<s>[INST] Mixed number fractions vs regular fractions? $3\frac{1}{6}-1\frac{11}{12}$ I just passed Calculus 2 in college with an A and I'm rather embarrassed that I'm asking this question.  My wife is taking an intermediate Algebra course in college and they gave her the below problem.
$$3\frac{1}{6}-1\frac{11}{12}$$
Well I guess I gave her bad advice because I told her that this problem is equivalent to multiplying the whole numbers $3$ and $1$ by the fraction simplifying the problem to:
$\frac{3}{6}-\frac{11}{12}$ or $\frac{1}{2}-\frac{11}{12}$
After solving I got an answer of $-\frac{5}{12}$ which is not the correct answer according to her book.  
Is true that the mixed fraction gives a different result than a normal fraction multiplied by a number?
 [/INST] $3 \dfrac16$ denoted $3+\dfrac16 = \dfrac{19}6$ and not $3 \cdot \dfrac16$. 
Similarly, $1\dfrac{11}{12}$ denotes $1+\dfrac{11}{12} = \dfrac{23}{12}$ and not $1 \cdot \dfrac{11}{12}$.
Hence,
$$3 \dfrac16 - 1\dfrac{11}{12} = \dfrac{19}6 - \dfrac{23}{12} = \dfrac{38-23}{12} = \dfrac{15}{12} = \dfrac54$$
</s>