When we multiply fractions, we follow a simple rule. We multiply the numerators together to get the new numerator, and we multiply the denominators together to get the new denominator. Let's see how this works with an example of one half times two thirds.
Let's work through our example step by step. We start with one half times two thirds. First, we multiply the numerators: one times two equals two. Then we multiply the denominators: two times three equals six. This gives us two sixths, which we can simplify to one third.