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

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1
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2answers
71 views

How do you simplify an algebraic expression?

Please explain how to simplify an expression that is similar to this one $\displaystyle\frac{a+3}{6}+\frac{a-4}{4}+\frac{a+2}{-3}$
3
votes
2answers
152 views

Absolute value on the top of a fraction

What is the answer to a question similar to this one, where the absolute value bars are only around the numerator of the fraction? $$\frac{|2+4(2)|}{5-10}$$ Would the fraction be equal to ...
2
votes
2answers
98 views

Fraction With Scientific Notation As A Percentage

I have this fraction $\frac{3.09\times 10^{-9}}{0.02\times 10^{-9}}$ and I need to convert it to a percentage. What I do know is that the $10^{-9}$ cancels out and we are left with $\frac{309}2$, but ...
0
votes
1answer
44 views

cancell common factors

p³ - PQ² --------- Divided by (P+Q)² Apparently the answer is P(P-Q) --------- Divided by P+Q But how? - What I was thinking P-P (P-Q), (P+Q) ------------------ Divided by (P+Q) which is P-P ...
6
votes
5answers
274 views

Show that $\frac{\sqrt{8-4\sqrt3}}{\sqrt[3]{12\sqrt3-20}} =2^\frac{1}{6}$

This was the result of evaluating an integral by two different methods. The RHS was obtained by making a substitution, the LHS was obtained using trigonometric identity's and partial fractions. Now I ...
1
vote
2answers
76 views

How to solve this algebraic fraction?

Could someone please help me with solving this algebraic fraction. I tried it a few times and I got the wrong answer all of the times. My brother also tried, who had recently finished Matric and he is ...
0
votes
3answers
283 views

Splitting the numerator

Can someone explain how we can get the second fraction by splitting the numerator? $$\frac{x^3}{x^2+x+1}=x-1+\frac{1}{x^2+x+1}$$ I can get the LHS from the RHS but not the other way around. What ...
0
votes
1answer
170 views

Deradicalization of denominators

Task: Develop a fraction equivalent to $$ 1\over{\sum\limits_{i=0}^{n-1}c_in^{i/n}} $$ in which the denominator is rational.
0
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4answers
42 views

Rank odds without converting

Brazil are currently playing Mexico, and at the start of the game Brazil were 2/5 to win. As it's the 38th minute and still 0-0, their odds have changed to 8/15. Now, if I'm not wrong that represents ...
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3answers
78 views

Basic algebra, isolating the variable

So I have the equation $$\tan30=\frac{4.9t-\frac{10}{t}}{\frac{8.77}{t}}$$ And I want to find t, but my algebra has failed me. This is my working so far. ...
0
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1answer
103 views

Rearranging algebraic formula when subject is on both sides

I have run into some difficulty with a question on making a variable the subject of an equation where the variable is on both sides. I am really struggling to find a method for making "a" the ...
0
votes
1answer
1k views

Is three halves a fraction?

Is three halves (3/2) a fraction? I understand there may be a more accurate name for this kind of number (improper fraction?) which would be interesting to know. But that isn't what I'm after me, I ...
4
votes
3answers
1k views

Can you give me a visual representation on 1/6 of 4/5 to get 4/30?

I'm trying to understand fractions more by using a visual representation, and I having a hard time making a visual representation of the 1/6 of 4/5 and getting a visual understandable representation ...
1
vote
2answers
109 views

Why is the word “of” equivalent to multiplying in fraction word problems?

I know this is a very easy problem, but I'm having a hard time getting my head around this concept, consider this example from a book. *Jerry bought a pie and ate 1⁄5 of it. Then his wife Doreen ate ...
3
votes
5answers
136 views

How do I prove $\frac{ \sqrt{x+h}-\sqrt{x} }{ h}=\frac{1}{\sqrt{x+h}+\sqrt{x}}$?

$$\frac{ \sqrt{x+h}-\sqrt{x} }{ h}=\frac{1}{\sqrt{x+h}+\sqrt{x}}$$ I know I just asked a question and I did figure out how that one worked but I'm not sure how I would go about this one.
0
votes
1answer
27 views

Comparing Fractions that contain epsilon

Given $\epsilon$ a constant s.t. $0<\epsilon<1$, and $n,p$ positive integers, $n >= 2p$, is the following true: $\frac{(1+\epsilon)n}{(2+\epsilon)p} \geq \lceil\frac{n}{2p}\rceil$
2
votes
3answers
47 views

Simplifying fraction with square root as denominator

I'm trying to find the integral of: $$\dfrac {2\sqrt{x} - 3x + x^2}{\sqrt{x}}$$ but I first need to simplify it so I tried dividing by the $\sqrt{x}$ for each of the numbers on the top like so: ...
0
votes
1answer
48 views

What's the difference between “continued fractions” and “compound fractions”?

