Yes, you multiply the numerator by the numerator, and the denominator by the denominator, and then reduce the fraction. For instance:
One half of two fifths is
1/2 x 2/5 = 2/10 which, when reduced, equals 1/5. Logically, if you have half of two fifths, you have one fifth. If you had half of four fifths, you would have two fifths, and so on.
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No.
You DO need a common denominator to add, subtract, or compare fractions. You DO NOT need a common denominator to multiply or divide fractions.
yes
YES.
No.