Question

2 1/3÷(5/8-8/3)-2×1 3/7

Answer 1

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