Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) +\left(\frac{-7}{3}\right) +\left(\frac{-8}{4}\right)\\= \frac{-6}{5}- \frac{7}{3}-\frac{8}{4}\\=\frac{-6}{5}-\frac{7}{3}-\frac{2}{1}\\=\frac{-18}{15}-\frac{35}{15}-\frac{30}{15}\\=\frac{-18-35-30}{15}\\=\frac{-83}{15}\)
2. \(-\left(\frac{10}{-7}\right) +\left(\frac{9}{-10}\right) +\left(\frac{5}{6}\right)\\= \frac{10}{7}- \frac{9}{10}+\frac{5}{6}\\=\frac{300}{210}-\frac{189}{210}+\frac{175}{210}\\=\frac{300-189+175}{210}\\=\frac{286}{210}\\=\frac{143}{105}\)
3. \(+\left(\frac{6}{5}\right) +\left(\frac{-2}{10}\right) +\left(\frac{3}{-10}\right)\\= \frac{6}{5}- \frac{2}{10}-\frac{3}{10}\\=\frac{6}{5}-\frac{1}{5}-\frac{3}{10}\\=\frac{12}{10}-\frac{2}{10}-\frac{3}{10}\\=\frac{12-2-3}{10}\\=\frac{7}{10}\)
4. \(-\left(\frac{-2}{-9}\right) +\left(\frac{5}{-8}\right) -\left(\frac{10}{9}\right)\\= \frac{-2}{9}- \frac{5}{8}-\frac{10}{9}\\=\frac{-16}{72}-\frac{45}{72}-\frac{80}{72}\\=\frac{-16-45-80}{72}\\=\frac{-141}{72}\\=\frac{-47}{24}\)
5. \(+\left(\frac{-8}{-5}\right) +\left(\frac{4}{3}\right) -\left(\frac{4}{-10}\right)\\= \frac{8}{5}+ \frac{4}{3}+\frac{4}{10}\\=\frac{8}{5}+\frac{4}{3}+\frac{2}{5}\\=\frac{24}{15}+\frac{20}{15}+\frac{6}{15}\\=\frac{24+20+6}{15}\\=\frac{50}{15}\\=\frac{10}{3}\)
6. \(-\left(\frac{7}{-4}\right) +\left(\frac{7}{-8}\right) +\left(\frac{3}{9}\right)\\= \frac{7}{4}- \frac{7}{8}+\frac{3}{9}\\=\frac{7}{4}-\frac{7}{8}+\frac{1}{3}\\=\frac{42}{24}-\frac{21}{24}+\frac{8}{24}\\=\frac{42-21+8}{24}\\=\frac{29}{24}\)
7. \(-\left(\frac{-6}{5}\right) +\left(\frac{-5}{6}\right) -\left(\frac{-12}{-7}\right)\\= \frac{6}{5}- \frac{5}{6}-\frac{12}{7}\\=\frac{252}{210}-\frac{175}{210}-\frac{360}{210}\\=\frac{252-175-360}{210}\\=\frac{-283}{210}\)
8. \(+\left(\frac{-2}{-5}\right) -\left(\frac{7}{3}\right) -\left(\frac{8}{-12}\right)\\= \frac{2}{5}- \frac{7}{3}+\frac{8}{12}\\=\frac{2}{5}-\frac{7}{3}+\frac{2}{3}\\=\frac{6}{15}-\frac{35}{15}+\frac{10}{15}\\=\frac{6-35+10}{15}\\=\frac{-19}{15}\)
9. \(+\left(\frac{6}{7}\right) -\left(\frac{7}{2}\right) +\left(\frac{-7}{3}\right)\\= \frac{6}{7}- \frac{7}{2}-\frac{7}{3}\\=\frac{36}{42}-\frac{147}{42}-\frac{98}{42}\\=\frac{36-147-98}{42}\\=\frac{-209}{42}\)
10. \(+\left(\frac{8}{3}\right) -\left(\frac{2}{2}\right) +\left(\frac{10}{7}\right)\\= \frac{8}{3}- \frac{2}{2}+\frac{10}{7}\\=\frac{8}{3}-\frac{1}{1}+\frac{10}{7}\\=\frac{56}{21}-\frac{21}{21}+\frac{30}{21}\\=\frac{56-21+30}{21}\\=\frac{65}{21}\)
11. \(+\left(\frac{-9}{-2}\right) +\left(\frac{7}{-8}\right) -\left(\frac{-4}{6}\right)\\= \frac{9}{2}- \frac{7}{8}+\frac{4}{6}\\=\frac{9}{2}-\frac{7}{8}+\frac{2}{3}\\=\frac{108}{24}-\frac{21}{24}+\frac{16}{24}\\=\frac{108-21+16}{24}\\=\frac{103}{24}\)
12. \(-\left(\frac{-8}{-3}\right) -\left(\frac{10}{-3}\right) +\left(\frac{-10}{-7}\right)\\= \frac{-8}{3}+ \frac{10}{3}+\frac{10}{7}\\=\frac{-56}{21}+\frac{70}{21}+\frac{30}{21}\\=\frac{-56+70+30}{21}\\=\frac{44}{21}\)