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The exercise sheet is titled "Veranschaulichung der Subtraktion von Brüchen" (Visualizing the Subtraction of Fractions). The task requires solving fraction subtraction problems both algebraically and geometrically using the provided grids.

I'll guide you through solving these:

### 1. **Complete the following tasks in the same way as the given example:**

#### a) \( \frac{7}{15} - \frac{3}{15} \)
- Since both fractions have the same denominator (15), subtract the numerators:
  \[
  \frac{7 - 3}{15} = \frac{4}{15}
  \]
- The solution is \( \frac{4}{15} \).

#### b) \( \frac{8}{9} - \frac{5}{9} \)
- Again, both fractions have the same denominator (9):
  \[
  \frac{8 - 5}{9} = \frac{3}{9} = \frac{1}{3}
  \]
- The solution is \( \frac{1}{3} \).

### 2. **Solve the following tasks using the same method geometrically:**

#### a) \( \frac{4}{5} - \frac{3}{4} \)
- Convert both fractions to a common denominator, the least common denominator (LCD) of 5 and 4 is 20:
  \[
  \frac{4}{5} = \frac{16}{20}, \quad \frac{3}{4} = \frac{15}{20}
  \]
  Now, subtract the fractions:
  \[
  \frac{16}{20} - \frac{15}{20} = \frac{1}{20}
  \]
- The solution is \( \frac{1}{20} \).

#### b) \( \frac{2}{3} - \frac{7}{7} \)
- Since \( \frac{7}{7} = 1 \), the result will be negative:
  \[
  \frac{2}{3} - 1 = \frac{2}{3} - \frac{3}{3} = -\frac{1}{3}
  \]
- The solution is \( -\frac{1}{3} \).

#### c) \( \frac{5}{6} - \frac{3}{4} \)
- Find the least common denominator of 6 and 4, which is 12:
  \[
  \frac{5}{6} = \frac{10}{12}, \quad \frac{3}{4} = \frac{9}{12}
  \]
  Subtract the fractions:
  \[
  \frac{10}{12} - \frac{9}{12} = \frac{1}{12}
  \]
- The solution is \( \frac{1}{12} \).

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Do you want more details or have any questions?

Here are five related questions to deepen your understanding:
1. How do you find the least common denominator (LCD) of two fractions?
2. Why do we need a common denominator to subtract fractions?
3. What happens when you subtract a fraction from a whole number?
4. How would you handle subtraction involving improper fractions?
5. What is the difference between geometric and algebraic representation of fraction subtraction?

**Tip:** Always simplify your fractions at the end to their lowest terms if possible.

This problem involves subtracting fractions and visualizing the process with diagrams. Learn how to subtract fractions with common denominators and different denominators, including the steps to find the least common denominator (LCD). Suitable for students in Grades 6-8.

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