Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{5}\right) -\left(\frac{-8}{-2}\right) +\left(\frac{12}{-4}\right)\\= \frac{7}{5}- \frac{8}{2}-\frac{12}{4}\\=\frac{7}{5}-\frac{4}{1}-\frac{3}{1}\\=\frac{7-4-3}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)
2. \(+\left(\frac{7}{6}\right) +\left(\frac{-3}{6}\right) +\left(\frac{-2}{5}\right)\\= \frac{7}{6}- \frac{3}{6}-\frac{2}{5}\\=\frac{7}{6}-\frac{1}{2}-\frac{2}{5}\\=\frac{35}{30}-\frac{15}{30}-\frac{12}{30}\\=\frac{35-15-12}{30}\\=\frac{8}{30}\\=\frac{4}{15}\)
3. \(+\left(\frac{7}{-2}\right) -\left(\frac{6}{4}\right) -\left(\frac{-10}{-9}\right)\\= \frac{-7}{2}- \frac{6}{4}-\frac{10}{9}\\=\frac{-7}{2}-\frac{3}{2}-\frac{10}{9}\\=\frac{-63}{18}-\frac{27}{18}-\frac{20}{18}\\=\frac{-63-27-20}{18}\\=\frac{-110}{18}\\=\frac{-55}{9}\)
4. \(-\left(\frac{8}{-5}\right) -\left(\frac{-10}{-3}\right) +\left(\frac{8}{4}\right)\\= \frac{8}{5}- \frac{10}{3}+\frac{8}{4}\\=\frac{8}{5}-\frac{10}{3}+\frac{2}{1}\\=\frac{24}{15}-\frac{50}{15}+\frac{30}{15}\\=\frac{24-50+30}{15}\\=\frac{4}{15}\)
5. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-3}{2}\right) +\left(\frac{9}{-8}\right)\\= \frac{10}{9}+ \frac{3}{2}-\frac{9}{8}\\=\frac{80}{72}+\frac{108}{72}-\frac{81}{72}\\=\frac{80+108-81}{72}\\=\frac{107}{72}\)
6. \(+\left(\frac{-6}{-7}\right) -\left(\frac{10}{-4}\right) -\left(\frac{-11}{6}\right)\\= \frac{6}{7}+ \frac{10}{4}+\frac{11}{6}\\=\frac{6}{7}+\frac{5}{2}+\frac{11}{6}\\=\frac{36}{42}+\frac{105}{42}+\frac{77}{42}\\=\frac{36+105+77}{42}\\=\frac{218}{42}\\=\frac{109}{21}\)
7. \(-\left(\frac{3}{-7}\right) +\left(\frac{9}{8}\right) +\left(\frac{9}{-11}\right)\\= \frac{3}{7}+ \frac{9}{8}-\frac{9}{11}\\=\frac{264}{616}+\frac{693}{616}-\frac{504}{616}\\=\frac{264+693-504}{616}\\=\frac{453}{616}\)
8. \(-\left(\frac{3}{-2}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{4}{5}\right)\\= \frac{3}{2}- \frac{5}{6}+\frac{4}{5}\\=\frac{45}{30}-\frac{25}{30}+\frac{24}{30}\\=\frac{45-25+24}{30}\\=\frac{44}{30}\\=\frac{22}{15}\)
9. \(-\left(\frac{10}{-3}\right) +\left(\frac{3}{-4}\right) -\left(\frac{6}{8}\right)\\= \frac{10}{3}- \frac{3}{4}-\frac{6}{8}\\=\frac{10}{3}-\frac{3}{4}-\frac{3}{4}\\=\frac{40}{12}-\frac{9}{12}-\frac{9}{12}\\=\frac{40-9-9}{12}\\=\frac{22}{12}\\=\frac{11}{6}\)
10. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-10}{2}\right)\\= \frac{-10}{3}+ \frac{5}{7}-\frac{10}{2}\\=\frac{-10}{3}+\frac{5}{7}-\frac{5}{1}\\=\frac{-70}{21}+\frac{15}{21}-\frac{105}{21}\\=\frac{-70+15-105}{21}\\=\frac{-160}{21}\)
11. \(-\left(\frac{7}{-3}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-9}{10}\right)\\= \frac{7}{3}- \frac{8}{8}+\frac{9}{10}\\=\frac{7}{3}-\frac{1}{1}+\frac{9}{10}\\=\frac{70}{30}-\frac{30}{30}+\frac{27}{30}\\=\frac{70-30+27}{30}\\=\frac{67}{30}\)
12. \(-\left(\frac{5}{9}\right) +\left(\frac{2}{7}\right) -\left(\frac{11}{6}\right)\\= \frac{-5}{9}+ \frac{2}{7}-\frac{11}{6}\\=\frac{-70}{126}+\frac{36}{126}-\frac{231}{126}\\=\frac{-70+36-231}{126}\\=\frac{-265}{126}\)