Use a model to explain why \( 1 / 2+3 / 8 \) do not equal \( 4 / 10 \).

To visualize why \( \frac{1}{2} + \frac{3}{8} \) doesn’t equal \( \frac{4}{10} \), let's use the concept of pie charts! Imagine a pie divided into 2 equal parts. One half represents \( \frac{1}{2} \). Now, imagine another pie, but this time it’s split into 8 equal slices. When we take 3 out of those 8 slices, that represents \( \frac{3}{8} \). If you add those two amounts together, slice up the two pies according to their fractions, you'll find it doesn't fit into \( \frac{4}{10} \), which actually represents 4 out of 10 equal slices of a different pie. Now, let’s check the math! First, finding a common denominator for \( \frac{1}{2} \) and \( \frac{3}{8} \) is key. The common denominator is 8. So \( \frac{1}{2} \) becomes \( \frac{4}{8} \). Therefore, \( \frac{4}{8} + \frac{3}{8} = \frac{7}{8} \). Now, converting \( \frac{4}{10} \) to the same scale involves a little math magic too! When simplified, it becomes \( \frac{2}{5} \), or just 4 out of 10 slices. Clearly, \( \frac{7}{8} \) and \( \frac{4}{10} \) don’t match up, reinforcing that they’re distinct amounts!