# Confusion regarding the increase of the fraction

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?

• subtract the result from $$5\frac{7}{12}$$ and take the absolute value of this – Dr. Sonnhard Graubner Sep 18 '17 at 17:24
• @Dr.SonnhardGraubner $\frac{4489}{72}-\frac{402}{12}=\frac{4087}{72}=56\frac{55}{72}$, isn't there a mistake in the question? – user438365 Sep 18 '17 at 17:35
• 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. – Dave L. Renfro Sep 18 '17 at 17:35
• if it increased by $11\frac{1}{6}$, then it's going to be 3 times increase – Vasya Sep 18 '17 at 17:48
• @Vasya Could you show how it is? – user438365 Sep 18 '17 at 17:50

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: $\large{\frac{5\frac{7}{12}+11\frac{1}{6}}{5\frac{7}{12}}}=3$
• 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? – user438365 Sep 18 '17 at 18:12