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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Dividing by Fractions in Algebra

You can divide by a fraction by multiplying by its reciprocal (i.e. $\frac{a}{b}\div\frac{c}{d} = \frac{a}{b}\times\frac{d}{c}$). Given the equation $\frac{1}{2}x = 5$, intuitively, you could either multiply both sides by two or divide both sides by…
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How to isolate algebraic fraction in this case

i have a question about of how to isolate an equation, when it has a multiplication in the denominator. a/b/3 is same than a*(3/b) but, when is: a/(b/3 * 4/a) If i want to isolate the 4/a that is multiplying the b/3 and in turn dividing to a, so…
ESCM
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When dividing by a fraction, why can you not take the reciprocal of term involving addition/subtraction?

Given something like: $$\frac{a}{\frac{a}{b}}$$ You would multiply the numerator $a$ by the reciprocal of the denominator, $\tfrac ba$ to get: $$ a\cdot\frac{b}{a}= \frac{ab}{a}=b $$ Given $$ \frac{1}{\frac 1a + \frac 1b} $$ By taking the LCM and…
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Why can you not multiply by the LCD when adding fractions?

So given: $\frac{2}{15x^2} + \frac{3}{5x}$ LCD: $15x^2$ Therefore you change the second term to a equal term with the LCD as its denominator by multiplying by $3x$: $\frac2{15x^2} + \frac{9x}{15x^2}$ For an answer of $\frac{2 + 9x}{15x^2}$…
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Adding fractions with like denominators

When we adding fractions why do not add denominators? For example, 2/15 + 3/15 = 5/15 not 5/30.
amjadomar
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Simplifying Fractions With A Variable

Simplify: $$\frac{1}{P(1-\frac{P}{N})(1-\frac{m}{P})}$$ To show that it is equal to: $$\frac{N}{N-m} \left[\frac{1}{N-P}+\frac{1}{P-m}\right].$$ I honestly have no idea how to even start the question. I am wondering if the question is asking to go…
dsjkd
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Is 5/10/20/40 a valid mathematical expression?

The Wikipedia article on Fractions says: If, in a complex fraction, there is no unique way to tell which fraction lines takes precedence, then this expression is improperly formed, because of ambiguity. So 5/10/20/40 is not a valid mathematical…
Corey
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Why does this fraction flip?

Can someone please explain the logic as to why this fraction flips? 1/1-1/4 = 4/3 Why does it equal 4/3 when my calculator says 3/4? Thank you
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Finding the nature of trailing decimals for a given fraction

I would like to know if there is a way to find out the type of trailing decimals a fraction would create i.e. terminating or non terminating repeating decimals, without actually doing a division. Like $14641/256 = 57.19140625$ which has a…
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why does multiplying a fraction e.g. enumerator/divisor with divisor/enumerator give 1?

I just found out that if you want to get 1 with the fraction: $$\frac{5}{2}$$ Then you multiply it with: $$ \frac{2}{5} $$ Does anyone have a good way to think about this?
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What formula or rule has been used here?

I was in between proving a trigonometric identity but couldn't succeed. I went through the solution and saw this in between \begin{align}\frac{\cos A \cos B}{\sin A \sin B}&= \frac{3}{1}\\\\ \frac{\cos A \cos B +\sin A \sin B}{\cos A \cos B - \sin A…
Raknos13
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Finding lowest number to multiply a fraction and get a whole

I am trying to find the multiplier for a fraction that will let me get a whole number. So trying to solve $c = a \times b$ Where $a$ is a number like $1.6$ or $0.7$ or $5.24$ Where $b$ is the lowest number that $a$ can be multiplied by to make $c$ a…
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$p_1+\cdots+p_k=1$, can those be written as rational numbers $p_1=n_1/m,~p_2=n_2/m,~\ldots,~p_k=n_k/m$?

I'm now thinking about a question that: If $0
Eric
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Simple fraction problem from book

How does the step from $$=\biggr(\frac{7}{4}\biggr)^{k-2}\biggr(\frac{11}{4}\biggl)$$ To $$=\biggr(\frac{7}{4}\biggr)^{k-2}\biggr(\frac{7}{4}\biggl)^2$$ work given $(\frac{7}{4})^2 \neq (\frac{11}{4})$
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How to expand a fraction to 100 as the denominator.

I'm working with some code that calculates point values based on computer hardware. On one computer as an example, the computer ends up with 29 possible points. Now lets say that I run the same code on another computer, and it tries to match…