Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) +\left(\frac{-7}{6}\right) +\left(\frac{-4}{2}\right)\\= \frac{6}{5}- \frac{7}{6}-\frac{4}{2}\\=\frac{6}{5}-\frac{7}{6}-\frac{2}{1}\\=\frac{36}{30}-\frac{35}{30}-\frac{60}{30}\\=\frac{36-35-60}{30}\\=\frac{-59}{30}\)
2. \(+\left(\frac{9}{-8}\right) +\left(\frac{-3}{5}\right) -\left(\frac{-10}{3}\right)\\= \frac{-9}{8}- \frac{3}{5}+\frac{10}{3}\\=\frac{-135}{120}-\frac{72}{120}+\frac{400}{120}\\=\frac{-135-72+400}{120}\\=\frac{193}{120}\)
3. \(-\left(\frac{-4}{3}\right) -\left(\frac{6}{2}\right) +\left(\frac{9}{-8}\right)\\= \frac{4}{3}- \frac{6}{2}-\frac{9}{8}\\=\frac{4}{3}-\frac{3}{1}-\frac{9}{8}\\=\frac{32}{24}-\frac{72}{24}-\frac{27}{24}\\=\frac{32-72-27}{24}\\=\frac{-67}{24}\)
4. \(-\left(\frac{-7}{-5}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-7}{5}- \frac{4}{10}+\frac{5}{4}\\=\frac{-7}{5}-\frac{2}{5}+\frac{5}{4}\\=\frac{-28}{20}-\frac{8}{20}+\frac{25}{20}\\=\frac{-28-8+25}{20}\\=\frac{-11}{20}\)
5. \(+\left(\frac{-8}{-7}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-9}{-7}\right)\\= \frac{8}{7}+ \frac{5}{4}-\frac{9}{7}\\=\frac{32}{28}+\frac{35}{28}-\frac{36}{28}\\=\frac{32+35-36}{28}\\=\frac{31}{28}\)
6. \(+\left(\frac{3}{2}\right) +\left(\frac{7}{-10}\right) -\left(\frac{3}{10}\right)\\= \frac{3}{2}- \frac{7}{10}-\frac{3}{10}\\=\frac{15}{10}-\frac{7}{10}-\frac{3}{10}\\=\frac{15-7-3}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
7. \(-\left(\frac{-6}{-5}\right) +\left(\frac{10}{-5}\right) -\left(\frac{4}{8}\right)\\= \frac{-6}{5}- \frac{10}{5}-\frac{4}{8}\\=\frac{-6}{5}-\frac{2}{1}-\frac{1}{2}\\=\frac{-12}{10}-\frac{20}{10}-\frac{5}{10}\\=\frac{-12-20-5}{10}\\=\frac{-37}{10}\)
8. \(+\left(\frac{5}{-2}\right) +\left(\frac{3}{-10}\right) -\left(\frac{-8}{9}\right)\\= \frac{-5}{2}- \frac{3}{10}+\frac{8}{9}\\=\frac{-225}{90}-\frac{27}{90}+\frac{80}{90}\\=\frac{-225-27+80}{90}\\=\frac{-172}{90}\\=\frac{-86}{45}\)
9. \(-\left(\frac{-7}{-9}\right) -\left(\frac{-5}{3}\right) -\left(\frac{10}{10}\right)\\= \frac{-7}{9}+ \frac{5}{3}-\frac{10}{10}\\=\frac{-7}{9}+\frac{5}{3}-\frac{1}{1}\\=\frac{-7+5-1}{9}\\=\frac{-3}{9}\\=\frac{-1}{3}\)
10. \(-\left(\frac{-8}{9}\right) +\left(\frac{-6}{9}\right) -\left(\frac{-4}{-11}\right)\\= \frac{8}{9}- \frac{6}{9}-\frac{4}{11}\\=\frac{8}{9}-\frac{2}{3}-\frac{4}{11}\\=\frac{88}{99}-\frac{66}{99}-\frac{36}{99}\\=\frac{88-66-36}{99}\\=\frac{-14}{99}\)
11. \(+\left(\frac{7}{8}\right) +\left(\frac{6}{-7}\right) -\left(\frac{5}{-5}\right)\\= \frac{7}{8}- \frac{6}{7}+\frac{5}{5}\\=\frac{7}{8}-\frac{6}{7}+\frac{1}{1}\\=\frac{49}{56}-\frac{48}{56}+\frac{56}{56}\\=\frac{49-48+56}{56}\\=\frac{57}{56}\)
12. \(-\left(\frac{4}{-7}\right) +\left(\frac{5}{7}\right) -\left(\frac{-12}{3}\right)\\= \frac{4}{7}+ \frac{5}{7}+\frac{12}{3}\\=\frac{4}{7}+\frac{5}{7}+\frac{4}{1}\\=\frac{4+5+4}{7}\\=\frac{13}{7}\)