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

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0
votes
2answers
68 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
42 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 ...
1
vote
4answers
69 views

Why does $\dfrac{8}{\frac{8\sqrt{145}}{145}} = \sqrt{145}$? [on hold]

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?
2
votes
6answers
31 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
48 views

Dividing line segments with ratios vs. fractions [on hold]

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
37 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
685 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 ...
1
vote
3answers
75 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
51 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
13 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
53 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
38 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
25 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
38 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
76 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
47 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
24 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
56 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
36 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
28 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
39 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
34 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
53 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
30 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
130 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
27 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
54 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
26 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
86 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
60 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
45 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
99 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
21 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
25 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
34 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
21 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 ...
4
votes
4answers
96 views

why do equations work and how do they relate to each other?

Ok, so I understand that an equation is something like 15 = 15 , and that the only criteria as far as I can tell for it being an equation is that both sides are equal to each other. I have a few ...
0
votes
2answers
23 views

Fractions from least to greatest

What is the fastest way to find the least common denominator of all the fractions without losing too much time? 7/9 , 1/4, 14/15, 2/3, 1/2 Thanks.
2
votes
0answers
60 views

All those unit fractions add to 1?

Consider $$S(n)=\{x \mid x=(a_1 ,a_2,a_3 \cdots a_n) \text{ where } \sum_{r=1}^{n}\frac{1}{a_r} =1 \}$$ Now let $|S(n)|$ denote the cardinaly (order) of set $S(n)$. Thus: $S(1)= \{(1)\} \implies ...
2
votes
2answers
42 views

Cannot find length of repeating block in decimal expansion for $\frac{17}{78}$

I am trying to find the length of of the repeating block of digits in the decimal expansion of $\frac{17}{78}$. On similar problems, that has not been an issue. Take for instance $\frac{17}{380}$. My ...
0
votes
2answers
48 views

Convergence of a series ${}\qquad{}$

Does this series converge? $$\sum_{x=2}^n \left(\frac{1}{x}\right)^{\left(\frac{1}{x}\right)}$$ I tried hard but stil had problems... Could someone help me?
0
votes
1answer
19 views

Solving for $x$ [not homework]

How do I bring the remaining $x$ to the LHS? $\pm x=\frac{(2-x)\sqrt{|q_2|} } {\sqrt{|q_1|}}$ to get $x=\frac{2 \sqrt{|q_2|}}{\sqrt{|q_2|} \pm \sqrt{|q_1|}}$ I'm just not sure about the ...
3
votes
3answers
49 views

confusion related to elementary operation on numbers

Let's take for example an fraction: $\dfrac{1+4}{2-4}$ and another fraction $\dfrac{1*4}{2*4}$. In the second fraction we can cancel 4 from both numenator and denominator but on the first we cannot ...
2
votes
2answers
83 views

Can fractions be relatively prime?

Two numbers are relatively prime if they do not share any factors, other than 1. Is it possible for fractions to be relatively prime? To reword this, do fractions even have factors?
-1
votes
2answers
57 views

Negative mixed fractions

I'm comfortable with fractions like $\frac{-3}{8}$ being the same as $\frac{3}{-8}$ (though I'd think the latter anachronistic and would in any case probably prefer to write either of those two as ...
0
votes
2answers
42 views

Fractional Exponents powers

I am having problems understanding how to answer questions containing fractional exponents to a given power ie $(2x^{1/2})^6$, i do not understand how to go about answering the question. I know this ...
0
votes
2answers
58 views

How to transform $2,(9)$ to form $\frac{a}{b}$

How to transform $2,(9)$ to form $\frac{a}{b}$. My attemp: $$x=2,(9)/\cdot 10$$ $$10x=29,(9)$$ $$10x-x=29,(9)-2(9)$$ $$9x=27$$ $$x=3$$ but do not know if I have done the exact. Please help me
1
vote
1answer
35 views

My small theory…

It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:- a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and ...