Final answer:
The two 1's above 684 represent the process of carrying over in addition when the sum of a column exceeds 9. Hans accurately finds the value of 684 + 237 by using the standard addition algorithm, which includes adding digits column by column and carrying as needed, resulting in the correct sum.
Step-by-step explanation:
Hans' calculation likely involves a mathematical process known as carrying or regrouping when performing addition. The two 1's written above the number 684 represent the tens that are being carried over from the addition of the units and tens place of the numbers 684 and 237. In the process of addition, when the sum of the digits in a column is more than 9, the digit in the tens place of that sum is carried over to the next column.
For example, when adding the units column (4 + 7), the sum is 11. You write down the 1 in the units place and carry over the other 1 to the tens column. This is the first 1 above 684. Then, adding the tens column — 8, 3 from the number 237, and the carried 1 — gives you 12. Again, you would write down the 2 and carry over the other 1 to the hundreds column, which is the second 1 above 684. This carrying over helps ensure that each column's addition is accurate and that the sum of the two numbers reflects the correct value when added together.
Hans' strategy accurately finds the value of 684 + 237 because he is correctly applying the standard algorithm for addition, which involves adding digits column by column from right to left and carrying over when necessary. The correct addition would be as follows:
- Add the units (4 + 7 = 11), write 1, carry over 1.
- Add the tens (8 + 3 + carried 1 = 12), write 2, carry over 1.
- Add the hundreds (6 + 2 + carried 1 = 9), write 9.
- Thus, the sum of 684 + 237 is 921.