What is half of 2/3 cup in a recipe?

I'm making a batch of my favorite cookie dough for a bake sale at work and I'm having trouble scaling down the recipe. The original calls for 2 and 1/3 cups of flour, but I need to make half as much. How do I convert this measurement into just cups? I've tried doing math in my head, but I always get confused with fractions and decimals. Can someone help me figure out what is half of 2/3 cup in a recipe like this?