The easy one.
Just multiply straight across.
Unlike addition, you don't need matching bottoms.
Top x Top, Bottom x Bottom.
In Plain English: Multiplying fractions is usually cleaner than adding them. You just multiply the numerators together and the denominators together. Think of 'of' as multiply: 'Half OF half' is a quarter.
In The Real World: Scaling a recipe down. You need half of a 3/4 cup of sugar.
Cross multiplying. That's for solving equations (x/2 = 3/4), NOT for multiplying fractions.