What is an expanded algorithm? Son doesn't know and didn't bring home his textbook, any ideas?

An expanded algorithm refers to a specific method or process used to solve mathematical problems, particularly in the context of arithmetic operations like addition, subtraction, multiplication, and division.

To explain how to get the answer using an expanded algorithm, let's take the example of addition.

In the expanded form of addition, you break down each number into its place value components and then perform the addition from right to left. Here's a step-by-step process:

1. Write down the two numbers you want to add, one below the other, aligning them by place value (ones, tens, hundreds, etc.).

2. Start from the rightmost column (the ones place). Add the digits in that column and write the sum directly below.

3. Move to the next column (the tens place) and add the digits in that column, along with any carrying from the previous step. Write the sum below.

4. Repeat this process for each subsequent column, working from right to left, until you have added all the digits.

5. If there is any carrying in the leftmost column, write it as an additional digit to the left of the final answer.

For instance, let's say you want to add 356 and 489 using the expanded algorithm:

356
+489
------
( Ones place: 6 + 9 = 15, write 5 and carry over 1)
( Tens place: 5 + 8 + carry-over of 1 = 14, write 4 and carry over 1)
( Hundreds place: 3 + 4 + carry-over of 1 = 8)

Adding up these individual sums, the final answer is 845.

Remember, the expanded algorithm can be used for other arithmetic operations like subtraction, multiplication, and division, with slight variations in the process.