Worksheet 2 A 1. Write in simplest form: 1.1 6:48 1.22 hours : 15 min $$ 1.3 \quad 2 \frac{1}{4}: 1 \frac{1}{2} $$ $$ 1.425 \mathrm{~cm}^{2}: 0,5 \mathrm{~m} $$ (2) Divide 110 sweets between Daniel and Carli in the ratio $$ 5: 6 $$. 3. If R640 is divided among $$ A, B $$ and $$ C $$ in the ratio $$ 2: 5 \cdot 1 $$ rocnotion (4) An amount is divided among $$ A, B $$ $$ C $$ in the ratio $$ 2: 5: 7 $$ respectively. gets R30. 4.1 How much does A get? 4.2 What is the total amount? (5.) George, Carl and Peter start a business. They contribute a capita amount of R50000, R70 000 and R80 000 respectively.

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Sure, let's work through each of the problems you've provided step-by-step.

---

### **Worksheet 2 A**

#### **1. Write in Simplest Form**

**1.1** $$6 : 48$$

To simplify the ratio, divide both numbers by their greatest common divisor (GCD).

- **GCD of 6 and 48** is **6**.

$$
\frac{6}{6} : \frac{48}{6} = 1 : 8
$$

**Simplified Ratio:** **1 : 8**

---

**1.2** $$22$$ hours : $$15$$ minutes

First, convert both measurements to the same unit. We'll convert hours to minutes.

$$
22 \text{ hours} = 22 \times 60 = 1320 \text{ minutes}
$$

Now, the ratio is $$1320 : 15$$.

Simplify by dividing both numbers by their GCD, which is **15**.

$$
\frac{1320}{15} : \frac{15}{15} = 88 : 1
$$

**Simplified Ratio:** **88 : 1**

---

**1.3** $$2 \frac{1}{4} : 1 \frac{1}{2}$$

Convert mixed numbers to improper fractions.

$$
2 \frac{1}{4} = \frac{9}{4}, \quad 1 \frac{1}{2} = \frac{3}{2}
$$

Now, the ratio is $$\frac{9}{4} : \frac{3}{2}$$.

To simplify, find a common denominator:

$$
\frac{9}{4} : \frac{6}{4} = 9 : 6
$$

Simplify by dividing both numbers by **3**:

$$
\frac{9}{3} : \frac{6}{3} = 3 : 2
$$

**Simplified Ratio:** **3 : 2**

---

**1.4** $$1.425 \, \text{cm}^2 : 0.5 \, \text{m}$$

First, ensure both measurements are in the same unit. However, since one is in square centimeters and the other in meters (a unit of length), it's unclear how to directly compare them. Assuming it's a ratio of numerical values without considering units:

$$
1.425 : 0.5
$$

Simplify by dividing both numbers by **0.025** to eliminate decimals:

$$
\frac{1.425}{0.025} : \frac{0.5}{0.025} = 57 : 20
$$

**Simplified Ratio:** **57 : 20**

*Note: Ensure that the units are compatible when dealing with ratios involving different dimensions.*

---

#### **2. Divide 110 Sweets Between Daniel and Carli in the Ratio $$5 : 6$$**

**Total Parts:** $$5 + 6 = 11$$

**Value of Each Part:**

$$
\frac{110}{11} = 10 \text{ sweets per part}
$$

**Daniel's Share:**

$$
5 \times 10 = 50 \text{ sweets}
$$

**Carli's Share:**

$$
6 \times 10 = 60 \text{ sweets}
$$

**Result:**

- **Daniel:** 50 sweets
- **Carli:** 60 sweets

---

#### **3. Divide R640 Among A, B, and C in the Ratio $$2 : 5 : 1$$**

**Total Parts:** $$2 + 5 + 1 = 8$$

**Value of Each Part:**

$$
\frac{640}{8} = R80 \text{ per part}
$$

**A's Share:**

$$
2 \times R80 = R160
$$

**B's Share:**

$$
5 \times R80 = R400
$$

**C's Share:**

$$
1 \times R80 = R80
$$

**Result:**

- **A:** R160
- **B:** R400
- **C:** R80

---

#### **4. An Amount is Divided Among A, B, and C in the Ratio $$2 : 5 : 7$$ Respectively. A Gets R30.**

**4.1. How Much Does A Get?**

Given that A gets R30, and A's portion corresponds to **2 parts** in the ratio.

**Determining the Value of One Part:**

$$
2 \text{ parts} = R30 \
1 \text{ part} = \frac{R30}{2} = R15
$$

**4.2. What is the Total Amount?**

**Total Parts:** $$2 + 5 + 7 = 14$$

**Total Amount:**

$$
14 \times R15 = R210
$$

**Result:**

- **A's Share:** R30
- **Total Amount:** R210

---

#### **5. George, Carl, and Peter Start a Business. They Contribute a Capital Amount of R50,000, R70,000, and R80,000 Respectively.**

Since the problem statement for question 5 is incomplete, I'll provide a general method to find the ratio of their contributions or to divide profits based on their capital contributions.

**a. Determine the Ratio of Their Investments**

$$
\text{George} : \text{Carl} : \text{Peter} = 50000 : 70000 : 80000
$$

Simplify by dividing each by **10,000**:

$$
5 : 7 : 8
$$

**b. Dividing Profits Based on the Investment Ratio**

If the total profit is to be divided based on their investment ratios of $$5 : 7 : 8$$:

**Total Parts:** $$5 + 7 + 8 = 20$$

**Value of Each Part:** $$\frac{\text{Total Profit}}{20}$$

**George's Share:** $$5 \times \frac{\text{Total Profit}}{20} = \frac{5}{20} = \frac{1}{4}$$ of the profit

**Carl's Share:** $$7 \times \frac{\text{Total Profit}}{20}$$

**Peter's Share:** $$8 \times \frac{\text{Total Profit}}{20}$$

*Please provide additional details if there's a specific question related to these contributions.*

---

Feel free to ask if you need further assistance or clarification on any of these problems!
**Worksheet 2 A Solutions** 1. **Simplify the Ratios:** - **1.1** $$6 : 48$$ simplifies to **1 : 8** - **1.2** $$22$$ hours : $$15$$ minutes simplifies to **88 : 1** - **1.3** $$2 \frac{1}{4} : 1 \frac{1}{2}$$ simplifies to **3 : 2** - **1.4** $$1.425 \, \text{cm}^2 : 0.5 \, \text{m}$$ simplifies to **57 : 20** 2. **Divide 110 Sweets:** - **Daniel:** 50 sweets - **Carli:** 60 sweets 3. **Divide R640:** - **A:** R160 - **B:** R400 - **C:** R80 4. **Divide Amount Among A, B, and C:** - **A's Share:** R30 - **Total Amount:** R210 5. **George, Carl, and Peter's Business Contributions:** - **Investment Ratio:** $$5 : 7 : 8$$ - **Profit Sharing:** Based on the ratio, profits are divided accordingly. *Note: Question 5 is incomplete. Please provide more details for a complete solution.*

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