Question

2 1/3÷(5/8-8/3)-2×1 3/7

Answer 1

$\sf 2\frac{1}{3} \div \left (\frac{5}{8} - \frac{8}{3} \right ) - 2 \cdot 1 \frac{3}{7} = -4 \\ \\ \sf 1) \frac{{5}^{(\cdot 3}}{8} - \frac{{8}^{(\cdot 8}}{3} = \frac{15}{24} - \frac{64}{24} = \frac{15-64}{24} = - \frac{49}{24} = -2\frac{1}{24} \\ \\ \sf 2) 2 \frac{1}{3} \div \left ( - 2 \frac{1}{24} \right)= \frac{2 \cdot 3 + 1}{3} \div \left (-\frac{2 \cdot 24 + 1}{24} \right) = \frac{7}{3} \div \left (-\frac{49}{24} \right) = \frac{7}{3} \cdot \left (-\frac{24}{49} \right)=- \frac{7 \cdot 24}{3 \cdot 49} = -\frac{8}{7} = -1\frac{1}{7} \\ \\ \sf 3) 2 \cdot 1 \frac{3}{7} = 2 \cdot \frac{1 \cdot 7 + 3}{7} = 2 \cdot \frac{10}{7} = \frac{2 \cdot 10}{7} = \frac{20}{7} = 2 \frac{6}{7} \\ \\ \sf 4) - 1 \frac{1}{7} - 2\frac{6}{7} = -\frac{1 \cdot 7 + 1}{7} - \frac{2 \cdot 7 + 6}{7} =- \frac{8}{7} - \frac{20}{7} = \frac{-8-20}{7} = - \frac{28}{7} = - 4$