Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{-6}{8}\right)\\= \frac{-7}{2}+ \frac{3}{2}+\frac{6}{8}\\=\frac{-7}{2}+\frac{3}{2}+\frac{3}{4}\\=\frac{-14}{4}+\frac{6}{4}+\frac{3}{4}\\=\frac{-14+6+3}{4}\\=\frac{-5}{4}\)
2. \(-\left(\frac{-4}{5}\right) +\left(\frac{7}{-8}\right) -\left(\frac{8}{9}\right)\\= \frac{4}{5}- \frac{7}{8}-\frac{8}{9}\\=\frac{288}{360}-\frac{315}{360}-\frac{320}{360}\\=\frac{288-315-320}{360}\\=\frac{-347}{360}\)
3. \(+\left(\frac{8}{7}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{8}{12}\right)\\= \frac{8}{7}- \frac{2}{6}-\frac{8}{12}\\=\frac{8}{7}-\frac{1}{3}-\frac{2}{3}\\=\frac{24}{21}-\frac{7}{21}-\frac{14}{21}\\=\frac{24-7-14}{21}\\=\frac{3}{21}\\=\frac{1}{7}\)
4. \(-\left(\frac{3}{7}\right) -\left(\frac{-10}{7}\right) -\left(\frac{5}{-4}\right)\\= \frac{-3}{7}+ \frac{10}{7}+\frac{5}{4}\\=\frac{-12}{28}+\frac{40}{28}+\frac{35}{28}\\=\frac{-12+40+35}{28}\\=\frac{63}{28}\\=\frac{9}{4}\)
5. \(-\left(\frac{7}{2}\right) -\left(\frac{-2}{10}\right) +\left(\frac{9}{-11}\right)\\= \frac{-7}{2}+ \frac{2}{10}-\frac{9}{11}\\=\frac{-7}{2}+\frac{1}{5}-\frac{9}{11}\\=\frac{-385}{110}+\frac{22}{110}-\frac{90}{110}\\=\frac{-385+22-90}{110}\\=\frac{-453}{110}\)
6. \(-\left(\frac{-7}{8}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{-3}{-11}\right)\\= \frac{7}{8}- \frac{7}{7}+\frac{3}{11}\\=\frac{7}{8}-\frac{1}{1}+\frac{3}{11}\\=\frac{77}{88}-\frac{88}{88}+\frac{24}{88}\\=\frac{77-88+24}{88}\\=\frac{13}{88}\)
7. \(-\left(\frac{-10}{9}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{5}{-2}\right)\\= \frac{10}{9}- \frac{7}{5}+\frac{5}{2}\\=\frac{100}{90}-\frac{126}{90}+\frac{225}{90}\\=\frac{100-126+225}{90}\\=\frac{199}{90}\)
8. \(+\left(\frac{9}{-2}\right) -\left(\frac{4}{4}\right) -\left(\frac{-9}{8}\right)\\= \frac{-9}{2}- \frac{4}{4}+\frac{9}{8}\\=\frac{-9}{2}-\frac{1}{1}+\frac{9}{8}\\=\frac{-36}{8}-\frac{8}{8}+\frac{9}{8}\\=\frac{-36-8+9}{8}\\=\frac{-35}{8}\)
9. \(+\left(\frac{4}{-3}\right) +\left(\frac{-4}{6}\right) -\left(\frac{-7}{-9}\right)\\= \frac{-4}{3}- \frac{4}{6}-\frac{7}{9}\\=\frac{-4}{3}-\frac{2}{3}-\frac{7}{9}\\=\frac{-12}{9}-\frac{6}{9}-\frac{7}{9}\\=\frac{-12-6-7}{9}\\=\frac{-25}{9}\)
10. \(-\left(\frac{-7}{9}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{4}{12}\right)\\= \frac{7}{9}+ \frac{7}{2}-\frac{4}{12}\\=\frac{7}{9}+\frac{7}{2}-\frac{1}{3}\\=\frac{14}{18}+\frac{63}{18}-\frac{6}{18}\\=\frac{14+63-6}{18}\\=\frac{71}{18}\)
11. \(-\left(\frac{-9}{5}\right) -\left(\frac{9}{-4}\right) +\left(\frac{12}{7}\right)\\= \frac{9}{5}+ \frac{9}{4}+\frac{12}{7}\\=\frac{252}{140}+\frac{315}{140}+\frac{240}{140}\\=\frac{252+315+240}{140}\\=\frac{807}{140}\)
12. \(+\left(\frac{5}{8}\right) +\left(\frac{-2}{8}\right) +\left(\frac{9}{-11}\right)\\= \frac{5}{8}- \frac{2}{8}-\frac{9}{11}\\=\frac{5}{8}-\frac{1}{4}-\frac{9}{11}\\=\frac{55}{88}-\frac{22}{88}-\frac{72}{88}\\=\frac{55-22-72}{88}\\=\frac{-39}{88}\)