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 ^{3}/_{8} × 3 ?
Think of Pizzas.
1 ^{3}/_{8} is 1 pizza and 3 eighths of another pizza. 
First, convert the mixed fraction (1 ^{3}/_{8}) to an an improper fraction (^{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 ^{3}/_{8} × 3 = ^{11}/_{8} × ^{3}/_{1} = ^{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 ^{3}/_{8} × 3 = ^{11}/_{8} × ^{3}/_{1} = ^{33}/_{8} = 4 ^{1}/_{8}
Another Example: What is 1 ^{1}/_{2} × 2 ^{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 both to improper fractions
1 ^{1}/_{2} × 2 ^{1}/_{5} = ^{3}/_{2} × ^{11}/_{5}
Multiply the fractions (multiply the top numbers, multiply bottom numbers):
^{3}/_{2} × ^{11}/_{5} = ^{(3 × 11)}/_{(2 × 5)} = ^{33}/_{10}
Convert to a mixed number
^{33}/_{10} = 3 ^{3}/_{10}
If you are clever you can do it all in one line like this:
1 ^{1}/_{2} × 2 ^{1}/_{5} = ^{3}/_{2} × ^{11}/_{5} = ^{33}/_{10} = 3 ^{3}/_{10}
One More Example: What is 3 ^{1}/_{4} × 3 ^{1}/_{3} ?
Convert both to improper fractions
3 ^{1}/_{4} × 3 ^{1}/_{3} = ^{13}/_{4} × ^{10}/_{3}
Multiply
^{13}/_{4} × ^{10}/_{3} = ^{130}/_{12}
Convert to a mixed number (and simplify):
^{130}/_{12} = 10 ^{10}/_{12} = 10 ^{5}/_{6}
Once again, here it is in one line:
3 ^{1}/_{4} × 3 ^{1}/_{3} = ^{13}/_{4} × ^{10}/_{3} = ^{130}/_{12} = 10 ^{10}/_{12} = 10 ^{5}/_{6}
This One Has Negatives: What is 1 ^{5}/_{9} × 2 ^{1}/_{7} ?
Convert Mixed to Improper Fractions:
1 ^{5}/_{9} = ^{9}/_{9} + ^{5}/_{9} = ^{14}/_{9}
2 ^{1}/_{7} = ^{14}/_{7} + ^{1}/_{7} = ^{15}/_{7}
Then multiply the Improper Fractions (Note: negative times negative gives positive) :
^{14}/_{9} × ^{15}/_{7} = ^{14×15} / _{9×7} = ^{210}/_{63}
I then decided to simplify next, first by 7 (because I noticed that 21 and 63 are both multiples of 7), then again by 3 (but I could have done it in one step by dividing by 21):
^{210}/_{63} = ^{30}/_{9} = ^{10}/_{3}
Finally convert to a Mixed Fraction (because that was the style of the question):
^{10}/_{3} = ^{(9+1)}/_{3} = ^{9}/_{3} + ^{1}/_{3} = 3 ^{1}/_{3}