22.5: GCE JUNE 2017. PI 1. Evaluate $$ \frac{5}{8} \div \frac{5}{4}-\frac{3}{4} imes 1 \frac{1}{3} $$ gives A: $$ \frac{1}{2} $$ B: $$ -\frac{1}{2} $$ C. $$ \frac{25}{32} $$ D: $$ -\frac{7}{32} $$ 2. The value of the digit 5 in 0.0513 is: A: 5 units B: 5 hundreds C: 5 tens D: 5 hundredths 3. The product $$ y^{a} \cdot y^{2 a} $$ simplifies to A: $$ (2 y)^{3 a} $$ B: $$ y^{3 a} $$ C: $$ y^{3 a^{2}} $$ D: $$ y^{4^{a}} $$ 4. At town P , the temperature is $$ -10^{\circ} \mathrm{C} $$. At town Q , the temperature is $$ 30^{\circ} \mathrm{C} $$. the increase in temperature betw sen downs ? and Q is: A: $$ 40^{\circ} \mathrm{C} $$ B: $$ 20^{\circ} \mathrm{C} $$ C: $$ -40^{\circ} \mathrm{C} $$ D: $$ -20^{\circ} \mathrm{C} $$ 5. $$ \sqrt{45} $$ simplifies to: A: 15 3: $$ 5 \sqrt{3} $$ C: $$ 9 \sqrt{5} $$ D: $$ 3-\sqrt{5} $$ 6. 0.08 converted to a fras tirr is A: $$ \frac{4}{5} $$ B. $$ \frac{2}{25} $$ C: $$ \frac{8}{25} $$ D: $$ \frac{4}{25} $$

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22.5: GCE JUNE 2017. PI 1. Evaluate $$ \frac{5}{8} \div \frac{5}{4}-\frac{3}{4} 	imes 1 \frac{1}{3} $$ gives A: $$ \frac{1}{2} $$ B: $$ -\frac{1}{2} $$ C. $$ \frac{25}{32} $$ D: $$ -\frac{7}{32} $$ 2. The value of the digit 5 in 0.0513 is: A: 5 units B: 5 hundreds C: 5 tens D: 5 hundredths 3. The product $$ y^{a} \cdot y^{2 a} $$ simplifies to A: $$ (2 y)^{3 a} $$ B: $$ y^{3 a} $$ C: $$ y^{3 a^{2}} $$ D: $$ y^{4^{a}} $$ 4. At town P , the temperature is $$ -10^{\circ} \mathrm{C} $$. At town Q , the temperature is $$ 30^{\circ} \mathrm{C} $$. the increase in temperature betw sen downs ? and Q is: A: $$ 40^{\circ} \mathrm{C} $$ B: $$ 20^{\circ} \mathrm{C} $$ C: $$ -40^{\circ} \mathrm{C} $$ D: $$ -20^{\circ} \mathrm{C} $$ 5. $$ \sqrt{45} $$ simplifies to: A: 15 3: $$ 5 \sqrt{3} $$ C: $$ 9 \sqrt{5} $$ D: $$ 3-\sqrt{5} $$ 6. 0.08 converted to a fras tirr is A: $$ \frac{4}{5} $$ B. $$ \frac{2}{25} $$ C: $$ \frac{8}{25} $$ D: $$ \frac{4}{25} $$

UpStudy AI · Accepted Answer

Sure, let's go through each question one by one and determine the correct answers with explanations.

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### **1. Evaluate $$ \frac{5}{8} \div \frac{5}{4} - \frac{3}{4} \times 1 \frac{1}{3} $$**

**Step-by-Step Solution:**

1. **Division:**
   $$
   \frac{5}{8} \div \frac{5}{4} = \frac{5}{8} \times \frac{4}{5} = \frac{20}{40} = \frac{1}{2}
   $$

2. **Multiplication:**
   $$
   1 \frac{1}{3} = \frac{4}{3}
   $$
   $$
   \frac{3}{4} \times \frac{4}{3} = 1
   $$

3. **Subtract the results:**
   $$
   \frac{1}{2} - 1 = -\frac{1}{2}
   $$

**Answer:** **B: $$ -\frac{1}{2} $$**

---

### **2. The value of the digit 5 in 0.0513 is:**

**Explanation:**

- The number 0.0513 has digits in the following places:
  - **0**. **0** (Tenths)
  - **5** (Hundredths)
  - **1** (Thousandths)
  - **3** (Ten-Thousandths)

- The digit **5** is in the **hundredths** place.

**Answer:** **D: 5 hundredths**

---

### **3. The product $$ y^{a} \cdot y^{2a} $$ simplifies to:**

**Explanation:**

- When multiplying like bases, you add the exponents:
  $$
  y^{a} \cdot y^{2a} = y^{a + 2a} = y^{3a}
  $$

**Answer:** **B: $$ y^{3a} $$**

---

### **4. The increase in temperature between town P and Q is:**

**Given:**
- Temperature at town P: $$ -10^{\circ} \mathrm{C} $$
- Temperature at town Q: $$ 30^{\circ} \mathrm{C} $$

**Calculation:**
$$
30^{\circ} \mathrm{C} - (-10^{\circ} \mathrm{C}) = 40^{\circ} \mathrm{C}
$$

**Answer:** **A: $$ 40^{\circ} \mathrm{C} $$**

---

### **5. $$ \sqrt{45} $$ simplifies to:**

**Explanation:**

- Simplify $$ \sqrt{45} $$:
  $$
  \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
  $$

**Answer:** 
There seems to be a discrepancy in the provided options. The correct simplification is $$ 3\sqrt{5} $$, which isn't listed among the options. However, the closest option based on calculation would be:

**B: $$ 5 \sqrt{3} $$** *(Note: This is not equivalent to $$ 3\sqrt{5} $$ but is the closest available option.)*

---

### **6. 0.08 converted to a fraction is:**

**Calculation:**
$$
0.08 = \frac{8}{100} = \frac{2}{25} \quad \text{(after simplifying by dividing numerator and denominator by 4)}
$$

**Answer:** **B: $$ \frac{2}{25} $$**

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If you have any further questions or need more detailed explanations, feel free to ask!
1. **A: $$ -\frac{1}{2} $$** 2. **D: 5 hundredths** 3. **B: $$ y^{3a} $$** 4. **A: $$ 40^{\circ} \mathrm{C} $$** 5. **B: $$ 5 \sqrt{3} $$** 6. **B: $$ \frac{2}{25} $$**

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