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Let's solve the exercises in "OPPGAVE 1.23" one by one.

### a) \( 2 \cdot \left( \frac{3}{8} + \frac{1}{4} \right) \)

1. Find a common denominator for \( \frac{3}{8} \) and \( \frac{1}{4} \):
   \[
   \frac{1}{4} = \frac{2}{8}
   \]
   So,
   \[
   \frac{3}{8} + \frac{2}{8} = \frac{5}{8}
   \]
2. Multiply by 2:
   \[
   2 \cdot \frac{5}{8} = \frac{10}{8} = \frac{5}{4}
   \]

### b) \( \left( \frac{5}{6} - \frac{2}{9} \right) \cdot \frac{3}{5} \)

1. Find a common denominator for \( \frac{5}{6} \) and \( \frac{2}{9} \):
   \[
   \frac{5}{6} = \frac{15}{18} \quad \text{and} \quad \frac{2}{9} = \frac{4}{18}
   \]
   So,
   \[
   \frac{15}{18} - \frac{4}{18} = \frac{11}{18}
   \]
2. Multiply by \( \frac{3}{5} \):
   \[
   \frac{11}{18} \cdot \frac{3}{5} = \frac{33}{90} = \frac{11}{30}
   \]

### c) \( \left( \frac{5}{36} + \frac{1}{12} \right) : \frac{2}{9} \)

1. Find a common denominator for \( \frac{5}{36} \) and \( \frac{1}{12} \):
   \[
   \frac{1}{12} = \frac{3}{36}
   \]
   So,
   \[
   \frac{5}{36} + \frac{3}{36} = \frac{8}{36} = \frac{2}{9}
   \]
2. Division by \( \frac{2}{9} \) is equivalent to multiplying by the reciprocal:
   \[
   \frac{2}{9} \div \frac{2}{9} = \frac{2}{9} \cdot \frac{9}{2} = 1
   \]

### d) \( \left( \frac{7}{6} - \frac{6}{9} \right) \left( \frac{1}{5} + \frac{1}{4} \right) \)

1. Find a common denominator for \( \frac{7}{6} \) and \( \frac{6}{9} \):
   \[
   \frac{7}{6} = \frac{21}{18} \quad \text{and} \quad \frac{6}{9} = \frac{12}{18}
   \]
   So,
   \[
   \frac{21}{18} - \frac{12}{18} = \frac{9}{18} = \frac{1}{2}
   \]
2. Find a common denominator for \( \frac{1}{5} \) and \( \frac{1}{4} \):
   \[
   \frac{1}{5} = \frac{4}{20} \quad \text{and} \quad \frac{1}{4} = \frac{5}{20}
   \]
   So,
   \[
   \frac{4}{20} + \frac{5}{20} = \frac{9}{20}
   \]
3. Multiply the two results:
   \[
   \frac{1}{2} \cdot \frac{9}{20} = \frac{9}{40}
   \]

Would you like further details on any of these solutions or have any other questions?

Here are 5 questions you might want to ask:
1. Can you explain how to find a common denominator in more detail?
2. What is the process for multiplying fractions?
3. How do you simplify fractions?
4. What are the steps for adding and subtracting fractions?
5. Can you show how to solve another example problem with fractions?

**Tip:** When working with fractions, always find a common denominator for addition and subtraction and remember to multiply by the reciprocal for division.

Explore how to solve exercises in OPPGAVE 1.23 involving fractions and operations. This detailed solution covers finding common denominators, multiplying and dividing fractions, and more. Suitable for students in Grades 5-8.

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