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Let's go through the exercises one by one. I'll provide solutions and explanations for each section. The instructions are in Dutch, so I’ll also translate as necessary for clarity.

### Task 1: Vereenvoudig de volgende verhoudingen (Simplify the following ratios)
You need to simplify the given ratios to their lowest terms.

a) \( 40 : 4 \)  
- Simplified: \( \frac{40}{4} = 10 : 1 \)

b) \( 7 : 56 \)  
- Simplified: \( \frac{7}{56} = 1 : 8 \)

c) \( 8 : 20 \)  
- Simplified: \( \frac{8}{20} = 2 : 5 \)

d) \( 48 : 60 \)  
- Simplified: \( \frac{48}{60} = 4 : 5 \)

e) \( 35 : 30 \)  
- Simplified: \( \frac{35}{30} = 7 : 6 \)

f) \( 72 : 108 \)  
- Simplified: \( \frac{72}{108} = 2 : 3 \)

g) \( 12 : 30 \)  
- Simplified: \( \frac{12}{30} = 2 : 5 \)

h) \( 30 : 75 \)  
- Simplified: \( \frac{30}{75} = 2 : 5 \)

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### Task 2: Bereken de ontbrekende getallen (Calculate the missing numbers)
Here you are solving proportional relationships (ratios).

a) \( 3 : 8 = \dots : 24 \)  
- Multiply both sides of the ratio by 3: \( \frac{24}{8} = 3 \), so \( \dots = 9 \).  
Answer: \( 3 : 8 = 9 : 24 \)

b) \( \dots : 5 = 12 : 20 \)  
- Multiply both sides by \( \frac{5}{20} = 0.25 \), so \( \dots = 3 \).  
Answer: \( 3 : 5 = 12 : 20 \)

c) \( 3 : 4 = 27 : \dots \)  
- Multiply both sides by \( 27/3 = 9 \), so \( \dots = 36 \).  
Answer: \( 3 : 4 = 27 : 36 \)

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### Task 3: In de verhouding mogen alleen maar **gehele getallen** voorkomen (In the ratio, only **whole numbers** may appear)
Here, you are asked to simplify ratios with fractions and decimals into whole numbers.

Example: \( \frac{1}{2} : \frac{3}{4} \)  
- To simplify this: \( \frac{1}{2} : \frac{3}{4} = 2 : 3 \)

Now for the others:

a) \( 2 \frac{1}{2} : 1 \)  
- Convert \( 2 \frac{1}{2} = \frac{5}{2} \), so \( \frac{5}{2} : 1 = 5 : 2 \).  
Answer: \( 5 : 2 \)

b) \( \frac{3}{4} : \frac{2}{3} \)  
- Cross-multiply: \( \frac{3}{4} : \frac{2}{3} = 9 : 8 \).  
Answer: \( 9 : 8 \)

c) \( 1 \frac{1}{2} : 1 \frac{1}{3} \)  
- Convert \( 1 \frac{1}{2} = \frac{3}{2} \) and \( 1 \frac{1}{3} = \frac{4}{3} \). Cross-multiply: \( \frac{3}{2} : \frac{4}{3} = 9 : 8 \).  
Answer: \( 9 : 8 \)

d) \( 37.5 : 87.5 \)  
- Simplified: \( \frac{37.5}{87.5} = 3 : 7 \).  
Answer: \( 3 : 7 \)

e) \( \frac{13}{4} : 4 \frac{1}{2} \)  
- Convert \( 4 \frac{1}{2} = \frac{9}{2} \), cross-multiply: \( \frac{13}{4} : \frac{9}{2} = 26 : 36 = 13 : 18 \).  
Answer: \( 13 : 18 \)

f) \( 31.25 : 93.75 \)  
- Simplified: \( \frac{31.25}{93.75} = 1 : 3 \).  
Answer: \( 1 : 3 \)

g) \( \frac{1}{2} : \frac{3}{4} \)  
- Cross-multiply: \( \frac{1}{2} : \frac{3}{4} = 2 : 3 \).  
Answer: \( 2 : 3 \)

h) \( 7.36 : 13.8 \)  
- Simplified: \( \frac{7.36}{13.8} \approx 368 : 690 = 184 : 345 \).  
Answer: \( 184 : 345 \)

i) \( 2 \frac{1}{2} : 1 \frac{2}{3} \)  
- Convert \( 2 \frac{1}{2} = \frac{5}{2} \) and \( 1 \frac{2}{3} = \frac{5}{3} \), cross-multiply: \( \frac{5}{2} : \frac{5}{3} = 15 : 10 = 3 : 2 \).  
Answer: \( 3 : 2 \)

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Do you want any further details or clarifications? Here are five related questions to deepen understanding:

1. How do you simplify ratios involving decimals?
2. What is the process for converting mixed numbers to improper fractions?
3. Can you find the missing values in other proportional relationships?
4. How do cross-multiplication and cancellation help simplify ratios?
5. How do you deal with complex ratios involving fractions and decimals together?

**Tip**: When simplifying ratios with fractions, always convert them to improper fractions first before simplifying!

Simplify ratios, calculate missing numbers, and convert fractional and decimal ratios to whole numbers. Exercises involve simplifying ratios, solving proportional relationships, and handling fractions and decimals.

Learn how to simplify ratios, calculate missing values in proportional relationships, and convert fractional and decimal ratios into whole numbers. This exercise includes detailed steps on simplifying ratios and solving proportional problems, suitable for Grades 6-8.

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