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

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-4
votes
1answer
44 views

what would be the answer [closed]

The average of $3$ numbers is $14$ and the smallest of these numbers is $10$. If one of the other two numbers is $8$ less than the other number, which of the following equations represents the ...
0
votes
1answer
17 views

How to label a tenth of a second properly in a graph?

I'm making a graph for a science class, and the x-axis represents every tenth of a second. What's the best way of labeling that axis other than "time (one tenth of a second)", or is that the best way? ...
2
votes
1answer
23 views

Finding the limit by factoring the denominator and canceling

I have the problem $$\lim_{x\to10} \frac{x-3}{x^2+7x-30}$$ If I factor it to $\dfrac{x-3}{(x+10)(x-3)}$ then $x-3$ cancels and I'm left with $0$. I know the real answer is $1/20$, but why is zero ...
1
vote
1answer
35 views

Simplifying an expression written as the sum of three fractions

Specifically, I don't know what to do first given the following expression: $$ \frac{4x - 2}{6} - \frac{2 - x}{4} + \frac{x + 3}{3} $$ So I think of it as $\frac 16(4x-2) - \frac 14(2-x) + \frac ...
3
votes
2answers
54 views

Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$

If $x.y.z=1$ show that $\dfrac 1{1+x+y^{-1}}+\dfrac1{1+y+z^{-1}}+\dfrac1{1+z+x^{-1}}=1$ My attempt - L.H.S$=\dfrac 1{1+x+y^{-1}}+\dfrac1{1+y+z^{-1}}+\dfrac1{1+z+x^{-1}}$ $=\dfrac y{y+xy+1}+\dfrac ...
1
vote
3answers
29 views

Show that $\frac{(b+c)^2} {3bc}+\frac{(c+a)^2}{3ac}+\frac{(a+b)^2}{3ab}=1$

If $a^3+b^3+c^3=3abc$ and $a+b+c=0$ show that $\frac{(b+c)^2} {3bc}+\frac{(c+a)^2}{3ac}+\frac{(a+b)^2}{3ab}=1$
0
votes
2answers
76 views

Parametric solution of the Diophantine equation $\frac{1}{p}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z} ,x,y,z∈Z^+.$

I have prove that, for any given positive integer $p,$ parametric solution of the Diophantine equation $$\frac{1}{p}=\frac{1}{x}+\frac{1}{y}$$ can be written in the form $x=ac(a+b),y=bc(a+b),$ where ...
34
votes
6answers
767 views
0
votes
1answer
37 views

Could this be factored any further?

My friend recently told me that $\frac{-x}{x}$ could not be simplified any further. Is he correct or could it be simplified such that the answer isn't undefined when you ...
3
votes
1answer
174 views

How do I prove that any unit fraction can be represented as the sum of two other distinct unit fractions?

A number of the form $\frac{1}{n}$, where $n$ is an integer greater than $1$, is called a unit fraction. Noting that $\frac{1}{2} = \frac{1}{3} + \frac{1}{6}$ and $\frac{1}{3} = \frac{1}{4} + ...
0
votes
2answers
20 views

Using a factor tree to reduce a fraction? Good Idea?

I am trying to figure out how one reduces 180/100 to 9/5 My factor tree for 180 is 90 *2 - 30*3 -5*6 - 2*3 Thus my prime numbers are 2*3*5 = 30 Maybe I have totally forgotten how to reduce a ...
3
votes
1answer
38 views

How to go from 1/6 to 16 2/3

A VCR is programmed to record a TV show that lasts for a half hour. If the cassette tape used can accommodate 180 minutes of programming, what percent of the tape is used for this recording? I did ...
0
votes
1answer
13 views

Doing wrong in this fraction simplification?

$$ \frac{5}{2x-3} - \frac{3}{(2x-3)^2} $$ I have to simplify So I had the minimun common multiple in $$(2x-3)^2$$ which is $$(2x-3)(2x-3)$$ Then I divide the first fraction denominator by my ...
0
votes
1answer
30 views

Integration with partial fractions help please

I'm trying to work in my partial fractions chapter and some were easy but for whatever reason, I'm stuck now: ∫ (x-3) / (x2+2x+4)2 What I tried: since my denominator is of higher order and a ...
0
votes
1answer
56 views

$\frac{x}{y} \ge \frac{a_1}{b_1} \ge \frac{a_2}{b_2}$ and $b_1 \le b_2 \implies \frac{x+a_1}{y + b_1} \ge \frac{x+a_2}{y + b_2}$?

