $(0.9/1.1)^2 +(1.1/0.9)^2$ and 2. How can i do this without explicitly calculating the first value, by using some laws of exponents?
1
vote
3answers
34 views

Rationalization of a fraction

Can someone please explain how i can rationalize the fraction $\frac{2 +\sqrt{3}}{(2-\sqrt{3})^3}$ so that i obtain an answer that has an exponent of 6. I basically need to compare this value with ...
6
votes
4answers
604 views

How can I simplify this complex number to get a real number?

$$\large \frac {e^{i \frac{\pi a}{2}}[1-e^{i\pi a}]} {[1-e^{i2\pi a}]}$$ I am trying to arrive at $$\large \frac {1}{2\cos\left(\frac{\pi a}{2}\right)}$$ I've tried dividing top and bottom by one of ...
1
vote
3answers
138 views

Solving a rational equation with multiple and nested fractions

This is the equation to solve: $\dfrac{\dfrac{x+\dfrac{1}{2}} {\dfrac{1}{2}+\dfrac{x}{3}}}{\dfrac{1}{4}+\dfrac{x}{5}}=3$ What I did: $x+\dfrac{1}{2}=\dfrac{2x+1}{2}$ ...
2
votes
5answers
114 views

Is $(x^2 + 1) / (x^2-5x+6)$ divisible?

I'm learning single variable calculus right now and at current about integration with partial fraction. I'm stuck in a problem from few hours given in my book. The question is to integrate $$\frac{x^2 ...
0
votes
1answer
38 views

Removing a fraction in the denominator

What steps do I need to take to simplify $\frac{1}{\frac{1}{\sqrt{2}}}$ to $\frac{\sqrt{2}}{1}$? Can you please explain the steps i need to take in this problem and explain generally how to remove ...
0
votes
4answers
42 views

I can't understand the algebraic simplification below

I can't understand the last step of simplification in the following algebraic expression. I am aware that $\sqrt{3}=3^{\frac{1}{2}}$. Can't see how they get the $6$ in the denominator, and how ...
5
votes
1answer
61 views

Question on recurring decimal digits

In my discrete maths class, I have come across an interesting phenomenon for which I can't find an explanation! If we divide $1$ by $13$ we obtain $0.07692307\ldots$ If we divide $3$ by $13$ we ...
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votes
1answer
23 views

Fractions and decimals

Ten companies sponsored a tournament and decided to give M rupees collectively.Two companies dropped and remaing agreed on paying their share equally.What was the increase in share of each company? ...