Matematică, întrebare adresată de jdjdksks, 8 ani în urmă

Va rog, exercitiul din poza, nu e greu. Rezultatul trebuie sa fie 2.

Anexe:

Răspunsuri la întrebare

Răspuns de Trombolistul

Ai dreptate.

$[(3 \frac{2}{3} + 1 \frac{7}{10}) : 8 \frac{1}{20} - (2 \frac{7}{23} - 1 \frac{45}{46}) \times \frac{23}{45}] + \frac{1}{2} + 1 = \\ \\ 3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3} \\ \\ 1 \frac{7}{10} = \frac{1 \times 10 + 7}{10} = \frac{17}{10} \\ \\ \frac{11}{3} + \frac{17}{10} = \frac{11 \times 10}{3 \times 10} + \frac{17 \times 3}{10 \times 3} = \frac{110}{30} + \frac{51}{30} = \frac{110 + 51}{30} = \frac{161}{30} \\ \\ 8 \frac{1}{20} = \frac{8 \times 20 + 1}{20} = \frac{161}{20} \\ \\ \frac{161}{30} : \frac{161}{20} = \frac{161}{30} \times \frac{20}{161} = \frac{161 \times 20}{30 \times 161} = \frac{3220}{4830} = \frac{2}{3} \\ \\ 2 \frac{7}{23} = \frac{2 \times 23 + 7}{23} = \frac{53}{23} \\ \\ 1 \frac{45}{46} = \frac{1 \times 46 + 45}{46} = \frac{91}{46} \\ \\ \frac{53}{23} - \frac{91}{46} = \frac{53 \times 2}{23 \times 2} - \frac{91}{46} = \frac{106}{41} - \frac{91}{46} = \frac{106 - 91}{46} = \frac{15}{46} \\ \\ \frac{15}{46} \times \frac{23}{45} = \frac{15 \times 23}{46 \times 45} = \frac{345}{2070} = \frac{1}{6} \\ \\ \frac{2}{3} - \frac{1}{6} = \frac{2 \times 2}{3 \times 2} - \frac{1}{6} = \frac{4}{6} - \frac{1}{6} = \frac{4 - 1}{6} = \frac{3}{6} = \frac{1}{2} \\ \\ \frac{1}{2} + \frac{1}{2} = \frac{1 + 1}{2} = \frac{2}{2} = 1 \\ \\ 1 + 1 = 2$