Master Fraction Math Problems with Expert Help

Adding fractions (to find an equal) without known denominatorThe 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 it!

Addison Trujillo 2022-07-04

Calculate X of a math problem
I am trying to learn some more math and I got stuck on this:
$\frac{0.2}{X} = 140$
How do I calculate X?
EDIT
Sorry I meant to calculate
$\frac{28}{X} = 140$
So that $X = 0.2$ but how do I calculate it?

ziphumulegn 2022-07-04

Subtraction of two fractions.
I'm learning math by reading books only and the book I'm currently studying is Smart Math by Marcia Learner in which I practice basic operation on fractions. I can't solve the two following problems. Let me show you how I did it but my answers don't match the answers the book presents.
1. $- 7 / 8 - (- 1 / 3) = ?$
$- 7 / 8 X 3 / 3 = 21 / 24$ and $- 1 / 3 X 8 / 8 = 8 / 24$ $- 21 / 24 + 8 / 24 = 13 / 24$
My answer is $13 / 24$ but, according to the book the answer is $- 1 / 2$
2. $12 / 13 - (- 3 / 7) = ?$
$84 / 91 - (- 39 / 91)$ $84 / 91 + 39 / 91 = 123 / 91$
Book's answer is $105 / 14$
Please tell me where I've done the mistakes. I correctly did the other problems of similar kind but couldn't understand where I've done wrong.

antennense 2022-07-04

How to calculate the Integer portion of a fraction using only +, -, $\div$ and ?
I made something in excel that calculates the days left until a given date, and from that how many weeks were left. I had it so that 9 days displayed as 1.2 using this formula:
$\frac{(\frac{A}{B} - ⌊ \frac{A}{B} ⌋) \cdot B}{10} + ⌊ \frac{A}{B} ⌋$
Where B is the "base" you are counting in and A is the number you are trying to count.
This all works and the question is purely for personal interest only.
So, Is there a way to calculate the Integer portion of a fraction only using the operators +, -, $\div$ and ? Thanks In Advance

Frank Day 2022-07-04

If $x + y + z = 0$ , prove that $\frac{x^{2}}{2 x^{2} + y z} + \frac{y^{2}}{2 y^{2} + z x} + \frac{z^{2}}{2 z^{2} + x y} = 1$
A problem in my homework had asked me:
When $x + y + z = 0$ , evaluate
$\frac{x^{2}}{2 x^{2} + y z} + \frac{y^{2}}{2 y^{2} + z x} + \frac{z^{2}}{2 z^{2} + x y}$
Without too much difficulty, one can see that the value should be $1$ using $(x, y, z) = (1, 0, - 1)$
I decided to use $x = - y - z$ , which turned out not to be as difficult as initially thought. However, would someone care to enlighten me to some other methods of doing this?

therightwomanwf 2022-07-04

Can fractions be written with a one under them and can problems be solved this way
How would you write $\frac{a}{0.1}$ ?
Are either of these ways acceptable?
$\frac{\frac{a}{1}}{\frac{\frac{1}{10}}{1}} = \frac{a}{1} \times \frac{1}{\frac{1}{10}}$
or
$\frac{\frac{a}{1}}{\frac{1}{10}} = \frac{a}{1} \times \frac{10}{1}$

Waldronjw 2022-07-04

Simplifying a radical with complex fractions
So I understand to simplify this:
$\frac{\frac{- 3}{2 t^{4}}}{| \frac{1}{2 t^{3}} | \sqrt{\frac{1}{4 t^{6}} - 1}}$
I can just multiply
$\frac{\frac{- 3}{2 t^{4}}}{| \frac{1}{2 t^{3}} | \sqrt{\frac{1}{4 t^{6}} - 1}} \cdot \frac{2 t^{4}}{2 t^{4}}$
and get
$\frac{- 3}{t \sqrt{\frac{1}{4 t^{6}} - 1}}$
But how do you simplify further getting rid of the complex fraction inside the radical?

grenivkah3z 2022-07-04

Mathematical Induction getting the right side
So I 've been doing Mathematical Inductions but I seem to have a issue in simplify and getting the right side.
So I have this on the L.H.S
$\frac{k (k + 1) (2 k + 1)}{6} + (k + 1)^{2}$
And I'm trying to make it equal to
$\frac{(k + 1) (k + 2) (2 k + 3)}{6}$
I've check the book for help but for this it seems to be skipping some steps.
And I might as well post this as well which I had the same issue as above.
$\frac{3 (5^{k + 1} - 1)}{4} + 3 \cdot 5^{k + 1}$
to
$\frac{3 (5^{k + 2} - 1)}{4} .$

logiski9s 2022-07-03

How to prove that $\frac{\ln 12}{\ln 18}$ is irrational witout using the change of base rule?
I have to show that $\frac{\ln 12}{\ln 18}$ is irrational by using change of base rule.
At the beginning I have proved that $\ln r$ is irrational for any rational $r$ , $r \neq 1$ . Then using this we can say that $\ln 12$ and $\ln 18$ are irrational.
But from here it is difficult for me to show that the fraction is irrational knowing that both the numerator and the denominator are irrational.

