Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-3}\right) +\left(\frac{-7}{3}\right) -\left(\frac{6}{-2}\right)\\= \frac{2}{3}- \frac{7}{3}+\frac{6}{2}\\=\frac{2}{3}-\frac{7}{3}+\frac{3}{1}\\=\frac{2-7+3}{3}\\=\frac{-2}{3}\)
2. \(-\left(\frac{-9}{-4}\right) -\left(\frac{7}{-10}\right) +\left(\frac{-3}{-9}\right)\\= \frac{-9}{4}+ \frac{7}{10}+\frac{3}{9}\\=\frac{-9}{4}+\frac{7}{10}+\frac{1}{3}\\=\frac{-135}{60}+\frac{42}{60}+\frac{20}{60}\\=\frac{-135+42+20}{60}\\=\frac{-73}{60}\)
3. \(-\left(\frac{-5}{-6}\right) -\left(\frac{3}{-8}\right) +\left(\frac{-12}{8}\right)\\= \frac{-5}{6}+ \frac{3}{8}-\frac{12}{8}\\=\frac{-5}{6}+\frac{3}{8}-\frac{3}{2}\\=\frac{-20}{24}+\frac{9}{24}-\frac{36}{24}\\=\frac{-20+9-36}{24}\\=\frac{-47}{24}\)
4. \(+\left(\frac{-6}{5}\right) -\left(\frac{5}{-4}\right) -\left(\frac{4}{-3}\right)\\= \frac{-6}{5}+ \frac{5}{4}+\frac{4}{3}\\=\frac{-72}{60}+\frac{75}{60}+\frac{80}{60}\\=\frac{-72+75+80}{60}\\=\frac{83}{60}\)
5. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-8}{-2}\right) +\left(\frac{-12}{-10}\right)\\= \frac{-5}{6}+ \frac{8}{2}+\frac{12}{10}\\=\frac{-5}{6}+\frac{4}{1}+\frac{6}{5}\\=\frac{-25}{30}+\frac{120}{30}+\frac{36}{30}\\=\frac{-25+120+36}{30}\\=\frac{131}{30}\)
6. \(+\left(\frac{2}{-9}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{11}{4}\right)\\= \frac{-2}{9}- \frac{2}{6}+\frac{11}{4}\\=\frac{-2}{9}-\frac{1}{3}+\frac{11}{4}\\=\frac{-8}{36}-\frac{12}{36}+\frac{99}{36}\\=\frac{-8-12+99}{36}\\=\frac{79}{36}\)
7. \(+\left(\frac{10}{-7}\right) +\left(\frac{7}{4}\right) -\left(\frac{-2}{-7}\right)\\= \frac{-10}{7}+ \frac{7}{4}-\frac{2}{7}\\=\frac{-40}{28}+\frac{49}{28}-\frac{8}{28}\\=\frac{-40+49-8}{28}\\=\frac{1}{28}\)
8. \(+\left(\frac{5}{4}\right) +\left(\frac{6}{4}\right) +\left(\frac{11}{9}\right)\\= \frac{5}{4}+ \frac{6}{4}+\frac{11}{9}\\=\frac{5}{4}+\frac{3}{2}+\frac{11}{9}\\=\frac{45}{36}+\frac{54}{36}+\frac{44}{36}\\=\frac{45+54+44}{36}\\=\frac{143}{36}\)
9. \(-\left(\frac{10}{-7}\right) +\left(\frac{-10}{4}\right) -\left(\frac{7}{-8}\right)\\= \frac{10}{7}- \frac{10}{4}+\frac{7}{8}\\=\frac{10}{7}-\frac{5}{2}+\frac{7}{8}\\=\frac{80}{56}-\frac{140}{56}+\frac{49}{56}\\=\frac{80-140+49}{56}\\=\frac{-11}{56}\)
10. \(+\left(\frac{9}{-4}\right) +\left(\frac{-9}{5}\right) +\left(\frac{6}{-11}\right)\\= \frac{-9}{4}- \frac{9}{5}-\frac{6}{11}\\=\frac{-495}{220}-\frac{396}{220}-\frac{120}{220}\\=\frac{-495-396-120}{220}\\=\frac{-1011}{220}\)
11. \(+\left(\frac{-7}{-2}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{-11}{3}\right)\\= \frac{7}{2}- \frac{3}{7}+\frac{11}{3}\\=\frac{147}{42}-\frac{18}{42}+\frac{154}{42}\\=\frac{147-18+154}{42}\\=\frac{283}{42}\)
12. \(+\left(\frac{-2}{7}\right) +\left(\frac{3}{3}\right) +\left(\frac{-6}{-4}\right)\\= \frac{-2}{7}+ \frac{3}{3}+\frac{6}{4}\\=\frac{-2}{7}+\frac{1}{1}+\frac{3}{2}\\=\frac{-4}{14}+\frac{14}{14}+\frac{21}{14}\\=\frac{-4+14+21}{14}\\=\frac{31}{14}\)