What should we call a fraction which includes another fraction in its numerator or denominator, like $${ab\over {c \over d}}$$?
0
votes
1answer
50 views

Why does $ \frac {a}{b}$ of $c$ mean $ \frac {a}{b} \cdot c$ [closed]

When someone writes "$ \frac {a}{b}$ of $c$", why is the preposition "of" interpreted as multiplication of $c$ by $a/b$?
0
votes
1answer
154 views

Adding a natural number to a normalized fraction

I am currently writing yet another rational number class where the fraction should always be normalized. When adding a natural number to a normalized fraction, it possible to get a non-normalized ...
4
votes
4answers
152 views

why do equations work and how do they relate to each other?

Ok, so I understand that an equation is something like 15 = 15 , and that the only criteria as far as I can tell for it being an equation is that both sides are equal to each other. I have a few ...
0
votes
2answers
33 views

Fractions from least to greatest

What is the fastest way to find the least common denominator of all the fractions without losing too much time? 7/9 , 1/4, 14/15, 2/3, 1/2 Thanks.
3
votes
0answers
68 views

All those unit fractions add to 1?

Consider $$S(n)=\{x \mid x=(a_1 ,a_2,a_3 \cdots a_n) \text{ where } \sum_{r=1}^{n}\frac{1}{a_r} =1 \}$$ Now let $|S(n)|$ denote the cardinaly (order) of set $S(n)$. Thus: $S(1)= \{(1)\} \implies ...
3
votes
2answers
116 views

Cannot find length of repeating block in decimal expansion for $\frac{17}{78}$

I am trying to find the length of of the repeating block of digits in the decimal expansion of $\frac{17}{78}$. On similar problems, that has not been an issue. Take for instance $\frac{17}{380}$. My ...
0
votes
2answers
54 views

Convergence of a series ${}\qquad{}$

Does this series converge? $$\sum_{x=2}^n \left(\frac{1}{x}\right)^{\left(\frac{1}{x}\right)}$$ I tried hard but stil had problems... Could someone help me?
0
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1answer
20 views

Solving for $x$ [not homework]

How do I bring the remaining $x$ to the LHS? $\pm x=\frac{(2-x)\sqrt{|q_2|} } {\sqrt{|q_1|}}$ to get $x=\frac{2 \sqrt{|q_2|}}{\sqrt{|q_2|} \pm \sqrt{|q_1|}}$ I'm just not sure about the ...
3
votes
3answers
71 views

confusion related to elementary operation on numbers

Let's take for example an fraction: $\dfrac{1+4}{2-4}$ and another fraction $\dfrac{1*4}{2*4}$. In the second fraction we can cancel 4 from both numenator and denominator but on the first we cannot ...
2
votes
2answers
139 views

Can fractions be relatively prime?

Two numbers are relatively prime if they do not share any factors, other than 1. Is it possible for fractions to be relatively prime? To reword this, do fractions even have factors?
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votes
2answers
87 views

Negative mixed fractions

I'm comfortable with fractions like $\frac{-3}{8}$ being the same as $\frac{3}{-8}$ (though I'd think the latter anachronistic and would in any case probably prefer to write either of those two as ...
0
votes
2answers
63 views

Fractional Exponents powers

I am having problems understanding how to answer questions containing fractional exponents to a given power ie $(2x^{1/2})^6$, i do not understand how to go about answering the question. I know this ...
0
votes
2answers
67 views

How to transform $2,(9)$ to form $\frac{a}{b}$

How to transform $2,(9)$ to form $\frac{a}{b}$. My attemp: $$x=2,(9)/\cdot 10$$ $$10x=29,(9)$$ $$10x-x=29,(9)-2(9)$$ $$9x=27$$ $$x=3$$ but do not know if I have done the exact. Please help me
1
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1answer
39 views

My small theory…

It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:- a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and ...
2
votes
2answers
133 views

Solving a fractional quadratic equation problem by completing the square

I have the following problem to solve using the method of completing the square. $$2x^2-3x-1 = 0$$ Here is where I've gotten to so far on this problem. $$2x^2-3x = 1$$ $$x^2-\frac{3}{2}x = ...
1
vote
1answer
53 views

How did my book simplify this?

