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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What is this technique called?

It's been a long time since I've done algebra. I remember how to do it, but I'm at a loss to explain it. For instance, my son has the following problem; $$\frac{3}{Q+1}+\frac{2}{Q}$$ So I say, you just have to find a common denominator (like when…
uncle brad
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Why do we need to multiply the top and bottom of a compound fraction to solve it?

For example, $$\frac{\left(\frac{1}{x-1}\right)}{x-1}$$ I thought you would just need to multiply the top of the fraction, not both.
user212122
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How does the LCD in this fraction subtraction with variables work?

I have the following sum listed in Algebra Demystified: $\frac{71}{84} - \frac{13}{30x} = \frac{71}{84}\cdot \frac{5x}{5x} - \frac{13}{30x} \cdot \frac{14}{14} = \frac{355x}{420x} - \frac{182}{420x} = \frac{355x-182}{420x}$ However, I previously…
Hemmed
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Show that $\frac{1-2^{-x}}{1+2^{-x}}$ is equivalent to $\frac{2^x-1}{2^x+1}$

Show that $$\frac{1-2^{-x}}{1+2^{-x}}$$ is equivalent to $$\frac{2^x-1}{2^x+1}$$ I tried: $$\frac{1-2^{-x}}{1+2^{-x}} = \frac{1-\frac{1}{2^x}}{1+\frac{1}{2^x}}=…
Mark Read
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If $\frac{a}{b}=\frac{c+d}{e+f}$ so $a$ is equal to $c+d$?

I have these question, a is always c+d and b is e+f ?. Thanks.
valfar
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Why is this true? $p_x$ $x$ $(1 + {(1 - a) \over a})$ = $p_x w_x + p_y w_y$ $\Rightarrow$ $x$ = $a$ ${p_x w_x + p_y w_y } \over p_x$

I don't see why the following equation is true - although wolfram-alpha gives me the same result, I can't figure out the steps that were made. Sure, we can simply divide the equation by $p_x$, but what happens when we also divide $(1 + {(1 - a)…
user354391
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when the sum of some fractions equal to 1.

$r$ is a number such that $r=p^a$. If the sum of some fractions equal to $1$ and one of the denominators is divisible by $r$ then there is another denominators that is exactly divisible $r$. It seems to be really easy but I cannot prove it for…
Taha Akbari
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Partial fractions (How do I get from x to y)

how do I get from $$\gamma * \left( \frac{\frac{\lambda_0 w}{(1+r)^t \beta^t \alpha}}{\frac{\lambda_0 w}{(1+r)^t \beta^t \alpha}-\frac{\lambda_2}{\beta^t \alpha}} \right)$$ to $$\frac{\gamma r w \lambda_0 \beta^t}{w \lambda_0\beta^t -…
D.Loo
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World Problem Math Algebra Fraction

The denominator of a fraction in simplest form is greater than the numerator by $3$. If $7$ is added to the numerator, and $5$ added to the denominator, then the fraction itself is increased by $\dfrac 1 2$. Find the original fraction. I got the…
dan
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Convert fraction into decimal

Trying to help my daughter with a question for her maths that has got me stuck...wish I was better at maths! Convert the fraction 27/50 into decimal Could someone please help me with this question.
lara400
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Elementary Fractions

There are two identical water jugs, A and B. Jug A is 3/7 full of water and Jug B is 8/11 full. What fraction of the capacity of a jug should water be poured out from jug B to jug A so that they both have the same amount of water? Simple math, but…
Jasmine
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Fraction confusion

I read in a set of memoranda that if $ \frac{b-x}{x}=\frac{b}{a}$, then $$x = \frac{ab}{a+b}$$ How is this true? I tried working it out but I could not understand. Please help.
Aspiring Mathlete
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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 $-\frac{3}{8}$ ), and of course I'm comfortable with…
ClickRick
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Simplify fraction $4x/(x-1)$ to $ 4+(4/(x-1))$

I have put the fraction into Symbolab which gives some step-by-step explanation on why this os correct, but I am unable to grasp how this is possible.
Gertjan Brouwer
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Coincidence of 1/5/3 Being Equivalent to 3/5?

I was doing a math problem and realised that; $\frac 1{\frac 53}$ was equal to $\frac35$ Is this purely a coincidence or is there some way to prove that $\frac 1{\frac 53}$ is equal to $\frac35$ ? Any help would be appreciated!
IAmAlsoLearning
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