You may want to review reducing fractions first.
You can multiply two fractions by multiplying their numerators and their denominators. For example, if you have to multiply 1 ⁄ 2 by 5 ⁄ 3, you multiply the numerators (1 and 5) to get 5 and the denominators (2 and 3) to get 6. The answer is then 5 ⁄ 6. The rule for signs is the same as for whole numbers; if one fraction is negative, then the answer is also negative. If both are negative, though, then the answer is positive. (Of course, if neither is negative, then the answer is also positive.)
Again, remember that a whole number is just a fraction with denominator 1. So, if you have to multiply 1 ⁄ 5 by −2, you can rewrite −2 as −2 ⁄ 1. Then you multiply the numerators (1 and 2) to get 2 and the denominators (5 and 1) to get 5. Since one fraction was negative, the answer is also negative, so you write −2 ⁄ 5.
Be sure to reduce your answers! If you get the answer −2 ⁄ 6, say, you should divide the numerator and denominator by 2 and write −1 ⁄ 3 for your answer. Your teacher may or may not take off points for this — I generally give half credit — but when you get to harder problems then you'll have to do lots of steps. You're less likely to make a mistake on the next step if you have something simple to work with (like −1 ⁄ 3) instead of something complicated (like −2 ⁄ 6). In general, always reduce fractions if you can.