Question 4 Simplify the following without using a calculator. 4.1. $$ 1 \frac{2}{3}: 2 \frac{2}{3} $$ 4.2. $$ 2(\sqrt{64}+\sqrt{25}) $$ 4.3. $$ \left(3.6 imes 10^{6} ight)-\left(5.2 imes 10^{5} ight) $$ 4.4. $$ \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} $$ GRAND TOTAL: 50

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Question 4 Simplify the following without using a calculator. 4.1. $$ 1 \frac{2}{3}: 2 \frac{2}{3} $$ 4.2. $$ 2(\sqrt{64}+\sqrt{25}) $$ 4.3. $$ \left(3.6 	imes 10^{6}ight)-\left(5.2 	imes 10^{5}ight) $$ 4.4. $$ \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} $$ GRAND TOTAL: 50

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Below is the step‐by‐step solution in markdown with all the required LaTeX formatting.

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### 4.1. Simplify $$ 1 \frac{2}{3}: 2 \frac{2}{3} $$

1. **Convert mixed fractions to improper fractions:**

$$
   1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
   $$
   $$
   2 \frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{8}{3}
   $$

2. **Perform the division:**

$$
   \frac{5}{3} \div \frac{8}{3} = \frac{5}{3} \times \frac{3}{8} = \frac{5 \times 3}{3 \times 8}
   $$

3. **Cancel the common factor $$3$$:**

$$
   \frac{5 \cancel{3}}{\cancel{3} \times 8} = \frac{5}{8}
   $$

**Answer:** $$ \frac{5}{8} $$

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### 4.2. Simplify $$ 2(\sqrt{64}+\sqrt{25}) $$

1. **Evaluate the square roots:**

$$
   \sqrt{64} = 8 \quad \text{and} \quad \sqrt{25} = 5
   $$

2. **Substitute the values:**

$$
   2(8+5)
   $$

3. **Simplify inside the parenthesis and multiply:**

$$
   2 \times 13 = 26
   $$

**Answer:** $$ 26 $$

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### 4.3. Simplify $$ \left(3.6 \times 10^{6}\right)-\left(5.2 \times 10^{5}\right) $$

1. **Express both numbers with the same power of 10:**

We write $$5.2 \times 10^5$$ in terms of $$10^6$$:

$$
   5.2 \times 10^5 = 0.52 \times 10^6
   $$

2. **Subtract the coefficients:**

$$
   3.6 \times 10^6 - 0.52 \times 10^6 = (3.6 - 0.52) \times 10^6
   $$

3. **Compute the subtraction:**

$$
   3.6 - 0.52 = 3.08
   $$

4. **Combine the result:**

$$
   3.08 \times 10^6
   $$

**Answer:** $$ 3.08 \times 10^6 $$

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### 4.4. Simplify $$ \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} $$

1. **Convert the mixed number to an improper fraction:**

$$
   2 \frac{3}{4} = \frac{(2 \times 4 + 3)}{4} = \frac{11}{4}
   $$

2. **Find a common denominator for all the fractions:**

The common denominator for $$2$$ (which is $$\frac{1}{2}$$), $$\frac{11}{4}$$, and $$\frac{3}{8}$$ is $$8$$.

$$
   \frac{1}{2} = \frac{4}{8}, \quad \frac{11}{4} = \frac{22}{8}, \quad \frac{3}{8} = \frac{3}{8}
   $$

3. **Combine the fractions:**

$$
   \frac{4}{8} + \frac{22}{8} - \frac{3}{8} = \frac{4+22-3}{8} = \frac{23}{8}
   $$

**Answer:** $$ \frac{23}{8} $$

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### GRAND TOTAL: 50

Each sub-question has been simplified step by step as shown above.
4.1. $$ \frac{5}{8} $$ 4.2. $$ 26 $$ 4.3. $$ 3.08 \times 10^6 $$ 4.4. $$ \frac{23}{8} $$ GRAND TOTAL: 50

Question 4 Simplify the following without using a calculator. 4.1. \( 1 \frac{2}{3}: 2 \frac{2}{3} \) 4.2. \( 2(\sqrt{64}+\sqrt{25}) \) 4.3. \( \left(3.6 \times 10^{6}\right)-\left(5.2 \times 10^{5}\right) \) 4.4. \( \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} \) GRAND TOTAL: 50

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