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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Convert hexadecimal fraction to hexadecimal

I have been trying to convert a hexadecimal fraction to a hexadecimal value. 3/4(hex) = 0.C(hex) What are the steps needed to convert?
stefana
  • 123
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Dividing rational expressions

How come I am able to divide the following: $$\frac{2}{2} = 1$$ Yet I am not allowed to divide the $2x$'s in the following: $$x^2 + \frac{2x}{2x} = x^2 + 1$$ Why can't I divide the $2x$ in numerator with $2x$ in denominator to get $1$? They are both…
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Proportion Problem

I came across a problem about proportion as follow: There are 5 girls for every 12 boys, if the total number of children is 5200, how many are boys and girls? I tried following solution but the answer result to decimal number. Since this is number…
sprenna
  • 153
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Which way are nested fractions evaluated?

A YouTube video (https://www.youtube.com/watch?v=6SzZ_jAHasE) asked what was the answer to this type of fraction: $$\dfrac {1+1+1+1+1+1}{\dfrac {1+1+1+1+1}{\dfrac {1+1+1+1}{\dfrac{1+1+1}{\dfrac{1+1}{1}}}}}\\$$ I had thought that this was equivalent…
rghome
  • 227
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How consistent can solving an equation be if one way of solving it might give an undefined answer?

If solving for an equation one way gives me an undefined answer, does that mean solving it in other ways too will give me an undefined answer? If no, then how consistent is math? (I'm not sure if I'm using the term "consistent" correctly, since I'm…
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What does it mean to add something half times?

I want to ask what does to mean to add something "half times". Because, if we multiply fractions like $16 \times \frac12$, we are essentially adding $16$ one-half times, but it doesn't make any sense. So is there any way to explain the…
Mohd Saad
  • 321
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ratios: why is the ratio of this equation like so?

The equation is w = 3m and the ratio of w is to m is 3 : 1 Shouldn't it be 1 : 3? could you please explain the reasoning?
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Series of Fractional Sums

What is the sum of $$\frac{1}{2\times 5} + \frac{1}{5\times 8}+ \frac{1}{8\times 11}+...+ \frac{1}{2009\times 2012}?$$ What is the easiest way to solve this kind of problem?
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Simplification of multiplying fractions

Simplify $(1+\frac{1}{20\times22})(2+\frac{2}{21\times23})(2+\frac{2}{22\times24})(2+\frac{2}{23\times25})(13+\frac{13}{24\times26})$ I noticed the denominator of the five fractions are all in the form of:$$\frac{...}{(n-1)(n+1)}$$ Which can be…
Cyh1368
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Fraction question

Alvin and Bob had a total of 60 marbles. Alvin gave 1/4 of his marbles to Bob. Bob then gave 1/3 of the total number of marbles he had to Alvin. In the end, each of them had the same number of marbles. How many marbles did Alvin have at first? By…
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Simple fractions question

Mary and Henry shared a collection of stamps. Mary had 7/10 of the total number of stamps. If Mary gave 38 stamps to Henry, she will have thrice the number of stamps Henry have. How many stamps did Mary have? By the way, we cannot use algebra to…
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WHY does the difference between the fractions get smaller?

$\frac{51}{101} - \frac{50}{100} > \frac{52}{102} - \frac{51}{101}$ I get that by adding 1 to both the numerator and the denominator of the same fraction that has a numerator smaller than the denominator, the fraction gets bigger since…
Pier
  • 83
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Integer+fraction vs Top-heavy fraction

What is the name of a fraction like this: $$\frac{22}{7}$$ as opposed to one like this: $$3\frac{1}{7}$$ I've never actually had to describe this until today. Not only have I no idea how to describe the top-heavy fraction or the one with a whole…
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Complex fraction

my book uses a technique to write fractions in a way that I am not familiar with. How does $$\frac{\frac{1}{243}-1}{-\frac{2}{3}}$$ equate to $$\frac{3\left(1-\frac{1}{243}\right)}{2}$$ Thanks in advance.
Math Noob
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Where is the error in this apparent contradiction arising from the function $f(\pm n)=\left(\frac{n}{n+1}\right)^{\pm 1}$?

We define a function $ f \left( \pm n \right) =\left( \frac{ n }{ n + 1 } \right) ^ { \pm 1 } $. That is, $$ f \left( m \right) = \begin{cases}\frac{ m }{ m + 1 } &\text{ if } m \ge 0 \\ \frac{ -m + 1 }{ -m } & \text{ if }m \lt 0 \end{cases}.…