Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

A fraction is simply an expression $\frac{a}{b}$, where $a$ and $b$ are typically integers (where $b\neq 0$). This tag may be used, when $a$ and $b$ are more general expressions or algebraic objects; however, consider adding a more specific tag also:

Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number.

For arithmetic with fractions, this tag is appropriate along with .

2981 questions
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Rewriting to quintic equation

Consider the force $F_\Omega$: $$ F_\Omega= \Omega^2\left(x -\frac{\beta\left(x+\alpha R\right)R^3}{\left(\left(x+\alpha R\right)^2\right)^{3/2}} -\frac{\alpha\left(x-\beta R\right)R^3}{\left(\left(x-\beta R\right)^2\right)^{3/2}} \right) $$ Where…
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Find the value of x

$$\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)\ldots\left(1-\frac{1}{2011^2}\right)=\frac{x}{2\cdot 2012}$$ Help me solve this, obviously there is a shortcut to solve it, but I have tried a lot and I've come…
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Show that $\frac{(b+c)^2} {3bc}+\frac{(c+a)^2}{3ac}+\frac{(a+b)^2}{3ab}=1$

If $a^3+b^3+c^3=3abc$ and $a+b+c=0$ show that $\frac{(b+c)^2} {3bc}+\frac{(c+a)^2}{3ac}+\frac{(a+b)^2}{3ab}=1$
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How do I convert a fraction in base 10 to a quad fraction (base 4)?

I am totally confused when it comes to converting fractions or floating point numbers to a different base. I have no problem converting whole numbers to any base but when it comes to fractions or decimals I'm stumped. I got this question on an…
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Can a fraction be simplified like this?

Ridiculously embarrassing question, but can $\frac{x^2-x}{x^2-25}$ be simplified to simply $\frac{1-x}{1-25}$? Full thought process here is that this is essentially $\frac{x*x-x}{x*x-25}$ so the $x$s should cancel. The full problem…
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Spending fraction of salary

I have this question and kind of confused... Mary spent $1/4 $ of her salary in for rent and $1/4$ more than rent for car payment. Which of the following could be the fraction of her savings if her saving is not less than $30$ % of the remaining…
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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 very good at Maths. He also got the wrong…
Aaron
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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.
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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 numbers into fractions..even with remainder tagging…
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How to simpify this?

How to simplify following fraction? I have tried everything, but nothing seems to work... $$-a^3 (c^2 - b^2) + b^3 (c^2 - a^2) - c^3 (b^2 - a^2)\over (c-b)(c-a)(b-a)$$
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Dividing amount unequally in tournament winners?

Hi I am trying to write the algorithm to calculate the winning amount of the winners. My problem is as below, 1) I have open ended tournament in which participants can be in ratio of 2 (i.e 2,4,8,16 and so on) 2) I am going to declare 50% or 25% of…
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Distributive Property on Fractions: Swapping Denominators

I'm learning Algebra and am curious about some methodological fundamentals here. One, in particular is why the following equation: 6(2x + 1 / 3) = 6(x + 4 / 2) results in: 2(2x + 1) = 3(x + 4) It's obvious that the distributive property swaps the…
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Simplify this expression $w\left(\cfrac Q {1+\frac w r}\right)^2 + r\left(\cfrac Q {1 + \frac r w}\right)^2$

I can't figure out how to do the algebra to simplify this expression! $$w\left(\cfrac Q {1+\frac w r}\right)^2 + r\left(\cfrac Q {1 + \frac r w}\right)^2$$ It's supposed to turn out to $\cfrac {Q^2} {\frac 1 w + \frac 1 r}$. Could someone show the…
fool
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Calculating the time it takes to send a file

The time of sending a file is calculated: $$\textrm{time} = \frac{\textrm{file size}}{\textrm{link capacity}}.$$ In this example, $\textrm{file size} = 4492643566$ bytes, and $\textrm{link capacity} = 100$ Mbits/s. Sending the file and the header…
user567
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Magnitude relation of fractions for four real numbers with a condition

I would like to know if the following proposition holds or not. For all $a, b, c, d$ such that $a, b, c, d$ are positive real numbers, IF $a < b$ and $a - c > b - d \geq 0$ THEN $\frac{c}{a} < \frac{d}{b}$ . Could you kindly advise? It is really…