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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Algebraic Fractions, no I'm not kidding..

I know most of the people on this forum/site are very advanced, and I'm just sitting here wondering how in the world you do this equation, or "simplify" it. I know how to do equations like these when there are only two terms, as in (a/b + c/d), but…
Sam Chahine
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Grade calculation

My teacher said that $\frac{1}{3}$rd of the final grade will be based on Exam 1, $\frac{1}{12}$th each based on Exam 2-5, and $\frac{1}{3}$rd again based on Exam 6, how will my teacher calculate my final grade?
Jake
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How to create a series of fractions, such that each subsequence slice is smaller than the previous?

I need to develop a grading system for a course. The first assignment is evaluated based on only one criteria, a. The second assignment based on the first criteria, a, plus one new criteria, b, the third assignment based on three criteria, a, b, and…
Village
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Finding the value of a fraction according to a given information

$a,b$ and $c$ are real numbers such that: $abc=ab+ac+bc$. Find the value of $\frac{a+b}{b}+\frac{a+c}{c}+\frac{b+c}{a}$. I've tried simplifying the expression and eventually I got: $\frac{a}{b}+\frac{b}{a}+\frac{a}{c}+\frac{c}{a}+2$, but I couldn't…
Adrien
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Increase number to be equal to another keeping ratio

Sales team A consists of 100 people with 40 sales. Sales team B consist of 50 people with 25 sales. I would say that sales team B overall had a better performance in making sales considering its proportionate size to sales team A. I would like to…
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Why negative integer divided by positive is same as positive integer divided by negative

My query is - why -3/4 is same as 3/-4? For -3/4, -3 is less than 4 so when -3 is divided into 4 parts, the result will be less than -3 which is correct. In this case, it will be -0.75 And, for the case of 3/-4, 3 is more than -4. So, a larger…
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Is fraction a rounded version of repeated decimal?

My friend says that 1/3 is not 0.3333. She thinks that 1/3 is a rounded version of 0.3333... Is 1/3 the exact same as 0.3333333...?
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Dividing Fractions in differential equations

I know this has been asked in many forms. But still confused. I am re-learning differential equations and I was working on Verifying solutions. Is $g(x) = (\frac{\sqrt 3x^2}{2})$ a solution to $\displaystyle g'(x) = \frac{3x}{4g(x)}$ When plugging…
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Show that $\frac{-4z^{-1}}{(1-\frac{1}{4}z^{-1})(1-4z^{-1})} = \frac{16}{15}\frac{1}{(1-\frac{1}{4}z^{-1})}-\frac{16}{15}\frac{1}{(1-4z^{-1})}$

Can anyone help me clarify how this rewriting is done? $$\frac{-4z^{-1}}{(1-\frac{1}{4}z^{-1})(1-4z^{-1})} = \frac{16}{15}\frac{1}{(1-\frac{1}{4}z^{-1})}-\frac{16}{15}\frac{1}{(1-4z^{-1})}$$
Attaque
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Changing probabilities after the fact

I have a state which is a list of probabilities for next states as follows: $\left[0, \frac {1}{2}, 0, 0, \frac{1}{2}\right]$ I realise that the second element here actually has a $\left(\frac 2 7\right)$ chance of looping back to this state. So I…
DaraJ
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X = a/ (1+a) . Would the value of x increase or decrease if “a” increases?

It’s pretty easy to find the answer after putting in random values but I can’t wrap my head around with my below explanation which is in direct contradiction to the result. If the numerator increases the x value goes up and the value of x goes down…
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Convert numerator and denominator with decimals

Say I have a set of decimals such as [.25, .5, .75]. I want to convert the numerator and denominator of their fraction equivalents, such that: .25 = 4 .5 = 2 .75 = 1.333 I don't know what these numbers are beforehand, and this will be computed such…
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How do I solve $x^2+10x-y^2+25=A×(x+y+5) \Rightarrow A=?$

$x^2+10x-y^2+25=A×(x+y+5) \Rightarrow A=?$
black
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What is the most simplified formula for this fraction?

Let's consider the fraction: $$ \frac{1-\mathrm{e}^{-T/4}}{1-\mathrm{e}^{-T}}. $$ What is the most simplified expression of the above expression, I tried factorizing with the half-angle, but I come up with this complicated expression: $$…
Victor
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Is $9.\overline{9} = 10$?

If you divide $10$ by $3$, you get $3.\overline{3}$ but $3.\overline{3}\times{3}=9.\overline{9}$ Does this make $9.\overline{9}=10$?