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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Infinite repeated decimals in a number

I don't know how to convert infinite periodic decimal number $$x=3,1(42)=3.1424242...$$ to a fraction $$\frac{a}{b}$$ $a,b$ are integers. Need to find $a,b$
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Why do decimal places "move" when multiplying or dividing decimals?

Suppose we have the two decimal values, 0.2 and 0.3. Of course, multiplying these values yields the result: 0.06. Of course, this is simply the calculation 2*3 with the decimal place moved according to the sum of the number of significant digits…
AldenB
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Simplifying fraction with multiple radicals

I have an answer to a problem that I am working on but I have no idea how to rationalize the denominator because I have never worked with this type of problem before. The problem is: $\frac{\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}$. I know that I am…
Kot
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Simplified Fraction.

My son has been set homework with half-completed fractions along a line of $30$. He has to complete the missing half. For example, there is an indicator at the $10$th line and the fraction is half completed with a $1$ on the top half; therefore, he…
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Convert decimal numerator/denominator to integers

Given any fraction that is defined by a decimal numerator or denominator or both. Which operations can always lead to the correct integer values? Eg: $\frac{0.5}{1}=\frac{1}{2}$ In this multiplying both numbers by 2 worked out, however what is the…
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Show that $\frac 1x+\frac 1y =(\frac 27)^a$ does not produce integer solutions for $a > 3$.

Show that $\frac 1x+\frac 1y =(\frac 27)^a$ does not produce integer solutions for $a > 3$. I have shown it is not possible for $a=4$, but not for any a greater than $4$.
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Kids on a $45$-seat bus

(I'm only a Year $7$ so please explain clearly how you found the solution.) A bus has $45$ seats. Each seat can fit two children or one child with his backpack. If $2/3$ of the children have backpacks, how many children can be seated on the bus? I…
bio
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Does flipping the negative in a fraction flip all terms both sides?

This is an expression that contains a negative in the denominator. If I were to take the negative and place it in the numerator, would this change all positive terms to negative and vice-versa? Negative in denominator: $\frac{a+3-y^2}{-2}$ After…
NinetyFive
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How to simplify this fraction with different powers?

I happen to be stuck trying to simplify this: $$\left[\frac{(3x+2)(x+1)^\frac{3}{2}-(\frac{3}{2}x^2+2x)(\frac{3}{2})(x+1)^\frac{1}{2}}{(x+1)^3}\right]$$ here's the simplified solution that I'm trying to figure out how it was reached
yasseen
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Which is larger $2/3$ of 24 or $3/4$ of 20?

Found this exercise in the BBC Bitesize website: Fractions of amounts Asking which value is larger between $2/3$ of $24$ and $3/4$ of $20$. My calculations brought me to: $2/3$ of $24$ = $16/24$ while $3/4$ of $ 20$ = $15/20$. Making them with the…
Lino
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Fraction of a Fraction order of operation: $\pi/2/\pi^2$

I think I'm having a bit of a senior moment or something... I was evaluating $\pi/2/\pi^2$. My instinct was that the answer would be $\frac{\pi^3}2$ from $\frac{\pi}1 * \frac{\pi^2}2$ but I checked wolfram and got $\frac{1}{2\pi}$. I'm pretty sure I…
Scottmeup
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Improper fraction

Do the improper fractions include, "the fraction whose numerator is greater than or equal its denominator" or "the fraction whose numerator is greater only than the denominator"?
Neweshy
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Which should be evaluated? $\frac{\frac{a}{b}}{\frac{c}{0}}$ or $\frac{a}{b}\cdot\frac{0}{c}$?

You can never get answers with $\frac{\frac{a}{b}}{\frac{c}{0}}$ where $a, b, c$ $\ne$ $0$. $\frac{a}{c}$$\ne$ $0$ and $\frac{b}{0}$ $=$ $undefined$. But why is there a specific answer ($0$ definitely) if $\frac{a}{b}\cdot\frac{0}{c}$?
333-blue
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Reducing a fraction with the denominator as a root.

I have always been terrible with these, but how does $\frac{-36}{\sqrt{3^5}}$ equal $\frac{-4}{\sqrt{3}}$ ? completely butchered the latex... I have -36/(root3)^(5) where the exponent is in the denominator. This equals -4/root3.
Kyle H
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$3/3 = 1$. But what if I write it as $(1+1+1)/3$ or $1/3+1/3+1/3$?

I can write $3/3$ as $(1+1+1)/3$ or $1/3+1/3+1/3$. Now, $1/3$ is a recurring/repeating/non-ending decimal so if we add these three, i.e. $0.3333... + 0.3333... + 0.3333...$ we will get infinitesimally close to $1$ but not $1$. Is there a way to…
danish
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