Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right) -\left(\frac{-4}{2}\right) +\left(\frac{-2}{-6}\right)\\= \frac{10}{7}+ \frac{4}{2}+\frac{2}{6}\\=\frac{10}{7}+\frac{2}{1}+\frac{1}{3}\\=\frac{30}{21}+\frac{42}{21}+\frac{7}{21}\\=\frac{30+42+7}{21}\\=\frac{79}{21}\)
2. \(-\left(\frac{8}{5}\right) +\left(\frac{-4}{7}\right) +\left(\frac{-9}{7}\right)\\= \frac{-8}{5}- \frac{4}{7}-\frac{9}{7}\\=\frac{-56}{35}-\frac{20}{35}-\frac{45}{35}\\=\frac{-56-20-45}{35}\\=\frac{-121}{35}\)
3. \(-\left(\frac{8}{9}\right) +\left(\frac{-5}{-6}\right) -\left(\frac{-8}{-6}\right)\\= \frac{-8}{9}+ \frac{5}{6}-\frac{8}{6}\\=\frac{-8}{9}+\frac{5}{6}-\frac{4}{3}\\=\frac{-16}{18}+\frac{15}{18}-\frac{24}{18}\\=\frac{-16+15-24}{18}\\=\frac{-25}{18}\)
4. \(+\left(\frac{4}{5}\right) +\left(\frac{7}{10}\right) -\left(\frac{-9}{8}\right)\\= \frac{4}{5}+ \frac{7}{10}+\frac{9}{8}\\=\frac{32}{40}+\frac{28}{40}+\frac{45}{40}\\=\frac{32+28+45}{40}\\=\frac{105}{40}\\=\frac{21}{8}\)
5. \(+\left(\frac{-6}{-5}\right) -\left(\frac{6}{7}\right) +\left(\frac{9}{-11}\right)\\= \frac{6}{5}- \frac{6}{7}-\frac{9}{11}\\=\frac{462}{385}-\frac{330}{385}-\frac{315}{385}\\=\frac{462-330-315}{385}\\=\frac{-183}{385}\)
6. \(+\left(\frac{-10}{-3}\right) -\left(\frac{10}{-9}\right) -\left(\frac{7}{5}\right)\\= \frac{10}{3}+ \frac{10}{9}-\frac{7}{5}\\=\frac{150}{45}+\frac{50}{45}-\frac{63}{45}\\=\frac{150+50-63}{45}\\=\frac{137}{45}\)
7. \(-\left(\frac{10}{3}\right) +\left(\frac{10}{3}\right) -\left(\frac{-6}{10}\right)\\= \frac{-10}{3}+ \frac{10}{3}+\frac{6}{10}\\=\frac{-10}{3}+\frac{10}{3}+\frac{3}{5}\\=\frac{-50}{15}+\frac{50}{15}+\frac{9}{15}\\=\frac{-50+50+9}{15}\\=\frac{9}{15}\\=\frac{3}{5}\)
8. \(+\left(\frac{6}{5}\right) +\left(\frac{-3}{-3}\right) -\left(\frac{-12}{-9}\right)\\= \frac{6}{5}+ \frac{3}{3}-\frac{12}{9}\\=\frac{6}{5}+\frac{1}{1}-\frac{4}{3}\\=\frac{18}{15}+\frac{15}{15}-\frac{20}{15}\\=\frac{18+15-20}{15}\\=\frac{13}{15}\)
9. \(-\left(\frac{9}{-5}\right) +\left(\frac{4}{8}\right) -\left(\frac{6}{4}\right)\\= \frac{9}{5}+ \frac{4}{8}-\frac{6}{4}\\=\frac{9}{5}+\frac{1}{2}-\frac{3}{2}\\=\frac{18}{10}+\frac{5}{10}-\frac{15}{10}\\=\frac{18+5-15}{10}\\=\frac{8}{10}\\=\frac{4}{5}\)
10. \(-\left(\frac{-10}{9}\right) -\left(\frac{6}{6}\right) -\left(\frac{-10}{-9}\right)\\= \frac{10}{9}- \frac{6}{6}-\frac{10}{9}\\=\frac{10}{9}-\frac{1}{1}-\frac{10}{9}\\=\frac{10-1-10}{9}\\=\frac{-1}{9}\)
11. \(-\left(\frac{4}{-3}\right) +\left(\frac{-7}{9}\right) -\left(\frac{7}{-9}\right)\\= \frac{4}{3}- \frac{7}{9}+\frac{7}{9}\\=\frac{12}{9}-\frac{7}{9}+\frac{7}{9}\\=\frac{12-7+7}{9}\\=\frac{12}{9}\\=\frac{4}{3}\)
12. \(-\left(\frac{8}{3}\right) +\left(\frac{6}{2}\right) -\left(\frac{-7}{4}\right)\\= \frac{-8}{3}+ \frac{6}{2}+\frac{7}{4}\\=\frac{-8}{3}+\frac{3}{1}+\frac{7}{4}\\=\frac{-32}{12}+\frac{36}{12}+\frac{21}{12}\\=\frac{-32+36+21}{12}\\=\frac{25}{12}\)