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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Simplifying complex fraction

Trying to reduce this complex fraction to the answer given in my lecture notes. I've tried a few methods, which I haven't included here because it gets messy! Just wondering is there a trick/shortcut that I'm missing? I've tried reducing the small…
stuart
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Does adding an integer to a simplified fraction ensure it will always be simplified

$${A + BC\over B}$$ Assuming C is an integer and A divided by B is a simplified equation. Will this equation always be simplified? and is there a mathematical proof?
Matric
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What is the value of a?

$\frac{8−i}{3−2i}$ If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? All I know is that it equals $\frac{8-i}{3-2i}$ times $\frac{3+2i}{3+2i}$ and then i did not know what to do
Stevo
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100m Sprint involving Fractions: Who wins first and by how much?

I have a simple word problem involving division of fractions: Dan and Bart are competing in a 100-meter sprint. Dan can run 22/7 metres a second, and Bart can run 41/2 metres in 56/9 seconds. Which contestant finishes first, and by how many meters…
linada
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Alternative Proof of Stern-Brocot Tree - No Rationals Omitted

On CutTheKnot website there is an alternative proof (Prof. McWorter's Proof ) of this property of Stern-Brocot tree (that no rational numbers are omitted). I'm having a hard time understanding the second part of this proof - how does he construct…
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Fractional identity?

Is there any way to re-write the following $$p_{\hat y} \simeq\frac{1}{N-\frac{1}{T}U_1(x)+\frac{1}{2T^2}U_2(x)}$$ such that $$p_{\hat y}\propto \left(U_1-\frac{U_2}{2T}\right)/T $$ $N$ is a positive integer number, $U_1$ and $U_2$ are functions of…
Phys
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Simplifying Fractional Exponents and Can You Explain WHY

How do you solve questions like $2^{1/2}$ and can you explain how this works?
Vinod
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$3 \frac12$ divided by $\frac45\,$ ; why do I get 4.3?

This has been bothering me a lot, this is my thinking: $3\dfrac12 \implies \dfrac72 \implies \dfrac{35}{10}$ similarly $\dfrac45 \implies \dfrac{8}{10}$ So $$\dfrac{\dfrac{35}{10}}{\dfrac{8}{10}}=\dfrac{35}{8}=4.375$$ but... 35 % 8 = 3 ; 3/10?…
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Adding the numerator and denominator separately in a fraction.

We all know how to add two completely differently fractions, say we have fractions: - $\frac{a}{b}$ and $\frac{c}{d}$ We know that: - $$\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd} $$ Suppose (hypothetically) we add the aforementioned fractions…
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2 simple rule for fraction

I am embarassed to ask this question, but when a fraction divides a number, the rule is: $\dfrac{a}{\dfrac{b}{c}}$ it is supposed to be $\dfrac{a\cdot c}{b}$ $\dfrac{\dfrac{a}{b}}{c}$ it is supposed to be $\dfrac{a}{b\cdot c}$ Notice the bar for…
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How do I solve $x+{1\over x}=4 \Rightarrow x^2+{1 \over x^2}=?$

$x+{1\over x}=4 \Rightarrow x^2+{1 \over x^2}=?$
black
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Fraction as sum of fractions with prime power denominators

Given any fraction $\frac{s}{t}=\frac{s}{\Pi_pp^{i_p}}$ with $s,t$ relatively prime, I would like to know if it is possible to write $\frac{s}{\Pi_pp^{i_p}}=\sum_p\frac{s_p}{p^{i_p}}$ for some unique integers $s_p$. It seems like this is a simple…
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Period for decimals

How many positive integers n have the decimal expansion of 1/n purely periodic with period 3. I don't completely understand what a periodic decimal is so can you help me with that too?
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How many fractions of the form $\frac m{17}$ are between $\frac13$ and $\frac23$?

Of all fractions with a denominator of 17 and a whole number numerator, how many are between 1/3 and 2/3?