Identify the numerators and denominators of your two fractions. The numerator is the top number of the fraction, and the denominator is the bottom. For example, for the fraction 3/19, the numerator is 3 and the denominator is 19.
Multiply the numerators together, and put the value above a new fraction symbol. Multiply the denominators together, and put the value below the new fraction symbol. The result is the multiplied fraction. Now all you have to do is make sure it is simplified.
To simplify the fraction, test to see whether the numerator and denominator have any common divisors. For example, 6 and 9 have a common divisor of 3, while 3 and 7 have no common divisors (except for 1, which is trivial). The best way to test for common divisors is to write out all the divisors of the numerator and denominator and then look for matching values. For example, all the divisors of 6 are 1, 2, 3, and 6. All the divisors of 8 are 1, 2, 3, 4, and 8. The non-trivial common divisor of 6 and 8 is 2.
Divide the numerator and denominator by the common divisors. For example, if your fraction is 6/8, divide 6 by 2, which equals 3, and 8 by 2, which equals 4. The result is 3/4, which is the simplified version of 6/8.
As an example, consider a pie with 8 original slices, 3 of which have been eaten. If Mary eats 1/8 of the remaining pie, how much of the original pie did she eat? Because only 5 slices remained before Mary started eating, she started with only 5/8 of the pie. She ate 1/8 of that, so we can write 5/8 * 1/8 = Mary's share of the pie. Multiplying the numerators, we get 5, and multiplying the denominators, we get 64. Because 5 and 64 have no common factors, Mary ate 5/64 of the original pie.