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The image presents a table and an exercise related to the topic of "Adding and Subtracting with Rational Numbers" (in German: *Addieren und Subtrahieren mit rationalen Zahlen*). Herr Schmidt received an incomplete account statement due to a printer issue, and the task is to complete the missing numbers. The table lists dates, initial account balances (*Alter Kontostand*), changes (*Veränderung*), and new balances (*Neuer Kontostand*).

Here's a summary of the table:

| Datum    | Alter Kontostand | Veränderung | Neuer Kontostand |
|----------|------------------|-------------|------------------|
| 01.08.   | ?                | -14         | 6                |
| 02.08.   | 6                | 6           | ?                |
| 03.08.   | ?                | -52         | 80               |
| 04.08.   | 80               | 80          | ?                |
| 05.08.   | ?                | -220        | -67              |

Next, the exercise walks through solving for one of the missing values. It shows a number line with changes and demonstrates how to subtract the old balance from the new balance to find the difference.

#### Let's solve the missing values:

1. **For 01.08.**
   - We know the new balance is 6, and the change was -14.
   - To find the initial balance, reverse the operation: 
     \[
     \text{Initial Balance} = 6 - (-14) = 6 + 14 = 20
     \]
   So, the balance on 01.08. was 20.

2. **For 02.08.**
   - The old balance is 6, and the change is 6.
   - The new balance will be:
     \[
     \text{New Balance} = 6 + 6 = 12
     \]
   So, the new balance on 02.08. is 12.

3. **For 03.08.**
   - We know the new balance is 80, and the change is -52.
   - The old balance can be calculated:
     \[
     \text{Initial Balance} = 80 - (-52) = 80 + 52 = 132
     \]
   So, the balance on 03.08. was 132.

4. **For 04.08.**
   - The old balance is 80, and the change is 80.
   - The new balance will be:
     \[
     \text{New Balance} = 80 + 80 = 160
     \]
   So, the new balance on 04.08. is 160.

5. **For 05.08.**
   - The new balance is -67, and the change is -220.
   - To find the old balance:
     \[
     \text{Initial Balance} = -67 - (-220) = -67 + 220 = 153
     \]
   So, the balance on 05.08. was 153.

Now that the table is complete:

| Datum    | Alter Kontostand | Veränderung | Neuer Kontostand |
|----------|------------------|-------------|------------------|
| 01.08.   | 20               | -14         | 6                |
| 02.08.   | 6                | 6           | 12               |
| 03.08.   | 132              | -52         | 80               |
| 04.08.   | 80               | 80          | 160              |
| 05.08.   | 153              | -220        | -67              |

Would you like more details on any of these calculations or explanations?

---

Here are five related questions to expand the discussion:

1. How would you handle a case where the change is expressed as a percentage instead of an absolute value?
2. Can you explain why subtracting a negative number results in addition?
3. How would these calculations change if they were done using a different currency that involved conversion rates?
4. What would happen if you only had two out of the three values (old balance, change, new balance) for a series of transactions?
5. How would you structure this type of calculation in a financial management software program?

**Tip**: When working with changes (positive or negative), drawing a number line can help visualize how balances move over time.

Da der Drucker der Bank beschädigt ist, erhält Herr Schmidt einen unvollständigen Ausdruck der Bewegungen seines Kontos. Ergänzt die fehlenden Zahlen.

Learn how to calculate missing account balances by adding and subtracting rational numbers. The exercise involves determining the old balance, new balance, and changes in a bank account. Suitable for students in Grades 5-7, focusing on arithmetic operations with rational numbers.

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