of calculations. Simplify, without the use of a calculator. Show all steps of calculation in each case. 1.3.1. \( 1 \frac{2}{3}: 2 \frac{2}{3} \) 1.3.2. \( (9+10-9) \times 40+(25-30-5) \times 7 \) 1.3.3. \( \begin{array}{ll}\text { 1.3.4. } & \sqrt[3]{4}-\sqrt{94}+\sqrt{25}) \\ \text { 1.3.5. } & \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} \\ \text { 1.3.6. } & \left(2 \frac{1}{2}\right)^{2}+(0,5)^{2} \\ \text { WHOLE NUMBERS AND INTEGERS }\end{array} \)

To tackle the first problem \( 1 \frac{2}{3}: 2 \frac{2}{3} \), convert both mixed numbers to improper fractions. \( 1 \frac{2}{3} = \frac{5}{3} \) and \( 2 \frac{2}{3} = \frac{8}{3} \). Now, divide by multiplying the first fraction by the reciprocal of the second, giving us \( \frac{5}{3} \times \frac{3}{8} = \frac{5 \times 3}{3 \times 8} = \frac{5}{8} \). Next, let’s simplify \( (9 + 10 - 9) \times 40 + (25 - 30 - 5) \times 7 \): Start with the parentheses: \( 9 + 10 - 9 = 10 \) and \( 25 - 30 - 5 = -10 \). Substituting gives \( 10 \times 40 + (-10) \times 7 = 400 - 70 = 330 \). For \( \sqrt[3]{4} - \sqrt{94} + \sqrt{25} \): Since \( \sqrt{25} = 5 \), rewrite as \( \sqrt[3]{4} - \sqrt{94} + 5 \). Without a calculator, we can say \( \sqrt[3]{4} \approx 1.59 \) and \( \sqrt{94} \approx 9.7 \), giving you a rough calculation: \( 1.59 - 9.7 + 5 \approx -3.11 \) (a complex expression involving roots). Moving on to \( \frac{1}{2} + 2 \frac{3}{4} - \frac{3}{8} \): Convert \( 2 \frac{3}{4} \) to an improper fraction: \( \frac{11}{4} \), now the equation is \( \frac{1}{2} + \frac{11}{4} - \frac{3}{8} \). With a common denominator of 8, convert: \( \frac{1}{2} = \frac{4}{8}, \frac{11}{4} = \frac{22}{8}, \frac{3}{8} \) gives \( \frac{4 + 22 - 3}{8} = \frac{23}{8} \). Now, for \( \left(2 \frac{1}{2}\right)^{2} + (0.5)^{2} \): Start by converting \( 2 \frac{1}{2} = \frac{5}{2} \) and square it: \( \left(\frac{5}{2}\right)^{2} = \frac{25}{4} \), while \( (0.5)^2 = \frac{1}{4} \). Add them together: \( \frac{25}{4} + \frac{1}{4} = \frac{26}{4} = \frac{13}{2} \). Remember, math can be just like a treasure map—each equation leads to interesting discoveries! Join the journey to uncover the magic of numbers, where challenges transform into rewarding solutions! Happy calculating! 🌟