Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

1. \(-\left(\frac{5}{6}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{2}{-11}\right)\)
2. \(+\left(\frac{9}{-4}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-9}{-5}\right)\)
3. \(+\left(\frac{7}{8}\right) -\left(\frac{2}{8}\right) +\left(\frac{-8}{-7}\right)\)
4. \(-\left(\frac{-9}{7}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{-9}{-4}\right)\)
5. \(+\left(\frac{-7}{8}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{3}{3}\right)\)
6. \(-\left(\frac{-4}{3}\right) +\left(\frac{9}{10}\right) +\left(\frac{-11}{-2}\right)\)
7. \(-\left(\frac{3}{-2}\right) -\left(\frac{-3}{10}\right) -\left(\frac{4}{10}\right)\)
8. \(+\left(\frac{7}{4}\right) -\left(\frac{-2}{6}\right) -\left(\frac{6}{-8}\right)\)
9. \(+\left(\frac{-2}{3}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{-9}{-2}\right)\)
10. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-2}{8}\right) -\left(\frac{5}{9}\right)\)
11. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-7}{9}\right) -\left(\frac{11}{-2}\right)\)
12. \(+\left(\frac{-5}{6}\right) +\left(\frac{5}{8}\right) +\left(\frac{-4}{-5}\right)\)

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{6}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{2}{-11}\right)\\= \frac{-5}{6}+ \frac{2}{8}-\frac{2}{11}\\=\frac{-5}{6}+\frac{1}{4}-\frac{2}{11}\\=\frac{-110}{132}+\frac{33}{132}-\frac{24}{132}\\=\frac{-110+33-24}{132}\\=\frac{-101}{132}\)
2. \(+\left(\frac{9}{-4}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-9}{-5}\right)\\= \frac{-9}{4}+ \frac{7}{4}+\frac{9}{5}\\=\frac{-45}{20}+\frac{35}{20}+\frac{36}{20}\\=\frac{-45+35+36}{20}\\=\frac{26}{20}\\=\frac{13}{10}\)
3. \(+\left(\frac{7}{8}\right) -\left(\frac{2}{8}\right) +\left(\frac{-8}{-7}\right)\\= \frac{7}{8}- \frac{2}{8}+\frac{8}{7}\\=\frac{7}{8}-\frac{1}{4}+\frac{8}{7}\\=\frac{49}{56}-\frac{14}{56}+\frac{64}{56}\\=\frac{49-14+64}{56}\\=\frac{99}{56}\)
4. \(-\left(\frac{-9}{7}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{-9}{-4}\right)\\= \frac{9}{7}+ \frac{6}{7}-\frac{9}{4}\\=\frac{36}{28}+\frac{24}{28}-\frac{63}{28}\\=\frac{36+24-63}{28}\\=\frac{-3}{28}\)
5. \(+\left(\frac{-7}{8}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{3}{3}\right)\\= \frac{-7}{8}- \frac{10}{2}-\frac{3}{3}\\=\frac{-7}{8}-\frac{5}{1}-\frac{1}{1}\\=\frac{-7-5-1}{8}\\=\frac{-13}{8}\)
6. \(-\left(\frac{-4}{3}\right) +\left(\frac{9}{10}\right) +\left(\frac{-11}{-2}\right)\\= \frac{4}{3}+ \frac{9}{10}+\frac{11}{2}\\=\frac{40}{30}+\frac{27}{30}+\frac{165}{30}\\=\frac{40+27+165}{30}\\=\frac{232}{30}\\=\frac{116}{15}\)
7. \(-\left(\frac{3}{-2}\right) -\left(\frac{-3}{10}\right) -\left(\frac{4}{10}\right)\\= \frac{3}{2}+ \frac{3}{10}-\frac{4}{10}\\=\frac{3}{2}+\frac{3}{10}-\frac{2}{5}\\=\frac{15}{10}+\frac{3}{10}-\frac{4}{10}\\=\frac{15+3-4}{10}\\=\frac{14}{10}\\=\frac{7}{5}\)
8. \(+\left(\frac{7}{4}\right) -\left(\frac{-2}{6}\right) -\left(\frac{6}{-8}\right)\\= \frac{7}{4}+ \frac{2}{6}+\frac{6}{8}\\=\frac{7}{4}+\frac{1}{3}+\frac{3}{4}\\=\frac{21}{12}+\frac{4}{12}+\frac{9}{12}\\=\frac{21+4+9}{12}\\=\frac{34}{12}\\=\frac{17}{6}\)
9. \(+\left(\frac{-2}{3}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-2}{3}+ \frac{10}{4}+\frac{9}{2}\\=\frac{-2}{3}+\frac{5}{2}+\frac{9}{2}\\=\frac{-4}{6}+\frac{15}{6}+\frac{27}{6}\\=\frac{-4+15+27}{6}\\=\frac{38}{6}\\=\frac{19}{3}\)
10. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-2}{8}\right) -\left(\frac{5}{9}\right)\\= \frac{-7}{3}- \frac{2}{8}-\frac{5}{9}\\=\frac{-7}{3}-\frac{1}{4}-\frac{5}{9}\\=\frac{-84}{36}-\frac{9}{36}-\frac{20}{36}\\=\frac{-84-9-20}{36}\\=\frac{-113}{36}\)
11. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-7}{9}\right) -\left(\frac{11}{-2}\right)\\= \frac{2}{9}+ \frac{7}{9}+\frac{11}{2}\\=\frac{4}{18}+\frac{14}{18}+\frac{99}{18}\\=\frac{4+14+99}{18}\\=\frac{117}{18}\\=\frac{13}{2}\)
12. \(+\left(\frac{-5}{6}\right) +\left(\frac{5}{8}\right) +\left(\frac{-4}{-5}\right)\\= \frac{-5}{6}+ \frac{5}{8}+\frac{4}{5}\\=\frac{-100}{120}+\frac{75}{120}+\frac{96}{120}\\=\frac{-100+75+96}{120}\\=\frac{71}{120}\)