Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{6}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-5}{6}+ \frac{8}{10}-\frac{5}{9}\\=\frac{-5}{6}+\frac{4}{5}-\frac{5}{9}\\=\frac{-75}{90}+\frac{72}{90}-\frac{50}{90}\\=\frac{-75+72-50}{90}\\=\frac{-53}{90}\)
2. \(-\left(\frac{-6}{5}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{8}{6}\right)\\= \frac{6}{5}- \frac{3}{3}-\frac{8}{6}\\=\frac{6}{5}-\frac{1}{1}-\frac{4}{3}\\=\frac{18}{15}-\frac{15}{15}-\frac{20}{15}\\=\frac{18-15-20}{15}\\=\frac{-17}{15}\)
3. \(-\left(\frac{-7}{-8}\right) -\left(\frac{3}{7}\right) +\left(\frac{12}{10}\right)\\= \frac{-7}{8}- \frac{3}{7}+\frac{12}{10}\\=\frac{-7}{8}-\frac{3}{7}+\frac{6}{5}\\=\frac{-245}{280}-\frac{120}{280}+\frac{336}{280}\\=\frac{-245-120+336}{280}\\=\frac{-29}{280}\)
4. \(+\left(\frac{5}{8}\right) -\left(\frac{2}{8}\right) -\left(\frac{9}{-8}\right)\\= \frac{5}{8}- \frac{2}{8}+\frac{9}{8}\\=\frac{5}{8}-\frac{1}{4}+\frac{9}{8}\\=\frac{5-1+9}{8}\\=\frac{13}{8}\)
5. \(-\left(\frac{7}{5}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-8}{-3}\right)\\= \frac{-7}{5}+ \frac{3}{4}+\frac{8}{3}\\=\frac{-84}{60}+\frac{45}{60}+\frac{160}{60}\\=\frac{-84+45+160}{60}\\=\frac{121}{60}\)
6. \(+\left(\frac{-10}{7}\right) -\left(\frac{6}{-6}\right) +\left(\frac{10}{9}\right)\\= \frac{-10}{7}+ \frac{6}{6}+\frac{10}{9}\\=\frac{-10}{7}+\frac{1}{1}+\frac{10}{9}\\=\frac{-90}{63}+\frac{63}{63}+\frac{70}{63}\\=\frac{-90+63+70}{63}\\=\frac{43}{63}\)
7. \(+\left(\frac{3}{-2}\right) -\left(\frac{7}{6}\right) +\left(\frac{-12}{10}\right)\\= \frac{-3}{2}- \frac{7}{6}-\frac{12}{10}\\=\frac{-3}{2}-\frac{7}{6}-\frac{6}{5}\\=\frac{-45}{30}-\frac{35}{30}-\frac{36}{30}\\=\frac{-45-35-36}{30}\\=\frac{-116}{30}\\=\frac{-58}{15}\)
8. \(+\left(\frac{-8}{-9}\right) -\left(\frac{2}{-2}\right) -\left(\frac{10}{8}\right)\\= \frac{8}{9}+ \frac{2}{2}-\frac{10}{8}\\=\frac{8}{9}+\frac{1}{1}-\frac{5}{4}\\=\frac{32}{36}+\frac{36}{36}-\frac{45}{36}\\=\frac{32+36-45}{36}\\=\frac{23}{36}\)
9. \(+\left(\frac{-4}{7}\right) -\left(\frac{-8}{4}\right) +\left(\frac{5}{11}\right)\\= \frac{-4}{7}+ \frac{8}{4}+\frac{5}{11}\\=\frac{-4}{7}+\frac{2}{1}+\frac{5}{11}\\=\frac{-44}{77}+\frac{154}{77}+\frac{35}{77}\\=\frac{-44+154+35}{77}\\=\frac{145}{77}\)
10. \(+\left(\frac{9}{4}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{-4}{12}\right)\\= \frac{9}{4}- \frac{3}{5}-\frac{4}{12}\\=\frac{9}{4}-\frac{3}{5}-\frac{1}{3}\\=\frac{135}{60}-\frac{36}{60}-\frac{20}{60}\\=\frac{135-36-20}{60}\\=\frac{79}{60}\)
11. \(-\left(\frac{2}{7}\right) +\left(\frac{-3}{-2}\right) +\left(\frac{-3}{9}\right)\\= \frac{-2}{7}+ \frac{3}{2}-\frac{3}{9}\\=\frac{-2}{7}+\frac{3}{2}-\frac{1}{3}\\=\frac{-12}{42}+\frac{63}{42}-\frac{14}{42}\\=\frac{-12+63-14}{42}\\=\frac{37}{42}\)
12. \(-\left(\frac{9}{5}\right) -\left(\frac{10}{3}\right) +\left(\frac{10}{-5}\right)\\= \frac{-9}{5}- \frac{10}{3}-\frac{10}{5}\\=\frac{-9}{5}-\frac{10}{3}-\frac{2}{1}\\=\frac{-27}{15}-\frac{50}{15}-\frac{30}{15}\\=\frac{-27-50-30}{15}\\=\frac{-107}{15}\)