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

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2
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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
51 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
41 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
36 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
157 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
122 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
49 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
64 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
74 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
113 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
356 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 ...
0
votes
1answer
39 views

$5.30$ converted to a fraction or mixed number in lowest terms

$5.30$ converted to a fraction or mixed number in lowest terms The correct answer they got on my worksheet is $5 \frac3{50}$, but I get $5 \frac{15}{50}$.
1
vote
3answers
81 views

How to put a fraction in simplest form, such as $140/255$?

Given the fraction $$\dfrac{140}{255}$$ How do I find a common factor so it can be easily simplified? I have already tried $2$, $3$ and $4$.
2
votes
4answers
62 views

Why does the least common denominator work?

Take for instance the following problem. You have two beakers of the same height. One has tick marks that break it into thirds. The other has tick marks that separate it into fourths. The water levels ...
4
votes
5answers
2k views

why is PI considered irrational if it can be expressed as ratio of circumference to diameter? [duplicate]

Pi = C / D (circumference / diameter) . I have read that if circumference can be expressed as an integer then diameter cannot and vice-versa, so that the ratio can never be expressed as a/b where both ...
-1
votes
2answers
31 views

Fraction confusion

I read in a set of memoranda that if $ \frac{b-x}{x}=\frac{b}{a}$, then $$x = \frac{ab}{a+b}$$ How is this true? I tried working it out but I could not understand. Please help.
0
votes
1answer
54 views

How can I integrate $\int{1\over 2x+2}$

$$\int{1\over 2x+2}$$ Method 1 $$\int{1\over 2x+2} = \frac 12\int{1\over x+1} = \frac 12 ln(x+1) + c $$ Method 2 $$\int{1\over 2x+2} = \frac 12\int{2\over 2x+2} = \frac 12 ln(2x+2) + c $$ Wolfram ...
4
votes
6answers
125 views

Find $\lim_{x \to \infty} \left(\frac{x^2+1}{x^2-1}\right)^{x^2}$

How to calculate the following limit? $$\lim\limits_{x \to \infty} \left(\frac{x^2+1}{x^2-1}\right)^{x^2}$$
2
votes
5answers
132 views

Is $\frac{\sqrt7}{\sqrt[3]15}$ rational or irrational?

Is $\frac{\sqrt7}{\sqrt[3]15}$ rational or irrational? Prove it. I am having a hard time with this question. So far what I did was say, assume it's rational, then ...
7
votes
3answers
115 views

Show that $\frac{1}{a}+\frac{1}{b}\not=\frac{1}{a+b}$

Problem Assume that $a,b\in\mathbb{R}-\{0\}$ and that $a+b\not=0$. Prove that $\frac{1}{a}+\frac{1}{b}\not=\frac{1}{a+b}$. My Proof Let's assume that $\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b}$, then ...
0
votes
3answers
73 views

Find the fractional representation $p/q$…

Been trying to get some sort of solution for this for hours now, with no avail. Find the fractional representation $p/q$, with $p \in \mathbb{N}$ and $q \in \mathbb{N}$, of the rational number whose ...
2
votes
3answers
70 views

If an object halves its speed every second (but never gets to 0), will it eventually get from point A to point B?

There is a ball that starts at point A on a line and moves toward point B. Every second, it moves half of the distance left, but never stops moving: Etc. Would the ball ever reach point B? In one ...
0
votes
4answers
42 views

infinity sum of the fractional

Can anyone explain how to simplify $ \frac{2}{3} + \frac{6}{9} + \frac{12}{27} + \frac{20}{81} + \frac{30}{243} + . . . $ I have no any idea since i dont have pattern i can't do it with integral or ...
5
votes
0answers
52 views

Is there any elegant formalization of fractional numbers?

The question is just what is on the title, but I'll describe the context for completion: Natural numbers can be encoded quite elegantly on the Lambda Calculus as church numbers, that is, a function ...
0
votes
1answer
49 views

Fraction in other bases

How to convert a base 10 fraction into fraction in other bases?. For example base 10 fraction 17/94, How we convert this 17/94 into base 2 fraction ?
1
vote
4answers
116 views

How come $\left(\frac{n+1}{n-1}\right)^n = \left(1+\frac{2}{n-1}\right)^n$

I'm looking at one of my professor's calculus slides and in one of his proofs he uses the identity: $\left(\frac{n+1}{n-1}\right)^n = \left(1+\frac{2}{n-1}\right)^n$ Except I don't see why that's ...
0
votes
2answers
27 views

Compare colon notation with fraction

I'm working on a job interview test and there is one answer which I just don't get. The test states that statement below is true. To me it just seems wrong. No box is provided to check. Then how do I ...
2
votes
2answers
54 views

simplifying and factoring a fraction

how i get $\frac{(a+b)^2+(a+c)^2+(b+c)^2}{2}$ from $\frac{a^4}{(a-b)(a-c)}+\frac{b^4}{(b-a)(b-c)}+\frac{c^4}{(c-a)(c-b)}$ assuming that $a\ne b\ne c\ne a$ i tried to make $$\begin{align} ...
1
vote
5answers
514 views

Un-Simplifying a fraction, i.e. computing partial fraction decomposition

$\frac{3x^2+17x}{x^3+3x^2+-6x-8}$ I need to find the value of C in the form of $\frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{x+4}$ which is based on the fraction give at the top. I can get so far to do ...
1
vote
1answer
11 views

Explaining the non-application of the multiplication law of logarithms, when logs are in the denominators.

