Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{8}\right) -\left(\frac{3}{7}\right) -\left(\frac{2}{-7}\right)\\= \frac{-7}{8}- \frac{3}{7}+\frac{2}{7}\\=\frac{-49}{56}-\frac{24}{56}+\frac{16}{56}\\=\frac{-49-24+16}{56}\\=\frac{-57}{56}\)
2. \(-\left(\frac{2}{9}\right) +\left(\frac{-10}{3}\right) +\left(\frac{7}{-3}\right)\\= \frac{-2}{9}- \frac{10}{3}-\frac{7}{3}\\=\frac{-2-10-7}{9}\\=\frac{-19}{9}\)
3. \(+\left(\frac{3}{-4}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{-4}{8}\right)\\= \frac{-3}{4}- \frac{2}{10}-\frac{4}{8}\\=\frac{-3}{4}-\frac{1}{5}-\frac{1}{2}\\=\frac{-15}{20}-\frac{4}{20}-\frac{10}{20}\\=\frac{-15-4-10}{20}\\=\frac{-29}{20}\)
4. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{5}{-4}\right)\\= \frac{-3}{2}- \frac{10}{2}+\frac{5}{4}\\=\frac{-3}{2}-\frac{5}{1}+\frac{5}{4}\\=\frac{-6}{4}-\frac{20}{4}+\frac{5}{4}\\=\frac{-6-20+5}{4}\\=\frac{-21}{4}\)
5. \(+\left(\frac{5}{-9}\right) -\left(\frac{7}{4}\right) +\left(\frac{12}{10}\right)\\= \frac{-5}{9}- \frac{7}{4}+\frac{12}{10}\\=\frac{-5}{9}-\frac{7}{4}+\frac{6}{5}\\=\frac{-100}{180}-\frac{315}{180}+\frac{216}{180}\\=\frac{-100-315+216}{180}\\=\frac{-199}{180}\)
6. \(-\left(\frac{8}{-5}\right) -\left(\frac{-6}{5}\right) -\left(\frac{6}{-5}\right)\\= \frac{8}{5}+ \frac{6}{5}+\frac{6}{5}\\=\frac{8+6+6}{5}\\=\frac{20}{5}\\=\frac{4}{1}\)
7. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-10}{-3}\right) -\left(\frac{9}{5}\right)\\= \frac{8}{3}+ \frac{10}{3}-\frac{9}{5}\\=\frac{40}{15}+\frac{50}{15}-\frac{27}{15}\\=\frac{40+50-27}{15}\\=\frac{63}{15}\\=\frac{21}{5}\)
8. \(+\left(\frac{-2}{7}\right) +\left(\frac{4}{-10}\right) -\left(\frac{6}{4}\right)\\= \frac{-2}{7}- \frac{4}{10}-\frac{6}{4}\\=\frac{-2}{7}-\frac{2}{5}-\frac{3}{2}\\=\frac{-20}{70}-\frac{28}{70}-\frac{105}{70}\\=\frac{-20-28-105}{70}\\=\frac{-153}{70}\)
9. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-7}{5}\right) -\left(\frac{9}{9}\right)\\= \frac{8}{9}+ \frac{7}{5}-\frac{9}{9}\\=\frac{8}{9}+\frac{7}{5}-\frac{1}{1}\\=\frac{40}{45}+\frac{63}{45}-\frac{45}{45}\\=\frac{40+63-45}{45}\\=\frac{58}{45}\)
10. \(-\left(\frac{6}{-5}\right) -\left(\frac{-2}{8}\right) -\left(\frac{-4}{4}\right)\\= \frac{6}{5}+ \frac{2}{8}+\frac{4}{4}\\=\frac{6}{5}+\frac{1}{4}+\frac{1}{1}\\=\frac{24}{20}+\frac{5}{20}+\frac{20}{20}\\=\frac{24+5+20}{20}\\=\frac{49}{20}\)
11. \(-\left(\frac{2}{7}\right) +\left(\frac{6}{9}\right) +\left(\frac{-12}{-5}\right)\\= \frac{-2}{7}+ \frac{6}{9}+\frac{12}{5}\\=\frac{-2}{7}+\frac{2}{3}+\frac{12}{5}\\=\frac{-30}{105}+\frac{70}{105}+\frac{252}{105}\\=\frac{-30+70+252}{105}\\=\frac{292}{105}\)
12. \(-\left(\frac{7}{-4}\right) -\left(\frac{3}{6}\right) +\left(\frac{8}{-10}\right)\\= \frac{7}{4}- \frac{3}{6}-\frac{8}{10}\\=\frac{7}{4}-\frac{1}{2}-\frac{4}{5}\\=\frac{35}{20}-\frac{10}{20}-\frac{16}{20}\\=\frac{35-10-16}{20}\\=\frac{9}{20}\)