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 .

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A little explanation of square root in a fraction

I was on KhanAcademy when I ran into a problem involving a sine of a triangle, this was the solution: $$\frac{9}{3\sqrt{13}}$$ (9 being the length of the opposite and $3\sqrt{13}$ being the length of the hypotenuse) And in the given answers there…
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Short expression $\frac{x^2-y^2}{x(x-y)}+\frac{x^2-y^2}{x(x+y)}$

I tried to short this expression: $$\frac{x^2-y^2}{x(x-y)}+\frac{x^2-y^2}{x(x+y)}$$ The result should be $2$ but I get: \begin{align} &\frac{x^2-y^2}{x^2-xy}+\frac{x^2-y^2}{x^2+xy}\\ =& \frac{y^2}{yx}+\frac{-y^2}{yx}\\ =&0 \end{align} What did I do…
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Dividing an amount proportionately among unequal amounts

I have \$100000. I want to divide the amount proportionately to 300 employees. I want the money divided inversely from the top down. So, the top earner get \$0 and the lowest paid employee(s) get the most. If there are 10 employees at the lowest…
Roberto
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Proof of rational division...

I know that this how it's done but i used to know a simple proof which i have forgotten...so please if you know let me know.. $$\frac{\frac{a}{b}}{\frac{c}{d}} =\frac ab \frac dc.$$ When you have two factors dividing, you reverse the 2nd one and…
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How to work out these fractions?

$\dfrac{-x^4 + 4x^2 + 6}{x}$ $\dfrac{7x^8 - 5x^5 + 9x^3 + x^2}{x}$ I have no idea how to do this. I was first thinking of doing $-x$ or collecting up the $x's$ but I'm not sure as I haven't dealt with these before. Thanks.
user61406
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Calculating a Fraction's Reciprocal

Is there any way or equation that allows me to calculate the reciprocal of any fraction? I mean if i have 5/6 and i need it's reciprocal by using a formula or an equation to calculate it. Is there or not? thanks all
John
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Embarrassingly-basic fraction question

I'm trying to do a calculation at work to figure out what the average # of pages a visitor is viewing. I am given: 47,000 visits 12% of visits do not bounce (that is, 12% navigate the site at least one link after stumbling upon it) 1.23 pages/visit…
HC_
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Total Time Expression Question

How do I do this question? Thanks!
Jamie A
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How are fractions involving three numbers simplified.

This is something thats been bugging me since my high school. Is A/B/C = A/BC or AC/B
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Fractions and roots

I have this problem: $$\frac{\sqrt{18}+\sqrt{98}+\sqrt{50}+4}{2\sqrt{2}}$$ I'm able to get to this part by myself: $$\frac{15\sqrt{2}+2}{2\sqrt{2}}$$ But that's when I get stuck. The book says that the next step is: $$\frac{15\sqrt{2}}{2\sqrt{2}}+…
Jose
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Reducing a fraction with exponents

How do I reduce $$ \frac{(k+1)^2}{k^2} $$ to simplest terms? My algebra is really rusty... Thanks!
Ryan
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How to solve for x if it is on the top of the fraction?

so you have the equation: $$0.0850= \frac{x}{0.125} $$ How do you solve for x?
Marissa
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Is it possible for two simplified non integer fractions to have an integer sum and an integer product?

Is it possible for two simplified non integer fractions to have an integer sum and an integer product? Let’s say the fractions are $\frac{a}{b}$ and $\frac{c}{d}$. For them to multiply to an integer, $d$ must divide $a$ and $b$ must divide $c$. We…
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Is it possible to prove this inequality?

Suppose I have the following pairs of variables: $a$ , $\hat{a}$ $b$ , $\hat{b}$ $c$ , $\hat{c}$ $d$ , $\hat{d}$ Now, suppose I have the following functions: Function 1: $$ F(A, B, C, D) = \frac{\frac{A}{B}}{\frac{C}{D}}$$ Function 2: $$ G(A,…
stats_noob
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Ratio problem to find the woman weekly salary

A woman spend $5/8$ of her weekly salary on rent, and $1/3$ of the remainder on food, leaving $40 available for other expenses. What is the woman's weekly salary ? I have tried , i am really confused with finding remainder.
SSK
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