Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{9}\right) +\left(\frac{4}{-7}\right) -\left(\frac{-9}{-4}\right)\\= \frac{-2}{9}- \frac{4}{7}-\frac{9}{4}\\=\frac{-56}{252}-\frac{144}{252}-\frac{567}{252}\\=\frac{-56-144-567}{252}\\=\frac{-767}{252}\)
2. \(+\left(\frac{7}{-8}\right) -\left(\frac{4}{-8}\right) -\left(\frac{-8}{3}\right)\\= \frac{-7}{8}+ \frac{4}{8}+\frac{8}{3}\\=\frac{-7}{8}+\frac{1}{2}+\frac{8}{3}\\=\frac{-21}{24}+\frac{12}{24}+\frac{64}{24}\\=\frac{-21+12+64}{24}\\=\frac{55}{24}\)
3. \(-\left(\frac{3}{-2}\right) +\left(\frac{4}{9}\right) -\left(\frac{2}{-9}\right)\\= \frac{3}{2}+ \frac{4}{9}+\frac{2}{9}\\=\frac{27}{18}+\frac{8}{18}+\frac{4}{18}\\=\frac{27+8+4}{18}\\=\frac{39}{18}\\=\frac{13}{6}\)
4. \(+\left(\frac{7}{8}\right) -\left(\frac{4}{4}\right) +\left(\frac{-9}{8}\right)\\= \frac{7}{8}- \frac{4}{4}-\frac{9}{8}\\=\frac{7}{8}-\frac{1}{1}-\frac{9}{8}\\=\frac{7-1-9}{8}\\=\frac{-3}{8}\)
5. \(-\left(\frac{-9}{-2}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-10}{6}\right)\\= \frac{-9}{2}+ \frac{5}{7}-\frac{10}{6}\\=\frac{-9}{2}+\frac{5}{7}-\frac{5}{3}\\=\frac{-189}{42}+\frac{30}{42}-\frac{70}{42}\\=\frac{-189+30-70}{42}\\=\frac{-229}{42}\)
6. \(+\left(\frac{-2}{-3}\right) +\left(\frac{10}{10}\right) +\left(\frac{-2}{3}\right)\\= \frac{2}{3}+ \frac{10}{10}-\frac{2}{3}\\=\frac{2}{3}+\frac{1}{1}-\frac{2}{3}\\=\frac{2+1-2}{3}\\=\frac{1}{3}\)
7. \(-\left(\frac{8}{7}\right) +\left(\frac{8}{-7}\right) -\left(\frac{2}{11}\right)\\= \frac{-8}{7}- \frac{8}{7}-\frac{2}{11}\\=\frac{-88}{77}-\frac{88}{77}-\frac{14}{77}\\=\frac{-88-88-14}{77}\\=\frac{-190}{77}\)
8. \(-\left(\frac{-9}{-2}\right) +\left(\frac{5}{4}\right) +\left(\frac{-3}{7}\right)\\= \frac{-9}{2}+ \frac{5}{4}-\frac{3}{7}\\=\frac{-126}{28}+\frac{35}{28}-\frac{12}{28}\\=\frac{-126+35-12}{28}\\=\frac{-103}{28}\)
9. \(+\left(\frac{9}{7}\right) +\left(\frac{10}{7}\right) +\left(\frac{9}{7}\right)\\= \frac{9}{7}+ \frac{10}{7}+\frac{9}{7}\\=\frac{9+10+9}{7}\\=\frac{28}{7}\\=\frac{4}{1}\)
10. \(-\left(\frac{-8}{3}\right) +\left(\frac{-7}{2}\right) -\left(\frac{-11}{-10}\right)\\= \frac{8}{3}- \frac{7}{2}-\frac{11}{10}\\=\frac{80}{30}-\frac{105}{30}-\frac{33}{30}\\=\frac{80-105-33}{30}\\=\frac{-58}{30}\\=\frac{-29}{15}\)
11. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-8}{-7}\right) +\left(\frac{-10}{-7}\right)\\= \frac{-3}{2}+ \frac{8}{7}+\frac{10}{7}\\=\frac{-21}{14}+\frac{16}{14}+\frac{20}{14}\\=\frac{-21+16+20}{14}\\=\frac{15}{14}\)
12. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{-12}{-3}\right)\\= \frac{10}{7}- \frac{10}{7}+\frac{12}{3}\\=\frac{10}{7}-\frac{10}{7}+\frac{4}{1}\\=\frac{10-10+4}{7}\\=\frac{4}{7}\)