Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{4}{-4}\right) -\left(\frac{8}{7}\right)\\= \frac{10}{7}- \frac{4}{4}-\frac{8}{7}\\=\frac{10}{7}-\frac{1}{1}-\frac{8}{7}\\=\frac{10-1-8}{7}\\=\frac{1}{7}\)
2. \(+\left(\frac{-2}{-7}\right) +\left(\frac{2}{-8}\right) -\left(\frac{-2}{8}\right)\\= \frac{2}{7}- \frac{2}{8}+\frac{2}{8}\\=\frac{2}{7}-\frac{1}{4}+\frac{1}{4}\\=\frac{8}{28}-\frac{7}{28}+\frac{7}{28}\\=\frac{8-7+7}{28}\\=\frac{8}{28}\\=\frac{2}{7}\)
3. \(+\left(\frac{2}{5}\right) -\left(\frac{9}{2}\right) -\left(\frac{-2}{-2}\right)\\= \frac{2}{5}- \frac{9}{2}-\frac{2}{2}\\=\frac{2}{5}-\frac{9}{2}-\frac{1}{1}\\=\frac{4}{10}-\frac{45}{10}-\frac{10}{10}\\=\frac{4-45-10}{10}\\=\frac{-51}{10}\)
4. \(+\left(\frac{9}{2}\right) -\left(\frac{-2}{10}\right) -\left(\frac{-3}{9}\right)\\= \frac{9}{2}+ \frac{2}{10}+\frac{3}{9}\\=\frac{9}{2}+\frac{1}{5}+\frac{1}{3}\\=\frac{135}{30}+\frac{6}{30}+\frac{10}{30}\\=\frac{135+6+10}{30}\\=\frac{151}{30}\)
5. \(-\left(\frac{-9}{4}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{10}{7}\right)\\= \frac{9}{4}+ \frac{9}{9}-\frac{10}{7}\\=\frac{9}{4}+\frac{1}{1}-\frac{10}{7}\\=\frac{63}{28}+\frac{28}{28}-\frac{40}{28}\\=\frac{63+28-40}{28}\\=\frac{51}{28}\)
6. \(+\left(\frac{9}{2}\right) +\left(\frac{-2}{5}\right) +\left(\frac{-7}{-4}\right)\\= \frac{9}{2}- \frac{2}{5}+\frac{7}{4}\\=\frac{90}{20}-\frac{8}{20}+\frac{35}{20}\\=\frac{90-8+35}{20}\\=\frac{117}{20}\)
7. \(-\left(\frac{4}{3}\right) +\left(\frac{-4}{9}\right) +\left(\frac{7}{11}\right)\\= \frac{-4}{3}- \frac{4}{9}+\frac{7}{11}\\=\frac{-132}{99}-\frac{44}{99}+\frac{63}{99}\\=\frac{-132-44+63}{99}\\=\frac{-113}{99}\)
8. \(-\left(\frac{8}{7}\right) +\left(\frac{-3}{-4}\right) -\left(\frac{-11}{-9}\right)\\= \frac{-8}{7}+ \frac{3}{4}-\frac{11}{9}\\=\frac{-288}{252}+\frac{189}{252}-\frac{308}{252}\\=\frac{-288+189-308}{252}\\=\frac{-407}{252}\)
9. \(-\left(\frac{4}{9}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{12}{6}\right)\\= \frac{-4}{9}- \frac{4}{4}+\frac{12}{6}\\=\frac{-4}{9}-\frac{1}{1}+\frac{2}{1}\\=\frac{-4-1+2}{9}\\=\frac{-3}{9}\\=\frac{-1}{3}\)
10. \(+\left(\frac{-9}{7}\right) +\left(\frac{9}{-7}\right) -\left(\frac{-8}{-7}\right)\\= \frac{-9}{7}- \frac{9}{7}-\frac{8}{7}\\=\frac{-9-9-8}{7}\\=\frac{-26}{7}\)
11. \(-\left(\frac{5}{-2}\right) +\left(\frac{-10}{8}\right) +\left(\frac{-7}{-11}\right)\\= \frac{5}{2}- \frac{10}{8}+\frac{7}{11}\\=\frac{5}{2}-\frac{5}{4}+\frac{7}{11}\\=\frac{110}{44}-\frac{55}{44}+\frac{28}{44}\\=\frac{110-55+28}{44}\\=\frac{83}{44}\)
12. \(+\left(\frac{9}{4}\right) +\left(\frac{9}{-10}\right) +\left(\frac{12}{-4}\right)\\= \frac{9}{4}- \frac{9}{10}-\frac{12}{4}\\=\frac{9}{4}-\frac{9}{10}-\frac{3}{1}\\=\frac{45}{20}-\frac{18}{20}-\frac{60}{20}\\=\frac{45-18-60}{20}\\=\frac{-33}{20}\)