Explain how you can used a grid to subtract 1.65-0.98

To subtract 1.65 - 0.98 using a grid, you can represent each decimal number on the grid and then calculate the difference between them. Here's how you can do it step by step:

1. Draw a grid with two columns and three rows. Label the first column as "1.65" and the second column as "0.98."

| |
---|---|----
| 1 | 6
. | 5 | 0
| |
| 0 | 9
. | 8 |
|_____|

2. Start subtracting from the rightmost column, similar to how you would subtract using pen and paper. Subtract 0.98 from 1.65.

| |
---|---|----
| 1 | 6
. | 5 | 0
| |
- . | 0 | 9
|_____|
| |
| 0 | 8
|_____|
| 0 | 6
|_____|

3. Since you can't subtract 8 from 5, you need to "borrow" from the left column by subtracting 1 from 6, leaving you with 5. Add that borrowed 1 to the right column, giving you 15.

| |
---|---|----
| 1 | 5
. | 5 | 10
| |
- . | 0 | 9
|_____|
| |
| 1 | 8
|_____|
| 0 | 6
|_____|

4. Now you can subtract 9 from 15, giving you 6. Write that in the right column.

| |
---|---|----
| 1 | 5
. | 5 | 10
| |
- . | 0 | 9
|_____|
| |
| 1 | 8
|_____|
| 0 | 6
|_____|

5. Finally, bring down the 1 from the left column, as there is no more borrowing required.

| |
---|---|----
| 1 | 5
. | 5 | 10
| |
- . | 0 | 9
|_____|
| 1 | 1
|_____|
| 0 | 6
|_____|

6. The result is 0.67. Therefore, 1.65 - 0.98 = 0.67.

Using a grid helps visualize the subtraction process and ensures that you don't make any mistakes while carrying over or borrowing.