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?
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: $\large{\frac{5\frac{7}{12}+11\frac{1}{6}}{5\frac{7}{12}}}=3$