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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How can I simplify this step by step?

I want to simplify this : $$\frac{x^2}{a^2} + \frac{(x\tan \theta)^2}{b^2} = 1$$ The answer is supposed to be this : $$x = \frac{ab}{\sqrt{b^2+a^2\tan^2 \theta}}$$ I’d like to understand this step by step
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Which expression is equivalent to $\left(\frac{2}{3}-\frac{2}{x}\right) \div \frac{x-3}{x}$? (from Khan academy)

I've been trying to understand this problem for hours but not getting it. HELP!!! The correct answer is $\frac{2}{3}$, but I don't know why this is the correct answer. Thank you in advance for your help!
keab28
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$2/3$ of a tank contains $112$ litres of water. What will it contain when it is $3/4$ full?

$2/3$ of a tank contains $112$ litres of water. What will it contain when it is $3/4$ full?
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How to calculate a repeating decimal for any fraction?

I have been struggling for a while to try to code a program to convert any fraction 1/n to a repeating decimal. So far, my program works only for numbers that end in 1, 3, 7, or 9 (n cannot divide 2 or 5, since those numbers divide 10, our numeral…
eners49
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Is it correct to sum a daily rate for a period of time?

I have a table of daily events for a number of locations that I am trying to summarize for a week. For a weekly summary, are both of these methods correct, and how would they be interpreted? SUM(Events)/SUM(Loc. Count) = 8.63 | Interpretation: For…
psrpsrpsr
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Which rule has more hierarchy?

There are these 3 rules: $1)$ Any number divided by $0$ it is indeterminate $2)$ $0$ divided by any number is $0$ $3)$ Any number multiplied by its reciprocal is $1$ These rules are contradictory, when they are together in a…
ESCM
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Problem with fractions part and whole

A businessman instituted an annual award in a city school, with a part of the award given to the school itself to improve its facilities. It was stated that if a student from a wealthy family were to top the annual examination, the school would…
Kira
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Fraction problem for primary school

I saw a problem yesterday, which can be easily be solved if we are using fractions. But the problem is for the 4th grade children, and I don't know how to solved this using what they what learned. I tried solved it using the graphic method (…
Florin M.
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If I have a fraction that just has a negative number in the numerator or denominator, does this make the whole fraction negative?

For example: -3(negative numerator) over 4 (positive denominator) Would this whole fraction be considered negative?
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Why isn't $\frac{x^3+1}{x+1}$ equal to $x^2$?

Can someone please tell me why $$ \frac{x^3+1}{x+1} \neq x^2\;? $$ I thought you could expand the $x^3$ out like so and cancel it out, but I got it wrong on a test and I have not the slightest clue why. $$ \frac{x\cdot x\cdot x+1}{x+1} $$ I just…
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What's wrong with my workings? Adding fractions question.

Please could someone explain what is wrong with my workings? $$\left(\frac19+\frac12\right)+\left(\frac13-\frac12\right)=?$$ My workings are: $$\left(18\left(\frac19+\frac12\right)\right)+\left(6\left(\frac13-\frac12\right)\right) =…
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How do I express 0.999(9) as a fraction?

I'm noob in math. If 0.333(3) is 1/3, 0.666(6) is 2/3, then 0.999(9) is what? If 3/3 and 0.999(9) is the same, then how can I express one of them without expressing the other?
Gintas_
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Theorems of mine(?)

So I think that I have made $2$ theorems that are actually quite cool and I was wondering if they have already been proven by somebody else. Moreover are they really considered my theorems if they have not been claimed by anyone else? Definition:…
alienCY
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Critique reasoning

Molly is wrapping parts of sandwiches to sell at her sandwich cart . She cuts each sandwich in fourths and then wraps each fourth separately. She says that she wrapped 16 fourths, so she wrapped 16 hole sandwiches. What was Molly's mistake?
Cece
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What is the mean of these twelve mixed numbers?

How to solve the problem without trying one by one? I want to improve my knowledge in this area. So what should I read? There are twelve different mixed numbers that can be created by substituting three of the numbers 1, 2, 3 and 5 for a, b and c…
math
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