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

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1
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1answer
41 views

Can we write “fractional root” symbol in math?

Fractional exponents are legit but I have never seen fractional roots, so I just wonder if we can write fractional roots such as this: It sometimes can be convenient to think about too.
3
votes
6answers
315 views

Is $15/52$ equal to $17/59$?

Is $\frac{15}{52} = \frac{17}{59}$? I typed it into the calculator and found: $$\frac{15}{52} = 0.2884615 $$ $$\frac{17}{59} = 0.2881356 $$ So I thought they were different. But then my friend said ...
0
votes
1answer
25 views

Simplification imaginary fractions

In an exercise, a partial fraction expansion has to be done. I have no problem with that, but one of the last steps includes a simplification as follows: \begin{equation*} \left( -\frac 12 - \frac 16 ...
0
votes
3answers
28 views

Ordering an even and odd fraction that are close

We know that $1/4 < 5/11 < 1/2$. I did it this way from small to large: $$\frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}$$ $$\frac{5}{11}$$ $$\frac{1 \cdot 6}{2 \cdot 6} = \frac{6}{12}$$ It is ...
-4
votes
1answer
26 views

Question including Function and Radical [on hold]

For $f(x)= \sqrt{x-2}+1$ : How would I solve for $x$ make a table and graph? Thank you!
0
votes
1answer
33 views

Simplifying Radicals (Algebra II Basics) [closed]

Please help me with these problems! I have a quiz coming up and this is just practice. I already solved them, I just am asking for another set of eyes to solve these. (It is not homework, only extra ...
-1
votes
3answers
58 views

How to show simple inequality of fractions

If $$\frac {a}{a+b}<\frac{a'}{a'+b'}$$ then how can I show that $$\frac {a}{a+2b}<\frac{a'}{a'+2b'}\ \forall\ a,b,c>0$$ I tried puitting in a constant k so $$\frac ...
0
votes
1answer
12 views

Farey Sequence implemenatation

I'm trying to use the Farey sequence to get the next lowest reduced fraction in a list. For example, for $n = 8$, we have $\dots, \frac13, \frac38, \frac25, \frac37, \frac12, \dots$ So let's take ...
2
votes
2answers
30 views

Sign of fractional exponent [duplicate]

What is the sign of $-1^{\frac{2}{3}}$? I thought it was positive 1 because it involves squaring, but that doesn't seem to be the case. Why?
1
vote
2answers
41 views

Solving equations including floor function.

I got a little trouble solving equations that involve floor function in an efficient way. For example : $$ \left\lfloor\frac{x+3}{2}\right\rfloor = \frac{4x+5}{3} $$ In the one above, I get that ...
4
votes
4answers
89 views

How does $-\frac{1}{x-2} + \frac{1}{x-3}$ become $\frac{1}{2-x} - \frac{1}{3-x}$

I'm following a solution that is using a partial fraction decomposition, and I get stuck at the point where $-\frac{1}{x-2} + \frac{1}{x-3}$ becomes $\frac{1}{2-x} - \frac{1}{3-x}$ The equations are ...
1
vote
1answer
27 views

rational numbers as upper limit of a summation?

a quick question: Is it a legit way to use a fraction as the upper limit of a summation? Given is a frequency $f$ and a sample rate $f_s$. I want to use a sum like this: $\sum_{k=1}^{\frac{f_s}{2f}} ...
0
votes
5answers
47 views

canceling double fractions how?

I had this example: $$ \frac{\frac{11}{5}}{2} = \frac{11}{10} $$ then: $$ \frac{2\frac{1}{5}}{2} = \frac{11}{10} $$ $$ \frac{1}{5} \not= \frac{11}{10} $$ is this right canceling of double ...
1
vote
2answers
30 views

If $\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$, prove that $\frac{a}{d}=\sqrt{\frac{a^5+b^2c^2+a^3c^2}{b^4c+d^4+b^2cd^2}}$

What I've done so far; $$\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=k\\ a=bk, b=ck, c=dk\\ a=ck^2, b=dk^2\\ a=dk^3$$ I tried substituting above values in the right hand side of the equation to get ...
1
vote
1answer
23 views

Order approximation for rational polynomial

I have this fraction: $\frac{(-12a^3)d^3 + (4wa^3 - 16a^2)d^2 + (5wa^2 - 8a)d - a^2w^2 + 2aw - 1}{(- 12wa^4 + 12a^3)d^3 + (4a^4w^2 - 20a^3w + 16a^2)d^2 + (4a^3w^2 - 11a^2w + 7a)d + a^2w^2 - 2aw + 1}$ ...
0
votes
0answers
20 views

Calculating enrichment

My question concerns how enriched something is as im trying to combine several lists of uneven group size and the answer is escaping me. So basically, I have 6 groups and I want to compare them with ...
0
votes
2answers
47 views

