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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Reverse percentages

My mother recently started doing a distance learning course, and is struggling with her mathematical questions. I'm trying to explain to my mother how to answer the following question. Despite my trying, I simply can't phrase the question in such a…
Callum
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Ratio questions - negative number and zero in denominator

I have some two models and I need to compare the efficiency of one to another one. But if one model produces negative result e.g. -10 and another one positive eg 30, mathematically the ratio is 30/-10 = -3 meaning the first one is -300% effective to…
luky
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What is the most elegant way to calculate this fraction?

I can see some patterns, but still can’t find a way to calculate this fraction without doing it by hand. Just transcribing it is overwhelming enough.
user931509
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Find the fraction with smallest denominator between two bounds

Between the numbers 2.3 and 2.8, the fraction $\frac52$ exists, and it is the fraction between these bounds that has the smallest denominator. What algorithm can be applied to always find this fraction given two bounds? For example between 3.141 and…
minseong
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question about partial fractions why $\frac{6x^2+19x+15}{(x-1)(x-2)^2}=\frac{A}{(x-1)}+\frac{B}{(x-2)}+\frac{C}{(x-2)^2}$

can anyone tell me why $$\frac{6x^2+19x+15}{(x-1)(x-2)^2}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{(x-2)^2}$$ I don't undestand the $\frac{C}{(x-2)^2}$ and also what is wrong according to basic math rules if I write the equation in the following…
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Solving Simple Mixed Fraction problem?

How do you wrap your head around mixed fraction, does anyone knows how to figure out, can someone give me an example how it can be solved?
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Calculate the value of $x$

Given $\frac {11}2x - \frac {13} 3 = \frac 85$ So far, I have reached $33x = \frac{48}5 - 26$. However I cannot figure out how to progress further.
user837452
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Given a fraction with $ x $ is a real number, judge the scope of $ x $.

From an ACT Math test: Suppose that $ x $ is a real number and $ \frac { 4 x } { 6 x ^ 2 } $ is a rational number. Which of the following statements about $ x $ must be true? $ x $ is rational $ x $ is irrational $ x = 1 $ $ x = \frac 2 3 $ $ x =…
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Recurring decimals to fraction

$.\overline{36}=\frac{36}{99}$ $2.1\overline{36}=2\frac3{22}$ The part I do not understand however, is "you could used 1) to speed up the working of 2)" which is written in the book. How would I use 1) to help me work out 2)? Thanks.
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Why does $\frac {1}{a}-\frac{1}{b}=\frac {b-a}{ab}$?

I really don't understand the expression. $$\frac {1}{a}-\frac{1}{b}=\frac {b-a}{ab}$$ I generally have a hard time understanding non-intuitive things in math and this is one of them. Normally when I don't understand something I use an app ,…
Brucc
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How many different fractions can be made up of the numbers

How many different fractions can be made up of the numbers 3, 5, 7, 11, 13, 17 so that each fraction contains 2 different numbers? How many of them will be the proper fractions?
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Mixed number/fraction arithmetic

$28\frac{16}{63}-3\frac{9}{14}$ The answer is $24\frac{11}{18}$ I did this in my head to get the answer fast: 28 - 3 = 25 $\frac{16}{63}-\frac{9}{14}$ = $\frac{-49}{126}$ So it becomes $25\frac{126}{126}-1\frac{49}{126}$ and hence the answer…
dps1212
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Finding integer closest to value of given expression

Find the integer which is closest to the value of $\frac{1}{\sqrt[6]{5^6+1}-\sqrt[6]{5^6-1}}$ How do you do this? I try to rationalize but that gets to $\frac{\sqrt[6]{5^6+1}+\sqrt[6]{5^6-1}}{\sqrt[3]{5^6+1}-\sqrt[3]{5^6-1}}$ and I really don't…
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Rewriting of division

I've got a division of the sort $$\frac{a}{a+b}$$ which is for some reason rewritten as $$\frac{1}{1+\frac{b}{a}}$$ for numerical stability. But why would this be more stable and how do they rewrite the first formula into the second one?
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Why are fractions with a negative denominator valid?

Whenever in a fraction, there is $0$ in the denominator, the fraction becomes $\infty$ or indeterminate. But why do we consider those fractions valid that have some negative numbers in the denominator since those numbers are even smaller than $0$ ?
xyres
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