How did my book go from: $\frac{4}{5}=\frac{x}{30}$ to $\frac{4}{1}=\frac{x}{6}$ I understand that I could have cross multiplied it in the first place but what I don't understand is why my book ...
1
vote
2answers
354 views

Convert from decimal to fraction

I know this sounds silly, and it's easy for many situations. But sometimes i have been completely taken back as i don't know how to do it. So please tell me is there any way to convert certain ...
1
vote
1answer
230 views

Why a decimal fraction is not expressing exactly what a rational number is in base 2?

I am currently using rational numbers to express currency and math operations with currency, while dealing with rational numbers has provided a great convenience in over coming the limitations of ...
0
votes
1answer
25 views

Simplifying a fraction.

The answer of a "solve for x" equation equaled to -10/-19, and the website on which I am practicing says it needs to be simplified, but I have no idea how. Help?
2
votes
1answer
57 views

Confusing sum of fractions

Question is to find the sum of: $$(\frac{1}{2^2-1})+(\frac{1}{4^2-1})+(\frac{1}{6^2-1})+(\frac{1}{20^2-1})$$ I know that $a^2-b^2=(a+b)(a-b)$, and that with this I can find the LCM to be 1995, ...
8
votes
3answers
660 views

Numbers whose self and reciprocal are finitely decimally expressable that are close to one?

How would I go about finding numbers x such that x and 1/x are finitely decimally reciprocal and are also close to 1? I'm not entirely certain how to phrase this question, but take for example 2. 2 ...
1
vote
2answers
49 views

How to solve $\dfrac{7x}{8}+4-\dfrac{2x}{3}=4x-3$?

$$\frac{7x}{8}+4-\frac{2x}{3}=4x-3$$ I do not understand how to simplify this. Could anyone here help me, please? Thanks.
2
votes
2answers
174 views

Question in fraction (not simple )

I have a question and its answer but I don't know how can i solve $$\frac {37}{13} = 2+ \frac {1}{x+\frac{1}{5+\frac{1}{y}}} $$ the answer $ x =1, y=2$ Could any one explain how to solve this ?? ...
0
votes
2answers
346 views

Mixed repeating decimals

How can be proven that a fraction having at the denominator a multiple of both 2 and 3 is transformed to a mixed repeating decimal number? I thought to bring the denominator to the form of ...
1
vote
0answers
27 views

MultiEquations (with fractions)

Can you please help me solve these equations i don't understand how to solve them with fractions. 1=n-2/15 151/20 =2a+1 3/4 -3/5 -2 1/5k = - 26/25
0
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2answers
52 views

How to simplify this fraction?

Can anyone show me how to simplify this fraction: $$ \frac{(k + 1)((k + 1)+1)(2(k + 1)+1)}{6}\;\;. $$ What can be factored out and so forth? Thanks.
3
votes
2answers
319 views

When can't $dy/dx$ be used as a ratio/fraction?

By searching this question, I found this: Can I ever go wrong if I keep thinking of derivatives as ratios? However, the answers don't have what I'm looking for! (Edit: Meaning, a counterexample. ...
0
votes
1answer
40 views

Reducing an inquality with fractions

can you help me reduce the following inequality (i need to get a relation between x and y -- express x in terms of y) $\frac{n}{2x} < \frac{n}{(4+\epsilon)y}+1$ I would like to show somehow that ...
1
vote
3answers
199 views

If you add the same constant to the numerator and denominator, what is the relation between the new fraction and the original fraction?

If I add a constant $\varepsilon < 1$ to the numerator and denominator of a fraction, is the new fraction always greater than the original? That is, do I have $$ \frac{a}{b} \leq ...
2
votes
1answer
76 views

$\sqrt[\large m]{(x+y)}\over \sqrt[\large k]{(x+y)}$ $=\sqrt[\large m-k]{(x+y)} $?

Is it always true that: $\sqrt[\large m]{(x+y)}\over \sqrt[\large k]{(x+y)}$ $=\sqrt[\large m-k]{(x+y)} $ where $m,k \in \mathbb N$ ? I tried it with a few numbers and it seems to work every time.
0
votes
4answers
60 views

How to make sense of fractions concretely

I can solve fractions abstractly, for example, $\frac{5}{2}$ divided by $\frac{3}{2}$, you can flip $\frac{3}{2}$ so that $\frac{5}{2}$ multiplied by $\frac{2}{3}$. Specifically, math makes sense ...
0
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1answer
45 views

fraction as index number?

given these inputs x = 4, S = [1 2 3 4 5 6 7 8 9 10], and n = 10 ...