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### 1. Write each of these ratios in its simplest form:
**(a) \( 3 : 12 : 17 \)**  
This ratio is already in its simplest form because there are no common factors between 3, 12, and 17 other than 1.

**(b) \( 4 : 30 : 8 \)**  
The common factor here is 2:
\[
4 \div 2 = 2,\quad 30 \div 2 = 15,\quad 8 \div 2 = 4
\]
So, the simplified ratio is \( 2 : 15 : 4 \).

**(c) \( 9 : 21 : 7 \)**  
The common factor is 3:
\[
9 \div 3 = 3,\quad 21 \div 3 = 7,\quad 7 \div 3 = \text{already 7}.
\]
So, the simplified ratio is \( 3 : 7 : 1 \).

**(d) \( 11 : 99 : 9 \)**  
The common factor is 11:
\[
11 \div 11 = 1,\quad 99 \div 11 = 9,\quad 9 \div 11 = 1.
\]
Thus, the simplified ratio is \( 1 : 9 : 1 \).

**(e) \( 7 : 21 : 3 \)**  
The common factor is 3:
\[
7 \div 7 = 1,\quad 21 \div 7 = 3,\quad 3 \div 7 = \text{already simplified}.
\]
Thus, the simplest form is \( 1 : 3 \).

**(f) \( 12 : 15 : 4 : 5 \)**  
The greatest common divisor (GCD) here is 1, so this is already in its simplest form \( 12 : 15 : 4 : 5 \).

---

### 2. Write in the form \(1 : n\), each of the following ratios:
**(a) \( 2 : 5 \)**  
Divide both by 2:
\[
1 : \frac{5}{2}.
\]
Thus, the form is \( 1 : 2.5 \).

**(b) \( 8 : 40 \)**  
Divide both by 8:
\[
1 : 5.
\]

**(c) \( 5 : 7 \)**  
Divide both by 5:
\[
1 : \frac{7}{5},\quad \text{or} \quad 1 : 1.4.
\]

**(d) \( 5 : 2 \)**  
Divide both by 5:
\[
1 : \frac{2}{5},\quad \text{or} \quad 1 : 0.4.
\]

**(e) \( 10 : 37 \)**  
Divide both by 10:
\[
1 : 3.7.
\]

**(f) \( 20 : 50 \)**  
Divide both by 20:
\[
1 : 2.5.
\]

---

### 3. In a class there are 18 girls and 12 boys. Write the ratio of boys to girls:
**(a) In its simplest form:**
\[
\text{Ratio} = 12 : 18.
\]
Divide both by 6:
\[
2 : 3.
\]

**(b) In the form \(1 : n\):**
\[
\frac{12}{18} = \frac{2}{3}.
\]
So, the form is \( 1 : 1.5 \).

---

### 4. In a drink, 80 cm³ of pineapple juice is mixed with 20 cm³ of orange juice. Write the ratio of pineapple juice to orange juice:
**(a) In its simplest form:**
\[
\text{Ratio} = 80 : 20.
\]
Divide both by 20:
\[
4 : 1.
\]

**(b) In the form \(1 : n\):**
\[
\frac{80}{20} = 4,\quad \text{so the ratio is} \quad 1 : 0.25.
\]

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Would you like further clarification on any of these steps?

### Related Questions:
1. How do you find the simplest form of a ratio with three or more numbers?
2. What is the method to convert any ratio into the form \( 1 : n \)?
3. Can ratios compare more than two quantities?
4. How would you handle ratios in mixed measurements, like liters and milliliters?
5. What is the real-world significance of simplifying ratios?

#### Tip:
When simplifying ratios, always check the greatest common divisor (GCD) of all terms in the ratio and divide by that.

Help simplify ratios and write them in the form 1 : n from a set of extra exercises on ratio and proportion.

Learn how to simplify ratios and write them in the form 1 : n with detailed solutions for ratios like 3:12:17, 4:30:8, and more. This problem covers core mathematical concepts of ratio and proportion, suitable for Grades 7-9.

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