EXERCISE 1.4 Write all ratios in their simplest form. 1. There are three children in the Skosana family. Each wee R270, the middle child earns R180 and the youngest ear amounts as a ratio. 2. -To make a certain colour of household paint, you need t paint with 15 ml of red paint and 10 ml of yellow paint. mixture as a ratio. If you need a total volume of 31 litres much of each colour must you mix? 3. On Wednesday evening Sonto spent $$ \frac{1}{2} $$ hour doing home doing housework, 1 hour visiting friends and $$ 1 \frac{1}{2} $$ hours Write this information as a ratio. 4.- In a country there are 48000 people in the defence service army, navy and air force in the ratio $$ 5: 2: 3 $$. How many pec

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Sure, let's tackle **Exercise 1.4** step by step. The exercise involves simplifying ratios and applying them to various scenarios.

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### **Question 1**
**There are three children in the Skosana family. The eldest child earns R270, the middle child earns R180, and the youngest earns R? Write their earnings as a ratio in simplest form.**

*Note: It seems there might be a missing value for the youngest child's earnings. Assuming the youngest child earns an amount that fits into the ratio, we'll proceed with the given values.*

**Given:**
- Eldest child: R270
- Middle child: R180
- Youngest child: Let's assume R? (since it's missing, we'll proceed with the available data)

**Simplifying the Ratio:**
- The ratio of eldest to middle child is **270 : 180**.
- To simplify, divide both numbers by their greatest common divisor (GCD), which is 90.

$$
\frac{270}{90} : \frac{180}{90} = 3 : 2
$$

**Simplest Ratio:** **3 : 2**

*If the youngest child's earning is provided, you can include it similarly by simplifying the entire ratio.*

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### **Question 2**
**To make a certain color of household paint, you need to mix red and yellow paint in the ratio of 15 ml red to 10 ml yellow. If you need a total volume of 31 liters, how much of each color must you mix?**

**Given:**
- Ratio of red to yellow paint = **15 : 10**, which simplifies to **3 : 2**
- Total volume needed = **31 liters**

**Steps:**
1. **Simplify the Ratio:**  
   15 ml : 10 ml → 3 : 2

2. **Calculate Total Parts:**  
   3 (red) + 2 (yellow) = **5 parts**

3. **Determine Volume per Part:**  
   Total volume / Total parts = 31 liters / 5 = **6.2 liters per part**

4. **Calculate Individual Amounts:**  
   - **Red Paint:** 3 parts × 6.2 liters = **18.6 liters**
   - **Yellow Paint:** 2 parts × 6.2 liters = **12.4 liters**

**Answer:**  
To make 31 liters of paint, mix **18.6 liters of red paint** and **12.4 liters of yellow paint**.

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### **Question 3**
**On Wednesday evening, Sonto spent ½ hour doing housework, 1 hour visiting friends, and 1½ hours on another activity. Write this information as a ratio in simplest form.**

**Given:**
- Housework: **0.5 hours**
- Visiting friends: **1 hour**
- Another activity: **1.5 hours**

**Steps:**
1. **Express the Time Spent as a Ratio:**  
   0.5 : 1 : 1.5

2. **Eliminate Decimals by Multiplying All Terms by 2:**  
   0.5 × 2 : 1 × 2 : 1.5 × 2 = 1 : 2 : 3

**Simplest Ratio:** **1 : 2 : 3**

**Answer:**  
The ratio of time Sonto spent is **1 : 2 : 3**.

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### **Question 4**
**In a country, there are 48,000 people in the defense services (army, navy, and air force) in the ratio of 5:2:3. How many people are in each branch?**

**Given:**
- Ratio of army : navy : air force = **5 : 2 : 3**
- Total number of people = **48,000**

**Steps:**
1. **Calculate the Total Number of Parts:**  
   5 (army) + 2 (navy) + 3 (air force) = **10 parts**

2. **Determine the Number of People per Part:**  
   Total people / Total parts = 48,000 / 10 = **4,800 people per part**

3. **Calculate the Number of People in Each Branch:**  
   - **Army:** 5 parts × 4,800 = **24,000 people**
   - **Navy:** 2 parts × 4,800 = **9,600 people**
   - **Air Force:** 3 parts × 4,800 = **14,400 people**

**Answer:**  
- **Army:** 24,000 people  
- **Navy:** 9,600 people  
- **Air Force:** 14,400 people

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If **Question 1** has additional information or if there was a typo, please provide the missing details so I can assist you further!
**Solutions to Exercise 1.4:** 1. **Ratios in Simplest Form:** - **Eldest : Middle : Youngest** = **3 : 2** - **Red : Yellow Paint** = **18.6 liters : 12.4 liters** - **Housework : Visiting Friends : Another Activity** = **1 : 2 : 3** - **Army : Navy : Air Force** = **24,000 : 9,600 : 14,400** *Note: Ensure all values are accurate based on the provided information.*

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