Uses of balance scales

All of the lessons I've found thus far, involving balance scales, are used to show equality of whole numbers, or how to solve linear equations. Note that the effectiveness of using a balance scale depends on both the accuracy of the balance and the materials being weighed. For example, if we want to compare 1/2 + 1/2 with 1, it's unlikely that each 1/2 piece weighs exactly 1/2 of the 1 piece. If the scale is too accurate, this inequality might be too pronounced. However, the problem may also lie with the materials. For example, maybe the 1/2 pieces are extremely bevelled, and thus weigh significantly less than 1/2 of the 1 piece. It's something to keep in mind when selecting the scale and pieces to use in such activities.