Mathematics Stack Exchange
Mathematics Stack Exchange

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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Simplify a rational identity

Simplify: $$\frac{\dfrac{a}{b}-\dfrac{b}{a}}{1+\dfrac{b}{a}}$$ I have a feeling the solution has to do with factoring, but I'm really not sure, and would appreciate any help.
Sam Schlenner
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Which numbers will remain if I keep removing the second third of the remaining interval?

Inspired by this Google Code Jam problem - Vanishing Numbers There is a pool of numbers which are arbitrary decimal fractions from the interval (0, 1). In the first round of the game the middle third of the interval disappears, and the numbers…
Yohan
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Name and proof of the identity $c=\frac{a_1}{b_1}=\frac{a_2}{b_2}$ then $c=\frac{a_1+a_2}{b_1+b_2}$

I was shown in a textbook (though not a mathematics one) the following identity: If $$c=\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}=\dots=\frac{a_n}{b_n}$$ then $$c=\frac{a_1+a_2+a_3+\dots+a_n}{b_1+b_2+b_3+\dots+b_n}$$ Does this identity have a…
lightweaver
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Problem with slopes.

I currently have a slope that looks like this: $\frac{-5}{10}$ However, I need to bring it down to it's lowest terms, so I divided the numerator and denominator by -5 and I got: $\frac{1}{-2}$ Although, if I divide it by 5 I…
user60161
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Finding all rationals in a given range using Stern-Brocot tree

I know the Stern-Brocot tree lists out all the possible fractions. But how do I enumerate the fractions that are present in $[a, b]$ where $a$ and $b$ are two fractions.
Sathvik Swaminathan
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Algebraic Operations

How to find the value of $E=x^5 + x^{-5}$?. Knowing that $x^3 + x^{-3}=54$. At first it seemed like a simple exercise, but when I started to solve it I had difficulties. Try the "Remarkable Products", but I did not find it. Try to express $E$ in…
John
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Partializing fraction with 4th power for integration

How can I partialize the following fraction ? My query mainly lies with the term with 4th power . I want to use it in an integration problem .So , any clue to the dealing with integration will also be helpful... $$\frac{2p}{(1-p)(1+p^{4})}$$
Nehal Samee
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Simplifying an expression: Stuck with it

I have to prove that the expression $$\frac{\omega C - \frac{1}{\omega L}}{\omega C - \frac{1}{\omega L} + \omega L - \frac{1}{\omega C}}$$ is equal to $$\frac{1}{3-( (\frac{\omega_r}{\omega})^2 + (\frac{\omega}{\omega_r})^2)}$$ where $\omega_r=…
Granger Obliviate
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What am I doing wrong with this adding fractions problem: $\frac{5}{6} + \frac{2}{3}$?

The problem is $$\frac{5}{6} + \frac{2}{3}$$ I found the LCD which is $6$. Then I multiplied $2\times 3=6$ and $2\times 2=4$. So the new problem is $$\frac{5}{6} + \frac{4}{6} = \frac{11}{6}$$ $\frac{11}{6}$ simplified is $1 \frac{5}{6}$ but…
Mister Lance
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Let $a = \frac{9+\sqrt{45}}{2}$. Find $\frac{1}{a}$

I've been wrapping my head around this question lately: Let $$a = \frac{9+\sqrt{45}}{2}$$ Find the value of $$\frac{1}{a}$$ I've done it like this: $$\frac{1}{a}=\frac{2}{9+\sqrt{45}}$$ I rationalize the denominator like…
Cesare
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Why are fractions "multiplied across"?

Suppose we have two rationals, $\frac{a}b$ and $\frac{c}d$. I daresay anyone with some form of mathematical education would disagree that our result would be $\frac{a}b\times \frac{c}d=\frac{ac}{bd}$. That is, we multiply our numerators to get the…
AldenB
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Rationalizing fractions with multiple radicals

I am having trouble rationalizing $\frac{2}{\sqrt{2-\sqrt{2}}}$ I have tried multiplying the fraction by $\sqrt{2 + \sqrt{2}}$ and got $\frac{2\sqrt{2+\sqrt{2}}}{\sqrt{2}}$ I am not sure if that is correct or not but I then multiplied by $\sqrt{2}$…
Kot
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How does this denominator cancel out to create the next step?

I was following an example in my text, and there was one step I got stuck on. Given $\frac{2x(\Delta x) + (\Delta x)^{2}}{\Delta x}$, how does the denominator cancel out to produce $2c+\Delta x$? My thinking is that the formula expands to…
Jason
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Is this a proper way to solve fractions?

I'm doing Trades Math and as you can imagine it's bit confusing. Let's say I'm trying to solve for the below question. 22' - 5 3/16" 10' - 1 1/2" 13' - 4 9/16" + __________ so here is what we get v - v 45' - 10 ok then we now we work with 1/2.…
0111010001110000
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Optimal decomposition of $\frac{m}{n}$

Given a fraction $0 < \frac{m}{n} < 1$, what is the lowest $k$ so that you can write $$ \frac{m}{n} = \sum_{i=1}^k \frac{1}{n_i} $$ with the $n_i$ not neccessarily distinct? Obviously, $m$ is an upper bound. To see that you can do better than $m$ in…
Arthur
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