Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-5}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{-3}{-6}\right)\\= \frac{-2}{5}- \frac{6}{3}+\frac{3}{6}\\=\frac{-2}{5}-\frac{2}{1}+\frac{1}{2}\\=\frac{-4}{10}-\frac{20}{10}+\frac{5}{10}\\=\frac{-4-20+5}{10}\\=\frac{-19}{10}\)
2. \(+\left(\frac{5}{-9}\right) -\left(\frac{-3}{5}\right) +\left(\frac{2}{-10}\right)\\= \frac{-5}{9}+ \frac{3}{5}-\frac{2}{10}\\=\frac{-5}{9}+\frac{3}{5}-\frac{1}{5}\\=\frac{-25}{45}+\frac{27}{45}-\frac{9}{45}\\=\frac{-25+27-9}{45}\\=\frac{-7}{45}\)
3. \(-\left(\frac{4}{5}\right) +\left(\frac{-7}{9}\right) -\left(\frac{-7}{11}\right)\\= \frac{-4}{5}- \frac{7}{9}+\frac{7}{11}\\=\frac{-396}{495}-\frac{385}{495}+\frac{315}{495}\\=\frac{-396-385+315}{495}\\=\frac{-466}{495}\)
4. \(+\left(\frac{-5}{4}\right) -\left(\frac{4}{-9}\right) -\left(\frac{-7}{4}\right)\\= \frac{-5}{4}+ \frac{4}{9}+\frac{7}{4}\\=\frac{-45}{36}+\frac{16}{36}+\frac{63}{36}\\=\frac{-45+16+63}{36}\\=\frac{34}{36}\\=\frac{17}{18}\)
5. \(-\left(\frac{-8}{9}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{12}{4}\right)\\= \frac{8}{9}- \frac{2}{4}+\frac{12}{4}\\=\frac{8}{9}-\frac{1}{2}+\frac{3}{1}\\=\frac{16}{18}-\frac{9}{18}+\frac{54}{18}\\=\frac{16-9+54}{18}\\=\frac{61}{18}\)
6. \(-\left(\frac{4}{-7}\right) -\left(\frac{-2}{9}\right) -\left(\frac{-2}{-4}\right)\\= \frac{4}{7}+ \frac{2}{9}-\frac{2}{4}\\=\frac{4}{7}+\frac{2}{9}-\frac{1}{2}\\=\frac{72}{126}+\frac{28}{126}-\frac{63}{126}\\=\frac{72+28-63}{126}\\=\frac{37}{126}\)
7. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{12}{7}\right)\\= \frac{2}{9}- \frac{3}{10}+\frac{12}{7}\\=\frac{140}{630}-\frac{189}{630}+\frac{1080}{630}\\=\frac{140-189+1080}{630}\\=\frac{1031}{630}\)
8. \(+\left(\frac{-4}{7}\right) +\left(\frac{10}{-7}\right) -\left(\frac{10}{2}\right)\\= \frac{-4}{7}- \frac{10}{7}-\frac{10}{2}\\=\frac{-4}{7}-\frac{10}{7}-\frac{5}{1}\\=\frac{-4-10-5}{7}\\=\frac{-19}{7}\)
9. \(+\left(\frac{7}{9}\right) -\left(\frac{-9}{-5}\right) -\left(\frac{-12}{7}\right)\\= \frac{7}{9}- \frac{9}{5}+\frac{12}{7}\\=\frac{245}{315}-\frac{567}{315}+\frac{540}{315}\\=\frac{245-567+540}{315}\\=\frac{218}{315}\)
10. \(-\left(\frac{5}{3}\right) +\left(\frac{2}{-6}\right) +\left(\frac{-7}{-4}\right)\\= \frac{-5}{3}- \frac{2}{6}+\frac{7}{4}\\=\frac{-5}{3}-\frac{1}{3}+\frac{7}{4}\\=\frac{-20}{12}-\frac{4}{12}+\frac{21}{12}\\=\frac{-20-4+21}{12}\\=\frac{-3}{12}\\=\frac{-1}{4}\)
11. \(-\left(\frac{8}{-7}\right) -\left(\frac{10}{-6}\right) +\left(\frac{9}{-5}\right)\\= \frac{8}{7}+ \frac{10}{6}-\frac{9}{5}\\=\frac{8}{7}+\frac{5}{3}-\frac{9}{5}\\=\frac{120}{105}+\frac{175}{105}-\frac{189}{105}\\=\frac{120+175-189}{105}\\=\frac{106}{105}\)
12. \(+\left(\frac{9}{7}\right) -\left(\frac{-4}{6}\right) -\left(\frac{10}{11}\right)\\= \frac{9}{7}+ \frac{4}{6}-\frac{10}{11}\\=\frac{9}{7}+\frac{2}{3}-\frac{10}{11}\\=\frac{297}{231}+\frac{154}{231}-\frac{210}{231}\\=\frac{297+154-210}{231}\\=\frac{241}{231}\)