Grimanijd 2022-07-03

How does this seemingly-trivial simplification work?
In a section on inductive proofs in the book Modelling Computing Systems: Mathematics for Computer Science (Muller, Struth) there is a simplification that is assumed to be trivial, but that I can't figure out.
It occurs in this step:
$\frac{k (k + 1) (k + 2)}{3} + (k + 1) (k + 2) \overset{?}{=} \frac{(k + 1) (k + 2) (k + 3)}{3}$
How does one get from the first expression to the second?

cambrassk3 2022-07-03

How do you solve B and C for $\frac{s - 1}{s + 1} \frac{s}{s^{2} + 1} = \frac{A}{s + 1} + \frac{B s + C}{s^{2} + 1}$ ?
$A = {\frac{s^{2} - s}{s^{2} + 1} |}_{s = - 1} = \frac{1 - (- 1)}{1 + 1} = 1$

Araceli Clay 2022-07-03

Absolute values in logarithms in a solution of differential equation
How have the moduli signs disappeared in the following step:
$\frac{1}{k} (\ln | g + k v | - \ln | g + k u |) = - t$
Therefore
$\ln (\frac{g + k v}{g + k u}) = - k t$
$g$ , $k$ and $u$ are positive constants. $t$ is time, $v$ is velocity.
Context: the above calculations are from solving the equation $d v / d t = - g - k v$ given that $v = u$ when $t = 0$ , and that $u$ , $g$ and $k$ are positive constants.

sebadillab0 2022-07-03

Prove that $\frac{a}{b + 2 c + 3 d} + \frac{b}{c + 2 d + 3 a} + \frac{c}{d + 2 a + 3 b} + \frac{d}{a + 2 b + 3 c} \geq \frac{2}{3} .$
I was thinking of trying $a \geq b \geq c$ since the inequality is cyclic. I am not sure how to use this, though, or if this would help simplify the inequality. It also doesn't look like I can really use AM-GM or Cauchy-Schwarz.

Yesenia Obrien 2022-07-03

Is this fraction non-terminating?
I recently stumbled upon an observation: the fraction $\frac{x}{y}$ terminates if and only if $y$ only has prime factors $2$ and $5$
For example:
$\frac{1}{20} = \frac{1}{2 \cdot 2 \cdot 5} = 0.05$
$\frac{1}{6} = \frac{1}{2 \cdot 3} = 0.1 \bar{6}$
I think this is true because fractions are in the form:
$\frac{a}{10} + \frac{b}{100} + \frac{c}{1000} + \dots$
$\frac{a}{2 \cdot 5} + \frac{b}{2 \cdot 2 \cdot 5 \cdot 5} + \frac{c}{2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5} + \dots$
How can I rigorously prove this?\

Sonia Ayers 2022-07-03

Is there an example to demonstrate why $\frac{1}{(1 / 2)}$ equals 2?

Janet Forbes 2022-07-03

Partial Fraction Decomposition with complex poles
I have a function which I'd like to perform partial fraction decomposition on, to allow easier inverse laplace transform.
$F (s) = \frac{1}{s (s^{2} + 140 s + 10^{4})}$
I begin with finding the poles
$s = 0, s = - 70 \pm j \cdot 10 \sqrt{51}$
To which I then try putting $F (s)$ in this form:
$F (s) = \frac{A}{s} + \frac{B}{s - 70 + j \cdot 10 \sqrt{51}} + \frac{B^{}}{s - 70 - j \cdot 10 \sqrt{51}}$
Because one unknown ( $B^{}$ ) is just the complex conjugate of $B$ , I only need to find out what $A$ , and $B$ is.
$A = F (0) = 10^{- 4}$
$B = F (- 70 + j \cdot 10 \sqrt{51}) \approx 6.31514 \cdot 10^{9} + j \cdot 6.44274 \cdot 10^{9}$
Where the last step was done in Mathematica.
Answer, according to several other people, is supposed to be $B = - 70 + j \cdot 71.41$ , which looks a lot nicer, but I'm not sure HOW they got to that answer.

Frank Day 2022-07-02

Find $x$ in $\log x^{2} = (\log x)^{2}$
I couldn't find x.

veneciasp 2022-07-02

How do you add two fractions?
I have a fraction I am trying to solve. I know the answer already, as Wolfram says it is $\frac{143}{300}$ .
The fraction is:
$\frac{5}{12} + \frac{3}{50} = ?$
Please explain why and how your method works.

bandikizaui 2022-07-02

Get rid of the square roots of the denominator: $\frac{1}{\sqrt{7} - 2 \sqrt{5} + \sqrt{3}}$
I squared the whole denominator, but that didn't help.
Also I searched for a propriety or identity like $A^{2} - B^{2}$ , but I didn't see one that could fit. Any help is appreciated.

Caleb Proctor 2022-07-02

If the chance of an event was $1 / 128$ and increased by 20%, what is the new chance?
So I have something that has a 1/128 chance of occurring, let's say. Suddenly, the chances of that thing happening are increased by 20%. How is that fraction written? Would you multiply 1/128 by 6/5 (yielding 3/320), or would you take 128, multiply it by 4/5, and then invert it (1/102)?
This isn't for homework, I'm merely curious.
Thank you

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