Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right) +\left(\frac{2}{-8}\right) +\left(\frac{-11}{11}\right)\\= \frac{8}{7}- \frac{2}{8}-\frac{11}{11}\\=\frac{8}{7}-\frac{1}{4}-\frac{1}{1}\\=\frac{32}{28}-\frac{7}{28}-\frac{28}{28}\\=\frac{32-7-28}{28}\\=\frac{-3}{28}\)
2. \(-\left(\frac{-7}{-2}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{7}{-9}\right)\\= \frac{-7}{2}- \frac{9}{9}-\frac{7}{9}\\=\frac{-7}{2}-\frac{1}{1}-\frac{7}{9}\\=\frac{-63}{18}-\frac{18}{18}-\frac{14}{18}\\=\frac{-63-18-14}{18}\\=\frac{-95}{18}\)
3. \(-\left(\frac{-5}{-3}\right) +\left(\frac{3}{-2}\right) +\left(\frac{3}{-7}\right)\\= \frac{-5}{3}- \frac{3}{2}-\frac{3}{7}\\=\frac{-70}{42}-\frac{63}{42}-\frac{18}{42}\\=\frac{-70-63-18}{42}\\=\frac{-151}{42}\)
4. \(-\left(\frac{8}{-7}\right) -\left(\frac{4}{-8}\right) -\left(\frac{6}{-10}\right)\\= \frac{8}{7}+ \frac{4}{8}+\frac{6}{10}\\=\frac{8}{7}+\frac{1}{2}+\frac{3}{5}\\=\frac{80}{70}+\frac{35}{70}+\frac{42}{70}\\=\frac{80+35+42}{70}\\=\frac{157}{70}\)
5. \(-\left(\frac{10}{7}\right) -\left(\frac{7}{-2}\right) -\left(\frac{-5}{-8}\right)\\= \frac{-10}{7}+ \frac{7}{2}-\frac{5}{8}\\=\frac{-80}{56}+\frac{196}{56}-\frac{35}{56}\\=\frac{-80+196-35}{56}\\=\frac{81}{56}\)
6. \(-\left(\frac{-4}{9}\right) +\left(\frac{8}{-8}\right) +\left(\frac{9}{4}\right)\\= \frac{4}{9}- \frac{8}{8}+\frac{9}{4}\\=\frac{4}{9}-\frac{1}{1}+\frac{9}{4}\\=\frac{16}{36}-\frac{36}{36}+\frac{81}{36}\\=\frac{16-36+81}{36}\\=\frac{61}{36}\)
7. \(+\left(\frac{-10}{3}\right) +\left(\frac{4}{-10}\right) -\left(\frac{8}{-4}\right)\\= \frac{-10}{3}- \frac{4}{10}+\frac{8}{4}\\=\frac{-10}{3}-\frac{2}{5}+\frac{2}{1}\\=\frac{-50}{15}-\frac{6}{15}+\frac{30}{15}\\=\frac{-50-6+30}{15}\\=\frac{-26}{15}\)
8. \(-\left(\frac{4}{7}\right) +\left(\frac{10}{9}\right) -\left(\frac{8}{4}\right)\\= \frac{-4}{7}+ \frac{10}{9}-\frac{8}{4}\\=\frac{-4}{7}+\frac{10}{9}-\frac{2}{1}\\=\frac{-36}{63}+\frac{70}{63}-\frac{126}{63}\\=\frac{-36+70-126}{63}\\=\frac{-92}{63}\)
9. \(+\left(\frac{-5}{-9}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{10}{-12}\right)\\= \frac{5}{9}+ \frac{4}{9}-\frac{10}{12}\\=\frac{5}{9}+\frac{4}{9}-\frac{5}{6}\\=\frac{10}{18}+\frac{8}{18}-\frac{15}{18}\\=\frac{10+8-15}{18}\\=\frac{3}{18}\\=\frac{1}{6}\)
10. \(-\left(\frac{-5}{-7}\right) +\left(\frac{-6}{2}\right) +\left(\frac{-5}{-11}\right)\\= \frac{-5}{7}- \frac{6}{2}+\frac{5}{11}\\=\frac{-5}{7}-\frac{3}{1}+\frac{5}{11}\\=\frac{-55}{77}-\frac{231}{77}+\frac{35}{77}\\=\frac{-55-231+35}{77}\\=\frac{-251}{77}\)
11. \(+\left(\frac{10}{-7}\right) +\left(\frac{5}{4}\right) -\left(\frac{4}{-3}\right)\\= \frac{-10}{7}+ \frac{5}{4}+\frac{4}{3}\\=\frac{-120}{84}+\frac{105}{84}+\frac{112}{84}\\=\frac{-120+105+112}{84}\\=\frac{97}{84}\)
12. \(+\left(\frac{2}{-3}\right) +\left(\frac{-2}{3}\right) -\left(\frac{10}{3}\right)\\= \frac{-2}{3}- \frac{2}{3}-\frac{10}{3}\\=\frac{-2-2-10}{3}\\=\frac{-14}{3}\)