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. \( \frac{1}{2}+2 \frac{3}{4}-\frac{3}{6} \)

To simplify \( 1 \frac{2}{3}: 2 \frac{2}{3} \), first convert the mixed numbers to improper fractions: \( 1 \frac{2}{3} = \frac{5}{3} \) and \( 2 \frac{2}{3} = \frac{8}{3} \). Now, perform the division: \( \frac{5}{3} \div \frac{8}{3} = \frac{5}{3} \times \frac{3}{8} = \frac{5}{8} \). For \( 2(\sqrt[3]{64}+\sqrt{25}) \), first calculate the roots: \( \sqrt[3]{64} = 4 \) and \( \sqrt{25} = 5 \). Then, combine them: \( 4 + 5 = 9 \). Finally, multiply by 2: \( 2 \times 9 = 18 \). Now for \( \left(3.6 \times 10^{6}\right) - \left(5.2 \times 10^{5}\right) \), first express both numbers in the same powers of ten: \( 3.6 \times 10^{6} = 36 \times 10^{5} \). Thus, \( 36 \times 10^{5} - 5.2 \times 10^{5} = (36 - 5.2) \times 10^{5} = 30.8 \times 10^{5} \) which can also be written as \( 3.08 \times 10^{6} \). Finally, for \( \frac{1}{2} + 2 \frac{3}{4} - \frac{3}{6} \), convert all to improper fractions. \( 2 \frac{3}{4} = \frac{11}{4} \) and \( \frac{3}{6} = \frac{1}{2} \). Then combine: \( \frac{1}{2} + \frac{11}{4} - \frac{1}{2} = \frac{11}{4} = 2 \frac{3}{4} \). Overall, the simplified results are: 4.1: \( \frac{5}{8} \) 4.2: \( 18 \) 4.3: \( 3.08 \times 10^{6} \) 4.4: \( 2 \frac{3}{4} \)