How much is it $\frac{17a}{12}$ (in hexadecimal) I got $15$ with remainder $a$. Can someone confirm its true?
Thank you!
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115 is correct but there is no remainder. – cr001 Oct 16 '15 at 08:55
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1If you're using Windows, then: open the Start menu, write 'calc' and press Enter to launch the calculator, open the View menu, choose Programmer, choose Hex and enter $17A/12$. – barak manos Oct 16 '15 at 08:59
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@cr001 quick question, if it would be 18a/12, is my answer correct? – Mor Haviv Oct 16 '15 at 10:40
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I should note that different countries do long division differently. (It's the same algorithm, but the numbers are sometimes arranged differently.) – Akiva Weinberger Oct 16 '15 at 13:00
3 Answers
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No, it's false.
Since the claim is equivalent to $$17A_{16}=12_{16}\cdot15_{16}+A$$
One can confirm as the following way:
$$17A_{16}=16^2+7\cdot16+10=378$$
While
$$15_{16}\cdot12_{16}+A=(16+5)(16+2)+10=388\neq378$$
Obviously, by observation, we have
$$15_{16}\cdot12_{16}+A=17A_{16}+A$$ $$15_{16}\cdot12_{16}=17A_{16}$$
So it should be:
$$\frac{17A_{16}}{12_{16}}=15_{16}$$
Mythomorphic
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Just like in the case of the division algorithm in the base then system, first you take a look at $$17a:12$$
and you realize that $17/12=1$ and the remainder is $5$. So you have after the first step $$ \begin{matrix} 17a&:12&=&1\\ \color{white}{|}5 \end{matrix} $$ then you "bring down" the next digit of the dividend: $$ \begin{matrix} 17a&:12&=&1\\ \color{white}{|}\color{blue}{5a} \end{matrix} $$
then you guess the result of the division $\color{blue}{5a}:12$. My first guess is $5$. Indeed $12\times5=5a$.
You right this down the following way
$$ \begin{matrix} 17a&:12&=&1\color{red}5\\ \color{white}{|}\color{blue}{5a}\\ \ \color{red}{ 5a} \end{matrix} $$
now, you subtract $\color{red}{5a}$ from $\color{blue}{5a}$. The result would be the remainder, zero this time, because there is no more numbers in the divident to be brought down.
zoli
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