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Let $a\%b$ be the modulo operation, returning the remainder of $a$ when divided by $b$. Is it true that: $$\left(\frac{a}{b}\right)\% 5 = \frac{(a\% 5)}{(b\% 5)}$$

For instance, for $a=10$ and $b=2$ we have

$$\left(\frac{a}{b}\right)\%5=5\%5=0$$ $$\frac{(a\% 5)}{(b\% 5)}=\frac{(10\% 5)}{(2\% 5)}=0$$

Is this always true?

Milo Brandt
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hii
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  • What do you mean by the "modulo" function? It is usually treated as a binary operator, or perhaps a function of two variables. Just what does modulo(a) mean? – Rory Daulton Apr 05 '15 at 11:31
  • From what I'm seeing in the question, I think you're implying modulo 5. Are you? If so, mention it in your question. – Prasun Biswas Apr 05 '15 at 11:33
  • modulo is remainder function(generally reffered as % in programming languages). – hii Apr 05 '15 at 11:33
  • @hii, I have provided a counterexample in the answers. :) – Prasun Biswas Apr 05 '15 at 11:37
  • I edited the question; hopefully it will be clearer to other readers now. (I changed the modulo(a,b) notation to a%b, since you were already using both in the question; feel free to change it however you like though) – Milo Brandt Apr 06 '15 at 01:08

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Counterexample:

Take $a=29$ and $b=27$.

Prasun Biswas
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