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

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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. $$ 2(\sqrt[3]{64}+\sqrt{25}) $$ 4.3. $$ \left(3,6 	imes 10^{6}ight)-\left(5,2 	imes 10^{5}ight) $$ 4.4. $$ \frac{1}{2}+2 \frac{3}{4}-\frac{3}{6} $$

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

1. Convert mixed numbers 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. Set up the division:
   $$
   \frac{5}{3} \div \frac{8}{3}
   $$

3. Multiply by the reciprocal:
   $$
   \frac{5}{3} \times \frac{3}{8} = \frac{5 \times 3}{3 \times 8} = \frac{5}{8}
   $$

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

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**4.2. Simplify $$2(\sqrt[3]{64}+\sqrt{25})$$**

1. Evaluate the cube root and the square root:
   - $$\sqrt[3]{64} = 4$$ because $$4^3 = 64$$
   - $$\sqrt{25} = 5$$ because $$5^2 = 25$$

2. Substitute the values into the expression:
   $$
   2(4 + 5) = 2(9) = 18
   $$

**Answer:** $$18$$

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**4.3. Simplify $$\left(3,6 \times 10^{6}\right)-\left(5,2 \times 10^{5}\right)$$**

1. Write the numbers in a consistent form:
   - $$3,6 \times 10^{6} = 3.6 \times 10^6$$
   - $$5,2 \times 10^{5} = 5.2 \times 10^5$$

2. Express $$5.2 \times 10^5$$ in terms of $$10^6$$:
   $$
   5.2 \times 10^5 = 0.52 \times 10^6
   $$

3. Subtract:
   $$
   3.6 \times 10^6 - 0.52 \times 10^6 = (3.6 - 0.52) \times 10^6 = 3.08 \times 10^6
   $$

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

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**4.4. Simplify $$\frac{1}{2}+2 \frac{3}{4}-\frac{3}{6}$$**

1. Convert the mixed number and simplify the fraction:
   - $$2\frac{3}{4} = \frac{8+3}{4} = \frac{11}{4}$$
   - $$\frac{3}{6} = \frac{1}{2}$$

2. Write the expression:
   $$
   \frac{1}{2} + \frac{11}{4} - \frac{1}{2}
   $$

3. The $$\frac{1}{2}$$ terms cancel each other:
   $$
   \frac{11}{4}
   $$

**Answer:** $$\frac{11}{4}$$
**4.1. Simplify $$1 \frac{2}{3} \div 2 \frac{2}{3}$$:** $$\frac{5}{8}$$ **4.2. Simplify $$2(\sqrt[3]{64} + \sqrt{25})$$:** $$18$$ **4.3. Simplify $$(3.6 \times 10^6) - (5.2 \times 10^5)$$:** $$3.08 \times 10^6$$ **4.4. Simplify $$\frac{1}{2} + 2 \frac{3}{4} - \frac{3}{6}$$:** $$\frac{11}{4}$$

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

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