I have an A' Levels student who had to solve the following problem: $ log_2 x + log_4 x = 2$ This was to be solved using the Change of base rule, and then substitution, as follows: $ \frac{1}{log_x ...
0
votes
1answer
25 views

Is there a value for $a$ other than a factor or a multiple of $c$ in $\frac{a}{b}=\frac{c}{d}$

Suppose $a,b,c,d$ to be whatever quantities whatsoever that satisfy the proportion $\frac{a}{b}=\frac{c}{d}$. Is there a value for $a$ other than a factor or a multiple of $c$. Or, is there a value ...
0
votes
0answers
20 views

GCD and fraction problem

If x/y = 1/a + 1/b + 1/c and GCD of a , b and c is 9 then find a) minimum of x and y which do not cause x/y repeating decimal b) the best of x and y that cause x/y nearly to 3/10 many ...
0
votes
2answers
46 views

Does there exist $a,b,c,d$ such that $\frac{a+b+c+d}{4}$ is an integer?

Let $a,b,c,d$ be defined as such: $$\{a,b,c,d\} \geq 1,\\ a\neq b\neq c\neq d,\\ a \not\in \{bx,cx,dx\},\\ b \not\in \{ax,cx,dx\},\\ c \not\in \{ax,bx,dx\},\\ d \not\in \{ax,bx,cx\},\\ \{a,b,c,d\} ...
3
votes
1answer
62 views

When is $(12x+5)/(12y+2)$ not in lowest terms?

I am struggling to solve this problem and would appreciate any help: When is $\frac{12x+5}{12y+2}$ NOT in lowest terms? (x,y are nonnegative integers) I have found that it is not in lowest terms for ...
4
votes
3answers
68 views

Proving $\lim _{x\to \infty }\left(\frac{\sqrt{x+1}-\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-3}}\right) = \frac35$

$$\lim _{x\to \infty }\left(\frac{\sqrt{x+1}-\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-3}}\right)$$ Can someone help me to solve it? result of online calculator: 3/5
4
votes
2answers
371 views

Equivalent of adding to a denominator?

Given the inequality $\frac{n}{m} \ge \frac{1}{2}$, I want to add $1$ to both $n$ and $m$: $$\frac{n+1}{m+1}.$$ What would be the equivalent operation on the RHS of the equation? Adding $1$ to $n$ ...
1
vote
2answers
102 views

How is $\frac{1-x}{x^2-1}=\frac{1}{x+1}$?

When integrating $\int \frac{1-x}{x^2-1} dx$ Maple rewrote it as $-\int\frac{1}{x+1}dx$ How is $\frac{1-x}{x^2-1}=\frac{1}{x+1}$?
0
votes
1answer
53 views

Shorten $\frac{n}{n^\frac{1}{2}}$?

I have a short question to solve my problem. Can I simplify $\frac{n}{n^\frac{1}{2}}$ ? Thanks already for answers.
0
votes
1answer
39 views

Rearranging equation

I'm reading a textbook in which an equation is rearranged and I'm failing to see how they've done it. I've tried writing it down step by step in my notebook but can't come up with the right answer. ...
0
votes
1answer
100 views

Fractions vs Decimal numbers

I want to know if there is any difference between Fractions and Decimal numbers, are Decimal numbers just Fractions that are written in a different way according to a predefined rule: using "a group ...
0
votes
1answer
46 views

Fractional Exponents and Fractions

When dealing with fractional exponents like in the question below, how do you combine them so the two "n's" in the first fraction become one? ((how do i combine $4/3$ with $1/3$)) The aim is to end ...
2
votes
5answers
47 views

need help on this fraction equation $2/5 = 2/3 - r/5$

$$\frac{2}{5} = \frac{2}{3} - \frac{r}{5}$$ I'm trying to find $r$. Can anyone give me a step by step?
1
vote
1answer
47 views

What is the smallest fraction produced by a sum of fractions with bounded denominator?

For $x$ a sum of fractions: $$ x = \sum_{i=1}^{N}\frac{a_i}{b_i} $$ for all $a_i, b_i \in \mathbb{Z}$ with $ 0 < b_i \leq D$ and $N$ are non-zero positive integers, I know that the denominator of ...