Multiplying Mixed Fractions
("Mixed Fractions" are also called "Mixed Numbers")
To multiply Mixed Fractions:
 convert to Improper Fractions
 Multiply the Fractions
 convert the result back to Mixed Fractions
Example: What is 1\frac{3}{8} × 3 ?
Think of Pizzas.
1\frac{3}{8} is 1 pizza and 3 eighths of another pizza. 
First, convert the mixed fraction (1\frac{3}{8}) to an improper fraction (\frac{11}{8}):
Cut the whole pizza into eighths and how many eighths do you have in total? 1 lot of 8, plus the 3 eighths = 8+3 = 11 eighths. 
Now multiply that by 3:
1\frac{3}{8} × 3 = \frac{11}{8} × \frac{3}{1} = \frac{33}{8}

And, lastly, convert to a mixed fraction (only because the original fraction was in that form):
33 eighths is 4 whole pizzas (4×8=32) and 1 eighth left over. 
And this is what it looks like in one line:
1\frac{3}{8} × 3 = \frac{11}{8} × \frac{3}{1} = \frac{33}{8} = 4\frac{1}{8}
Another Example: What is 1\frac{1}{2} × 2\frac{1}{5} ?
Do the steps from above:
 convert to Improper Fractions
 Multiply the Fractions
 convert the result back to Mixed Fractions
Step, by step it is:
Convert Mixed to Improper Fractions:
1\frac{1}{2} = \frac{2}{2}+\frac{1}{2} = \frac{3}{2}
2\frac{1}{5} = \frac{10}{5}+\frac{1}{5} = \frac{11}{5}
Multiply the fractions (multiply the top numbers, multiply bottom numbers):
\frac{3}{2} × \frac{11}{5} = \frac{3 × 11}{2 × 5} = \frac{33}{10}
Convert to a mixed number
\frac{33}{10} = 3\frac{3}{10}
If you are clever you can do it all in one line like this:
1\frac{1}{2} × 2\frac{1}{5} = \frac{3}{2} × \frac{11}{5} = \frac{33}{10} = 3\frac{3}{10}
One More Example: What is 3\frac{1}{4} × 3\frac{1}{3} ?
Convert Mixed to Improper Fractions:
3\frac{1}{4} = \frac{13}{4}
3\frac{1}{3} = \frac{10}{3}
Multiply
\frac{13}{4} × \frac{10}{3} = \frac{130}{12}
Convert to a mixed number:
\frac{130}{12} = 10\frac{10}{12}
And simplify:
10\frac{10}{12} = 10\frac{5}{6}
Here it is in one line:
3\frac{1}{4} × 3\frac{1}{3} = \frac{13}{4} × \frac{10}{3} = \frac{130}{12} = 10\frac{10}{12} = 10\frac{5}{6}
This One Has Negatives: What is −1\frac{5}{9} × −2\frac{1}{7} ?
Convert Mixed to Improper Fractions:
1\frac{5}{9} = \frac{9}{9} + \frac{5}{9} = \frac{14}{9}
2\frac{1}{7} = \frac{14}{7} + \frac{1}{7} = \frac{15}{7}
Then multiply the Improper Fractions (note that negative times negative gives positive):
\frac{−14}{9} × \frac{−15}{7} = \frac{−14 × −15}{9 × 7} = \frac{210}{63}
We can simplify now. Here we use two steps, first by 7 (21 and 63 are both multiples of 7), then again by 3. But it could be done in one step by dividing by 21:
\frac{210}{63} = \frac{30}{9} = \frac{10}{3}
Finally convert to a Mixed Fraction (because that was the style of the question):
\frac{10}{3} = \frac{(9+1)}{3} = \frac{9}{3} + \frac{1}{3} = 3\frac{1}{3}