Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{8}\right) +\left(\frac{4}{10}\right) +\left(\frac{-5}{-4}\right)\\= \frac{3}{8}+ \frac{4}{10}+\frac{5}{4}\\=\frac{3}{8}+\frac{2}{5}+\frac{5}{4}\\=\frac{15}{40}+\frac{16}{40}+\frac{50}{40}\\=\frac{15+16+50}{40}\\=\frac{81}{40}\)
2. \(-\left(\frac{-7}{-2}\right) +\left(\frac{7}{10}\right) -\left(\frac{12}{4}\right)\\= \frac{-7}{2}+ \frac{7}{10}-\frac{12}{4}\\=\frac{-7}{2}+\frac{7}{10}-\frac{3}{1}\\=\frac{-35}{10}+\frac{7}{10}-\frac{30}{10}\\=\frac{-35+7-30}{10}\\=\frac{-58}{10}\\=\frac{-29}{5}\)
3. \(-\left(\frac{10}{7}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{11}{-3}\right)\\= \frac{-10}{7}- \frac{10}{10}+\frac{11}{3}\\=\frac{-10}{7}-\frac{1}{1}+\frac{11}{3}\\=\frac{-30}{21}-\frac{21}{21}+\frac{77}{21}\\=\frac{-30-21+77}{21}\\=\frac{26}{21}\)
4. \(-\left(\frac{5}{7}\right) +\left(\frac{-10}{3}\right) -\left(\frac{7}{5}\right)\\= \frac{-5}{7}- \frac{10}{3}-\frac{7}{5}\\=\frac{-75}{105}-\frac{350}{105}-\frac{147}{105}\\=\frac{-75-350-147}{105}\\=\frac{-572}{105}\)
5. \(+\left(\frac{6}{-5}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-6}{5}+ \frac{6}{10}-\frac{4}{11}\\=\frac{-6}{5}+\frac{3}{5}-\frac{4}{11}\\=\frac{-66}{55}+\frac{33}{55}-\frac{20}{55}\\=\frac{-66+33-20}{55}\\=\frac{-53}{55}\)
6. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-3}{3}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-3}{2}- \frac{3}{3}-\frac{11}{10}\\=\frac{-3}{2}-\frac{1}{1}-\frac{11}{10}\\=\frac{-15}{10}-\frac{10}{10}-\frac{11}{10}\\=\frac{-15-10-11}{10}\\=\frac{-36}{10}\\=\frac{-18}{5}\)
7. \(-\left(\frac{10}{-9}\right) -\left(\frac{6}{-8}\right) +\left(\frac{-8}{-4}\right)\\= \frac{10}{9}+ \frac{6}{8}+\frac{8}{4}\\=\frac{10}{9}+\frac{3}{4}+\frac{2}{1}\\=\frac{40}{36}+\frac{27}{36}+\frac{72}{36}\\=\frac{40+27+72}{36}\\=\frac{139}{36}\)
8. \(+\left(\frac{3}{-2}\right) -\left(\frac{-10}{6}\right) -\left(\frac{12}{7}\right)\\= \frac{-3}{2}+ \frac{10}{6}-\frac{12}{7}\\=\frac{-3}{2}+\frac{5}{3}-\frac{12}{7}\\=\frac{-63}{42}+\frac{70}{42}-\frac{72}{42}\\=\frac{-63+70-72}{42}\\=\frac{-65}{42}\)
9. \(-\left(\frac{4}{-5}\right) -\left(\frac{-4}{10}\right) +\left(\frac{-3}{-4}\right)\\= \frac{4}{5}+ \frac{4}{10}+\frac{3}{4}\\=\frac{4}{5}+\frac{2}{5}+\frac{3}{4}\\=\frac{16}{20}+\frac{8}{20}+\frac{15}{20}\\=\frac{16+8+15}{20}\\=\frac{39}{20}\)
10. \(+\left(\frac{-9}{-8}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{-6}{4}\right)\\= \frac{9}{8}- \frac{6}{7}+\frac{6}{4}\\=\frac{9}{8}-\frac{6}{7}+\frac{3}{2}\\=\frac{63}{56}-\frac{48}{56}+\frac{84}{56}\\=\frac{63-48+84}{56}\\=\frac{99}{56}\)
11. \(-\left(\frac{4}{3}\right) +\left(\frac{3}{6}\right) -\left(\frac{12}{-10}\right)\\= \frac{-4}{3}+ \frac{3}{6}+\frac{12}{10}\\=\frac{-4}{3}+\frac{1}{2}+\frac{6}{5}\\=\frac{-40}{30}+\frac{15}{30}+\frac{36}{30}\\=\frac{-40+15+36}{30}\\=\frac{11}{30}\)
12. \(+\left(\frac{2}{9}\right) +\left(\frac{-7}{3}\right) +\left(\frac{-12}{2}\right)\\= \frac{2}{9}- \frac{7}{3}-\frac{12}{2}\\=\frac{2}{9}-\frac{7}{3}-\frac{6}{1}\\=\frac{2-7-6}{9}\\=\frac{-11}{9}\)