Trolley, I wanted to clarify that a cup of something does not always weigh 8 ounces. You will need a chart of ingredients listing the weight of one cup if your recipe is not already written in ounces or grams. Almost all of Rose’s books have this chart.
For halving cakes with leavening, you made need to increase the leavening slightly if you want a perfectly level top.
For using less than a whole egg, I usually beat the egg first and then weigh what I need (but you could also measure by volume).
One more thing, if you need to half an unusual volume amount, such as 1/3 cup, you can convert it to tablespoons (16 in a cup) or teaspoons (48) to make it easier to measure precisely.
1/3 cup = 16 teaspoons
8 teaspoons = 2 tablespoons plus 2 teaspoons
So, for halving a recipe using 1/3 cup, you would use 2 tablespoons plus 2 teaspoons