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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How to rationalise the denominator when it comes out undefined?

$$\frac{3-{\sqrt 5}}{\sqrt 5 + 5}$$ This is probably ridiculously straightforward but I need to get to the answer $$ 1-\frac{2}{5}{\sqrt 5}$$ and can't figure out how to rationalise the denominator bc 5 - 5 = 0 and can't have that on the bottom of…
Ma Ha
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Sum of fraction series

I have been trying to solve this question but I am not sure how to, and would appreciate some help. Thanks. Simplify: $$\frac{1}{4} +\frac{1}{4^2} +\frac{4^2}{4^3} +\frac{4^2}{4^4} +\frac{4^4}{4^5} +\frac{4^4}{4^6} +\ldots…
Unknown
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Infinite non-periodic binary fraction

I have an infinite non-periodic binary fraction. For example: $frac_1=0.101111011100110010001001010010000001001...$ Is it always true that $1-frac_1$ = non-periodic binary fraction?
bvl
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How is this complex fraction getting cleared using this method?

Can someone please explain how multiplying these two fractions together is clearing the complex fraction? I know that by multiplying these two fractions clears the complex fraction, I just can't figure out how it…
Scott
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Php problem of the period of a fraction

Question A decimal representation of $\frac a b$ with coprime $a$, $b$ has at most period $b - 1$. What does the period of this fraction mean?
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How do I rewrite a fractional expression with a numerator that is a variable raised to an exponent...as an exponential?

For example: $(x^2)/2 = x^w$ where w stands in for the value I'm trying to find.
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Need understanding on the strategy used in a one gre question

The question is below Suppose x and y are 2 integers and that $0< x < y < 10 $. The tenths digit of the decimal representation of $x/16$ is $5$. What is the hundredths digit of $17/y$ ? I was able to solve the above answer (8). But i had to go…
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Multiplying reciprocal fractions with exponents

The question is as follows: If we multiply a fraction with its reciprocal then we get 1. So by this logic this should be equal to 1^(a/a+b). But, the solutions I have been provided with states the answer to be Where am I going wrong? Thanks
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How can I prove that if $|x|<1$, then $|x| \geq |x|^2$?

I was doing some geometric series stuff today and was thinking about how numbers that are in between $-1$ and $1$ are always ‘farther from $0$’ than their squared equivalents, but how is that proven? Is it just taken as something basic? I mean,…
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Is it possible for a positive number to exceed its reciprocal by exactly one?

I know that $8/5$ comes close $8/5 - 5/8 = 39/40.$ Is there a fraction that comes closer?
rain
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Simplifying multiple fractions in the numerator.

I'm trying to solve the following equation for a, my work is as…
Renari
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How to calculate how a percentage scales up?

Sorry i know this is probably a very stupid question. But given a pie, Let us say we have 3 slices of 50%, 30% and 20% now at each iteration i remove one slice (starting from the big one) so after removing the first slice of 50%, i am now left with…
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Subtracting fractions

I was watching this video: https://www.youtube.com/watch?v=aSId_Kgjzfg&index=55&list=PLg2tfDG3Ww4vrstKAZ0dajHx_hq85P0G At 10:25 I saw the following fractions subtracted on the third line going upwards: -1/8 -152/8 = 153/8 Why is the answer not in…
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Numerator and denominator definition

I am studying fractions and how to calculate them and the terms numerator and denominator appear a lot when I read about it, but I do not know the numerator and denominator definition. i.e. $$ \frac{4}{2} + \frac{8}{2} = \frac{4+8}{2} =…
gato
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If two fractions add up to 1, are their denominators the same?

If two fraction add up to 1, what is the relation between their denominators? Are their denominators equal? If $\frac{a}{b}+\frac{c}{d}=1$, then, is what is the relation between $b$ and $d$? I was working on a problem. To solve the problem i need to…
MrAP
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