$\frac{6}{4 \times 2} + \frac{7}{5 \times 2} + … + \frac{21}{19 \times 2}$

I got this exercise from school and I have no idea what notion to use, it resumes to Harmonic series, I can't find a generic answer. Do you have any idea? $\frac{6}{4 \times 2} + \frac{7}{5 \times 2} ...
2
votes
1answer
47 views

High School Probability and Contradiction

So I recently came across this question (2(a)) that my friend who teaches high school math posed to me. I thought the solution could be found by using the identities $P(B\,|\,A) = \dfrac{P(A\cap ...
-3
votes
4answers
72 views

How to prove that $\frac{\ln 12}{\ln 18}$ is irrational witout using the change of base rule? [closed]

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 $r$, $r\ne 1$. Then using this we ...
0
votes
4answers
35 views

Mixed Fractional Equation?

$$3 \frac{3}{5} + \frac{2}{x} = 4\frac{4}{15}$$ I tried subtracting by both sides, etc, but it didn't come out right. I also tried multiplying by both sides, but, it didn't seem to work. what would ...
1
vote
4answers
31 views

Monotonicity of a fraction.

So I want to prove that the following fraction is monotone increasing, as a part of another proof, that's why I stumbled on: $$\frac{4^{n+1}}{2\sqrt{n+1}} \ge \frac{4^{n}}{2\sqrt{n}}$$ I know it's ...
0
votes
0answers
28 views

Long division for multipolynomial expression, little o notation

I have this expression: $$\mathrm{Exp}=\frac{d^3(-12a^4)+d^2(4a^4-16a^3)+d(4a^3-6a^2-a)}{d^3(-12a^4+12a^3)+d^2(4a^4-20a^3+16a^2)+d(4a^3-11a+7a)+(1-2a+a^2)}$$ Is there any way I can take the second ...
1
vote
2answers
85 views

Can we say that $\sqrt{2}=2/(2/(2/(2/\ldots)))$?

Can we say that $\sqrt{2}= \cfrac{2}{\cfrac{2}{\cfrac{2}{\cfrac{2}{\ldots}}}}$? We have ...
0
votes
1answer
31 views

Equivalent forms of expressions with complex numbers

Which expressions are equivalent to $ {1\over{(9i+z)^4}} + {1\over{(9i-z)^4}}$ Select all that apply. $ {18i\over{(81−z)^8}}$ $ {−18i\over{(81+z)^8}}$ $ {18i\over{(81+z)^8}}$ $ ...
1
vote
4answers
47 views

What fraction of her salary does Joan manage to save?

Last Month, Joan spent 1/3 of her monthly salary on food, 2/5 on her child's tuition fees and 3/4 of the remainder on transportation. If she then saved the rest, what fraction of her salary did she ...
-1
votes
1answer
30 views

Elementary Fractions

There are two identical water jugs, A and B. Jug A is 3/7 full of water and Jug B is 8/11 full. What fraction of the capacity of a jug should water be poured out from jug B to jug A so that they both ...
1
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3answers
63 views

How is $\frac{(10^{4})^{6}-1}{10^4-1} = 1 + 10^{4} + 10^{8} + 10^{12} + 10^{16} + 10^{20}$?

As the title states, how is: $$\frac{(10^{4})^{6}-1}{10^4-1} = 1 + 10^{4} + 10^{8} + 10^{12} + 10^{16} + 10^{20}$$ I can't see the pattern. Can someone please help? Thanks.
-1
votes
4answers
57 views

Multiplying whole number with fractions.

I'm looking at a solution to a math problem and there are obviously some rules regarding multiplication of fractions that I don't know. Can someone make any sense of this? $$s_n = 625 \cdot ...
3
votes
1answer
44 views

Finding all possible pairs of positive integer values

The ratio of the sum of two positive integers to their difference is $7:5$. If the the sum of the two numbers is at most $25$, find all possible values for the pair of numbers. Let $m$ be the first ...
0
votes
1answer
24 views

Fraction Transforms

Here's a number theory problem I'm having some difficulty with: Say we transform a fraction by the following rule: we start with some fraction $\frac{m}{n}$ with $m > n$ and then convert it to ...
1
vote
5answers
75 views

How to compute $\frac{t^2}{t+1}$ to the form $\frac{1}{t+1} +t -1$

One of my attempts would look like below. $\frac{t^2}{t+1}$ = $\frac{t \times t+1-1}{t+1}$ = 1+ $\frac{t-1}{t+1}$ = $\frac{t-1+1-1}{t+1} + 1$ = $\frac{-2}{t+1} +2$ Also, I put into t an arbitrary ...
0
votes
3answers
29 views

Adding fractions with exponents

$$3^5 + {1\over3^5}=?$$ My first instinct was to rewrite the second term as $3^{-5}$. Since the base is $3$, rewrite as $3^{5+-5}$. It simplifies to $3^0= 1$. Apparently this is incorrect. Can anyone ...
0
votes
2answers
41 views

