\( \begin{array}{ll}\text { 4.1. } & 1 \frac{2}{3}: 2 \frac{2}{3} \\ \text { 4.2. } & 2(\sqrt[3]{64} \div \sqrt{25}) \\ \text { 4.3. } & (3,6 \times 109)-(5,2 \times 109) \\ \text { 4.4. } & \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8}\end{array} \)

Calculate the value by following steps: - step0: Calculate: \(2+\frac{2}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{2\times 3}{3}+\frac{2}{3}\) - step2: Transform the expression: \(\frac{2\times 3+2}{3}\) - step3: Multiply the numbers: \(\frac{6+2}{3}\) - step4: Add the numbers: \(\frac{8}{3}\) Calculate or simplify the expression \( 1/2 + 2 + 3/4 - 3/8 \). Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}+2+\frac{3}{4}-\frac{3}{8}\) - step1: Reduce fractions to a common denominator: \(\frac{2\times 2}{2\times 2\times 2}+\frac{2\times 2\times 2\times 2}{2\times 2\times 2}+\frac{3\times 2}{4\times 2}-\frac{3}{8}\) - step2: Multiply the terms: \(\frac{2\times 2}{8}+\frac{2\times 2\times 2\times 2}{2\times 2\times 2}+\frac{3\times 2}{4\times 2}-\frac{3}{8}\) - step3: Multiply the terms: \(\frac{2\times 2}{8}+\frac{2\times 2\times 2\times 2}{8}+\frac{3\times 2}{4\times 2}-\frac{3}{8}\) - step4: Multiply the numbers: \(\frac{2\times 2}{8}+\frac{2\times 2\times 2\times 2}{8}+\frac{3\times 2}{8}-\frac{3}{8}\) - step5: Transform the expression: \(\frac{2\times 2+2\times 2\times 2\times 2+3\times 2-3}{8}\) - step6: Multiply the numbers: \(\frac{4+2\times 2\times 2\times 2+3\times 2-3}{8}\) - step7: Multiply the terms: \(\frac{4+16+3\times 2-3}{8}\) - step8: Multiply the numbers: \(\frac{4+16+6-3}{8}\) - step9: Calculate: \(\frac{23}{8}\) Calculate or simplify the expression \( 2*(64^(1/3)/25^(1/2)) \). Calculate the value by following steps: - step0: Calculate: \(2\left(\frac{64^{\frac{1}{3}}}{25^{\frac{1}{2}}}\right)\) - step1: Remove the parentheses: \(2\times \frac{64^{\frac{1}{3}}}{25^{\frac{1}{2}}}\) - step2: Multiply: \(\frac{2\times 64^{\frac{1}{3}}}{25^{\frac{1}{2}}}\) - step3: Multiply: \(\frac{8}{25^{\frac{1}{2}}}\) - step4: Simplify: \(\frac{8}{5}\) Calculate or simplify the expression \( (3.6*109)-(5.2*109) \). Calculate the value by following steps: - step0: Calculate: \(\left(3.6\times 109\right)-\left(5.2\times 109\right)\) - step1: Multiply the numbers: \(392.4-\left(5.2\times 109\right)\) - step2: Multiply the numbers: \(392.4-566.8\) - step3: Subtract the numbers: \(-174.4\) Calculate or simplify the expression \( 1 + 2/3 \). Calculate the value by following steps: - step0: Calculate: \(1+\frac{2}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{3}{3}+\frac{2}{3}\) - step2: Transform the expression: \(\frac{3+2}{3}\) - step3: Add the numbers: \(\frac{5}{3}\) Let's solve each part step by step: ### 4.1. \( 1 \frac{2}{3} : 2 \frac{2}{3} \) First, we convert the mixed numbers to improper fractions: - \( 1 \frac{2}{3} = \frac{5}{3} \) - \( 2 \frac{2}{3} = \frac{8}{3} \) Now, we perform the division: \[ \frac{5}{3} \div \frac{8}{3} = \frac{5}{3} \times \frac{3}{8} = \frac{5 \times 3}{3 \times 8} = \frac{5}{8} \] ### 4.2. \( 2(\sqrt[3]{64} \div \sqrt{25}) \) Calculating the cube root and square root: - \( \sqrt[3]{64} = 4 \) - \( \sqrt{25} = 5 \) Now, we perform the division: \[ 4 \div 5 = \frac{4}{5} \] Then, multiply by 2: \[ 2 \times \frac{4}{5} = \frac{8}{5} = 1.6 \] ### 4.3. \( (3.6 \times 109) - (5.2 \times 109) \) Calculating each term: \[ 3.6 \times 109 = 392.4 \] \[ 5.2 \times 109 = 566.8 \] Now, subtract: \[ 392.4 - 566.8 = -174.4 \] ### 4.4. \( \frac{1}{2} + 2 \frac{3}{4} - \frac{3}{8} \) First, convert the mixed number: - \( 2 \frac{3}{4} = \frac{11}{4} \) Now, we can add and subtract: \[ \frac{1}{2} = \frac{2}{4} \] So, \[ \frac{2}{4} + \frac{11}{4} - \frac{3}{8} \] To combine these, we need a common denominator. The least common multiple of 4 and 8 is 8: \[ \frac{2}{4} = \frac{4}{8}, \quad \frac{11}{4} = \frac{22}{8} \] Now, we can add and subtract: \[ \frac{4}{8} + \frac{22}{8} - \frac{3}{8} = \frac{4 + 22 - 3}{8} = \frac{23}{8} = 2 \frac{7}{8} = 2.875 \] ### Summary of Results: - **4.1:** \( \frac{5}{8} \) - **4.2:** \( 1.6 \) - **4.3:** \( -174.4 \) - **4.4:** \( 2.875 \)