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
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4answers
25 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
28 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
36 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
34 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!
-1
votes
1answer
36 views

What is the real concept of decimals and it's relation with fractions?

Lets suppose 1/4 as an example. So I can conclude the following: I know when we used 1/4 that we are saying that we have a number that is bigger than 1 and smaller than 2. I also know from the ...
0
votes
1answer
20 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
35 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 ...
-5
votes
1answer
43 views

fraction math help please [closed]

What is $\frac{2}{5}-\frac{4}{9}$ and $5 \frac{3}{4}\pm\frac{5}{6}...$?
-3
votes
1answer
22 views

fraction word problem for Kaleb [closed]

If my flower pots are 3 and one half by 1 and three fourth inches in a 6x6 array with no spaces between, what is the area covered by the flower pots?
0
votes
0answers
20 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
15 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 ...
0
votes
1answer
17 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
110 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
43 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
58 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
77 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
57 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
65 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
81 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
67 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
339 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
30 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
63 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
57 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 ...
2
votes
2answers
47 views

Determine whether a fraction will produce a rational number with infinite digits after the decimal

This may be a naive question but I would like to know whether we can determine if a fraction (say $1/3$) will produce a rational number with an infinite number of digits after the decimal when ...
4
votes
5answers
180 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
28 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
50 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
105 views

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

How to calculate the following limit? $$\lim\limits_{x \to \infty} \left(\frac{x^2+1}{x^2-1}\right)^{x^2}$$
7
votes
3answers
113 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
38 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
56 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
36 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 ...
3
votes
0answers
37 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
33 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
107 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
21 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
50 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
504 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 ...
0
votes
2answers
109 views

Fibonacci number, combinatorics , fractions [closed]

Let $F_1 = F_2 = 1$ and $F_{n-1} + F_n = F_{n+1}$, Count and simplify $ \frac{1}{2} * nC1 *F_1 + \frac{2}{3} * nC2 *F_2 + \frac{3}{4} * nC3 *F_3 + \cdots + \frac{n}{n+1} * nCn *F_n $ Edit : I dont ...
1
vote
1answer
10 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
18 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
41 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
60 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
62 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
367 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
99 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 $\frac{1-x}{x^2-1}=\frac{1}{x+1}$?