Given $\frac{x}{y} \ge \frac{a_1}{b_1} \ge \frac{a_2}{b_2}$, where $x,y,a_i,b_i$ are positive numbers. I would like to prove the following: Claim: If $b_1 \le b_2$, then $\frac{x+a_1}{y + b_1} ...
0
votes
2answers
15 views

Simplifying algebric terms

I would like to clarify - when the equation was simplified by dividing both side by 61. why wasnt this equation instead a = 10/61 * b/61 + 230/61 61a = 10b + 230 a = 10/61b + 230
-1
votes
1answer
21 views

Simplify the numerical expression [closed]

9 1/3-12 1/2+(-4 1/6)-(-1 1/6) Simplify the numerical expression
4
votes
1answer
86 views

Prove that if $\frac{x+y}{3a-b}=\frac{y+z}{3b-c}=\frac{z+x}{3c-a}$ then $\frac{x+y+z}{a+b+c}=\frac{ax+by+cz}{a^2+b^2+c^2}$

If $\displaystyle\frac{x+y}{3a-b}=\frac{y+z}{3b-c}=\frac{z+x}{3c-a}$ then prove that $\displaystyle\frac{x+y+z}{a+b+c}=\frac{ax+by+cz}{a^2+b^2+c^2}$ I tried to prove this in many ways. First, I tried ...
0
votes
2answers
25 views

multiply fraction with what number to get a whole number?

I'm solving some programming puzzle and it has come down to this: I've a fraction, say 12/13, and I need to multiply it with a smallest possible natural number (say x) to get a whole number. How do I ...
1
vote
2answers
32 views

How do I convert a fraction in base 10 to a quad fraction (base 4)?

I am totally confused when it comes to converting fractions or floating point numbers to a different base. I have no problem converting whole numbers to any base but when it comes to fractions or ...
0
votes
1answer
19 views

Solving $\frac12 (3y+2)-\frac58=\frac34y$ for $y$ using LCD method

I am solving $$\frac12 (3y+2)-\frac58=\frac34y$$ for $y$ using LCD method. Can't figure out what I did wrong! The answer in the back of the book is $-1/2$. PS: In the first line that is a $1/2$ in ...
6
votes
3answers
195 views

Why do these fractions give $99…9$?

Today, as usual, we were doing all those boring numerical computations in our calculators. It all started when my professor replaced $0.2$ with $1/5$. I got into calculating the unit fractions one by ...
0
votes
4answers
69 views

Is $\frac{4x + 2}{12 x ^2}$ simplifiable?

I'd like to know what methods can I apply to simplify the fraction $\frac{4x + 2}{12 x ^2}$ Is it valid to divide above and below by 2? (I didn't know it but Geogebra's Simplify aparantly does ...
0
votes
1answer
31 views

How can I find $x$, $y$ values for $\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i$

$$ \frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i $$ I believe the format I need in order to solve this problem should be such that the real parts and imaginary parts are separated, ...
0
votes
3answers
66 views

Divison of Fractions

Intuitively answer of $(1/1)/(1/(5^{-2}))=25$ But assuming this mathematical logic of evaluating $(a/b) /(c/d) = (a*d) / (b*c)$ equation evaluates to $1/25$. Is there any specified rule to put ...
2
votes
3answers
90 views

Simplifying nested/complex fractions with variables

I have the equation $$x = \frac{y+y}{\frac{y}{70} + \frac{y}{90}} $$ and I need to solve for x. My calculator has already shown me that it's not necessary to know y to solve this equation, but I ...
0
votes
2answers
29 views

Simplifying Fractions with Radicals

How would I simplify a fraction that has a radical in it? For example: $$\frac{\sqrt{2a^7b^2}}{{\sqrt{32b^3}}}$$
3
votes
1answer
93 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
163 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 ...
4
votes
4answers
512 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
0answers
30 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
5k 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
86 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
54 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
78 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
44 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
338 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
111 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
77 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
99 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
41 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
91 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
50 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 $\large\frac{nb}{pa}=\frac{nd}{pc}$ , ...
5
votes
7answers
771 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
109 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
54 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
69 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 ...