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

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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
51 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
96 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
28 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
50 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
32 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
25 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
22 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
49 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
52 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 ...
-2
votes
4answers
81 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
33 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
29 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
94 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
41 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
64 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
31 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
vote
3answers
65 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
59 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
47 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
27 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
76 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
32 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
44 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
38 views

Adding drawnfractions (Very simple question)

I have been surprised not being able to solve this: ...
0
votes
1answer
35 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
84 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
89 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
48 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
49 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
47 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
26 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
39 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
33 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: ...
4
votes
4answers
150 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
24 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 ...
2
votes
3answers
120 views

Why$ 1/12$ is NOT an irreducible basic fraction?

I'm trying to solve this problem. A fraction $m/n$ is basic if $0 \le m < n$, It is irreducible if $\gcd( m,n ) = 1$ (greatest common divisor) In the example, when $n=12$, irreducible basic ...
1
vote
2answers
48 views

Find the fraction that creates a repeating decimal that repeats certain digits

Is there any way to find the fraction $x/y$ that, when converted to a decimal, repeats a series of digits $z$? For example: ${x}/{y} = z.zzzzzzzz...$ or with actual numbers, $x/y = 234.234234234...$ ...
1
vote
3answers
62 views

Expressing $\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{5}}$ with rational Denominator

could you please help me express this with a rational denominator $\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{5}}$ Thank you
-1
votes
3answers
88 views

How to simply this fraction with irrational denominators? [closed]

How to simplify? $\frac{1}{1+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{5}} + \frac{1}{\sqrt{5}+\sqrt{7}} \frac{1}{\sqrt{7}+3}$
3
votes
1answer
58 views

How to solve for $x$ in ${\sqrt{9+2x}} - {\sqrt{2x}} = \frac{5}{\sqrt{9+2x}}$

How can I solve for $x$ in the following equation? ${\sqrt{9+2x}} - {\sqrt{2x}} = \frac{5}{\sqrt{9+2x}}$
2
votes
3answers
71 views

How to simplify $(a^2+ab+b^2)/(a+\sqrt{ab}+b)$

How can I simplify as much as possible: $$\frac{a^2+ab+b^2}{a+\sqrt{ab}+b}$$ Also, first post here, looking forward to sticking around!
2
votes
2answers
88 views

What fraction is $\frac{2}{5}$ of $\frac{3}{4}$?

$\frac{2}{5}$ of blood donors at a centre have group O blood. $\frac{3}{4}$ of these donors are under 30. What fraction of the group O blood donors at the centre are under 30? What I did was divide ...
4
votes
3answers
100 views

“Canceling out” in division doesn't always work the same way does it?

I've been working on Nested Fractions at the Khan Academy. Recently I was doing a routine problem and came to the correct conclusion but I realized I didn't understand why I wouldn't keep dividing. ...
10
votes
2answers
355 views

Sum of series with binary parity in the numerator

I'm now stuck with this question, and I don't even know where to start: Find sum of series$$\sum_1^\infty \frac{f(n)}{n(n+1)}$$, where f(n) - number of ones in binary representation of n. I wish I ...