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If $5\frac{7}{12}$ is increased by $11\frac{1}{6}$, how many times has it increased?

I thought it is $5\frac{7}{12}\cdot11\frac{1}{6}=\frac{67^2}{72}$, but the answer says $3$, and I can't show why. (I hope I have translated the question correctly.) I have 3 more question: as I have written, doesn't increased by mean: $5\frac{7}{12}\cdot11\frac{1}{6}=\frac{67^2}{72}$? (because grammatically (logically also) it implies this meaning) So, in this case, it has increased by $11\frac{1}{6}$! But it turned out to be wrong, why it is increased by $3$ and not by $11\frac{1}{6}$? It seems to me that saying "increased by 3" means: $5\frac{7}{12}\cdot3=\frac{67}{4}$. Why is thinking in this way wrong?

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    $\begingroup$ subtract the result from $$5\frac{7}{12}$$ and take the absolute value of this $\endgroup$ – Dr. Sonnhard Graubner Sep 18 '17 at 17:24
  • $\begingroup$ @Dr.SonnhardGraubner $\frac{4489}{72}-\frac{402}{12}=\frac{4087}{72}=56\frac{55}{72}$, isn't there a mistake in the question? $\endgroup$ – user438365 Sep 18 '17 at 17:35
  • $\begingroup$ The answer is incorrect or you have not worded the question correctly, because if $5\frac{7}{12}$ is multiplied by $11\frac{1}{6},$ then by the usual meaning of "how many times has it increased", it follows that $5\frac{7}{12}$ has been increased $11\frac{1}{6}$ times. $\endgroup$ – Dave L. Renfro Sep 18 '17 at 17:35
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    $\begingroup$ if it increased by $11\frac{1}{6}$, then it's going to be 3 times increase $\endgroup$ – Vasya Sep 18 '17 at 17:48
  • $\begingroup$ @Vasya Could you show how it is? $\endgroup$ – user438365 Sep 18 '17 at 17:50
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I assume the problem says "increased by $11\frac{1}{6}$. Then to find how many times the initial value increased, we need to divide the final value by the original value: $\large{\frac{5\frac{7}{12}+11\frac{1}{6}}{5\frac{7}{12}}}=3$

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  • $\begingroup$ I have 3 more question: as I have edited, doesn't increased by mean: $5\frac{7}{12}\cdot11\frac{1}{6}=\frac{67^2}{72}?$ (because grammatically (logically also) it implies this meaning) So, in this case, it has increased by $11\frac{1}{6}!$ But it turned out to be wrong, why it is increased by $3$ and not by $11\frac{1}{6}$? It seems to me that saying "increased by 3" means $5\frac{7}{12}\cdot3=\frac{67}{4}$. Why is thinking in this way wrong? $\endgroup$ – user438365 Sep 18 '17 at 18:12
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    $\begingroup$ if we want to say the value is tripled, we say "the value increased by a factor of 3" or "3 times" $\endgroup$ – Vasya Sep 18 '17 at 18:22

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