\( \begin{array}{l}457+278=400+50+7+200+70+8=(400+200)+(50+70)+(7+8)=600+120+15=600+100+20+10 \\ +5=700+30+5=735 \\ \text { The steps in the addition algorithm are making use of the concept of } \\ \text { a. equal addition } \\ \text { b. lattice addition } \\ \text { c. expanded notation } \\ \text { d. decomposition }\end{array} \) ?

The steps in the addition algorithm showcased in the example prominently utilize expanded notation, which breaks down the numbers into their place values. This not only makes it easier to visualize the addition of each component but also enhances students' understanding of how numbers relate to each other in different forms. Additionally, this method reinforces the concept of decomposing numbers into parts, such as breaking down 457 into 400, 50, and 7. This approach can be engaging as it often leads to creative problem-solving and allows students to play around with numbers, fostering a deeper comprehension of arithmetic and enhancing mental math skills!