Reciprocal over a summation [closed]

Is this statement true? Can we take reciprocal over a summation? $$\frac 1{\sum_{n=1}^\infty\frac 1{(n+1)^3}}=\sum_{n=1}^\infty (n+1)^3$$
0
votes
2answers
37 views

Adding drawnfractions (Very simple question)

I have been surprised not being able to solve this: ...
0
votes
1answer
33 views

Recursive formula for partial fraction decomposition of a specific kind of fractions

I need to make a partial fraction decomposition of the following fraction : $$ \frac{1}{(x-a)^2(x-b)^2(x-c)^2(x-d)^2(x-e)} $$ The problem is that Wolfram doesn't give any answer : ...
2
votes
3answers
83 views

If $\frac{a}{b}=\frac{x}{y}$, is $\frac{x-a}{y-b}=\frac{x}{y}$? [closed]

Does this hold? $b,y \neq 0$, $b \neq y$.
0
votes
4answers
29 views

Simplifying $\frac{3(a^{1/4}+4)}{2a-32a^{1/2}}$

I have a fraction $\frac{3a^{1/4}+12}{2a-32a^{1/2}}$ which I have factored out into $\frac{3\left(a^{\frac{1}{4}}+4\right)}{2a-32a^{\frac{1}{2}}}$, but checking out W|A I also get that there ought to ...
0
votes
4answers
78 views

What is the reciprocal of $(-1/2)^k$?

What is the reciprocal of $(-1/2)^k$? The answer is meant to be $2^{-k}$ as if you flip something upside down the power becomes negative. However, I am not sure what happens to the negative in front ...
0
votes
4answers
39 views

Algebraic fractions: addition

I have very elementary question about adding algebraic fractions. Now, I know the following: $$\frac{a}{c} + \frac{b}{d} = \frac{da + cb}{dc}$$ My question is however, how given this expression: ...
1
vote
0answers
31 views

How many elements are in the following set?

The set is $$\{ x \in Q:x^2 =64/25 \} $$ I thought the answer was $\{ \frac{8}{5}, -\frac{8}{5} \}$ but I am told there are in fact 4 distinct elements: $$\{ \frac{8}{5}, \frac{8}{-5}, \frac{-8}{5}, ...
2
votes
1answer
45 views

algebra exponents and fractions

I could be over thinking or tired... But I am to embarrassed to ask my prof. this probably very simple algebra rule I am ignorant of... Also this is just a snip-it from a inductive proof example. ...
0
votes
1answer
44 views

Annuity present value formula explanation

Could somene please explain me how the formula evolves, ie. how does the fraction flip, etc? Thank you in advance!
0
votes
1answer
22 views

Pre-Algebra Fractional Exponent Question

Why does $t^{\frac{3}{2}} \cdot t^{\frac{1}{2}} = t^2$? What I tried to do was multiply the exponents together $\frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}$ so my final answer was $t^{\frac{3}{4}}$ ...
2
votes
3answers
36 views

How to calculate value of expressions when $a = 22$

$a = 22$ Round the answer to three significant figures: $\dfrac{77}{3a}$ for this one I am not sure if I do $\dfrac{77}{3(22)} = 1.17$ or $\dfrac{77}{3(22)} = 56$. Sorry if this is written in a ...
2
votes
1answer
27 views

How exactly is this happening?

I was studying Derivative and my book says if: Then its derivative is: I can't understand how the writer has changed the first derivative fraction into the second one. In other words, how did he ...
0
votes
0answers
24 views

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: ...
0
votes
0answers
17 views

Separate terms of different orders from fractional polynomial

I have an expression: $\frac{1}{1-A}+\frac{-12A^4D^3 + 4A^4D^2 -16A^3D^2+4A^3D -6A^2D - AD}{- 12A^4D^3 + 4A^4D^2+12A^3D^3 -20A^3D^2 +4A^3D +16A^2D^2 -11A^2D +A^2 +7AD -2A + 1}$ How do I write it as ...
4
votes
4answers
133 views

Find All Dimensions such that Volume of Box = Surface Area

A rectangular prism has integer edge lengths. Find all dimensions such that its surface area equals its volume. My Attempt at a Solution: Let the edge lengths be represented by the variables $l, w, ...
0
votes
1answer
20 views

Second Order Approximation for a Polynomial

if I have an expression: $L=\frac{12a^3d^3-4wa^3d^2+16a^2d^2-4wa^2d+6ad+1}{12a^3d^3-4wa^3d^2-4a^2wd+16a^2d^2+7ad-aw+1}$ what is the second order approximation in $\frac{d}{w}$? I know that ...
1
vote
0answers
17 views

Extracting a function of a variable from an expression

I have this expression: $\frac{d+2wd}{2w+3wd-3d-w^2-1}$ Is there anyway I can write it just as a function of f(d)? [To me this looks like it is already a function of d, but I want to confirm if ...