Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{8}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{-2}{-9}\right)\\= \frac{3}{8}- \frac{2}{4}+\frac{2}{9}\\=\frac{3}{8}-\frac{1}{2}+\frac{2}{9}\\=\frac{27}{72}-\frac{36}{72}+\frac{16}{72}\\=\frac{27-36+16}{72}\\=\frac{7}{72}\)
2. \(+\left(\frac{-6}{7}\right) +\left(\frac{3}{-8}\right) -\left(\frac{-9}{7}\right)\\= \frac{-6}{7}- \frac{3}{8}+\frac{9}{7}\\=\frac{-48}{56}-\frac{21}{56}+\frac{72}{56}\\=\frac{-48-21+72}{56}\\=\frac{3}{56}\)
3. \(-\left(\frac{-7}{9}\right) +\left(\frac{3}{5}\right) -\left(\frac{12}{12}\right)\\= \frac{7}{9}+ \frac{3}{5}-\frac{12}{12}\\=\frac{7}{9}+\frac{3}{5}-\frac{1}{1}\\=\frac{35}{45}+\frac{27}{45}-\frac{45}{45}\\=\frac{35+27-45}{45}\\=\frac{17}{45}\)
4. \(-\left(\frac{10}{-7}\right) -\left(\frac{-4}{8}\right) -\left(\frac{8}{-5}\right)\\= \frac{10}{7}+ \frac{4}{8}+\frac{8}{5}\\=\frac{10}{7}+\frac{1}{2}+\frac{8}{5}\\=\frac{100}{70}+\frac{35}{70}+\frac{112}{70}\\=\frac{100+35+112}{70}\\=\frac{247}{70}\)
5. \(+\left(\frac{-5}{-9}\right) -\left(\frac{-3}{-4}\right) +\left(\frac{4}{9}\right)\\= \frac{5}{9}- \frac{3}{4}+\frac{4}{9}\\=\frac{20}{36}-\frac{27}{36}+\frac{16}{36}\\=\frac{20-27+16}{36}\\=\frac{9}{36}\\=\frac{1}{4}\)
6. \(+\left(\frac{-2}{7}\right) +\left(\frac{-7}{5}\right) +\left(\frac{-6}{6}\right)\\= \frac{-2}{7}- \frac{7}{5}-\frac{6}{6}\\=\frac{-2}{7}-\frac{7}{5}-\frac{1}{1}\\=\frac{-10}{35}-\frac{49}{35}-\frac{35}{35}\\=\frac{-10-49-35}{35}\\=\frac{-94}{35}\)
7. \(-\left(\frac{-7}{-6}\right) -\left(\frac{-8}{-8}\right) +\left(\frac{-7}{-4}\right)\\= \frac{-7}{6}- \frac{8}{8}+\frac{7}{4}\\=\frac{-7}{6}-\frac{1}{1}+\frac{7}{4}\\=\frac{-14}{12}-\frac{12}{12}+\frac{21}{12}\\=\frac{-14-12+21}{12}\\=\frac{-5}{12}\)
8. \(-\left(\frac{7}{-9}\right) -\left(\frac{5}{-5}\right) +\left(\frac{-12}{-10}\right)\\= \frac{7}{9}+ \frac{5}{5}+\frac{12}{10}\\=\frac{7}{9}+\frac{1}{1}+\frac{6}{5}\\=\frac{35}{45}+\frac{45}{45}+\frac{54}{45}\\=\frac{35+45+54}{45}\\=\frac{134}{45}\)
9. \(+\left(\frac{2}{7}\right) -\left(\frac{7}{8}\right) +\left(\frac{6}{10}\right)\\= \frac{2}{7}- \frac{7}{8}+\frac{6}{10}\\=\frac{2}{7}-\frac{7}{8}+\frac{3}{5}\\=\frac{80}{280}-\frac{245}{280}+\frac{168}{280}\\=\frac{80-245+168}{280}\\=\frac{3}{280}\)
10. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-6}{10}\right) +\left(\frac{12}{-6}\right)\\= \frac{4}{3}+ \frac{6}{10}-\frac{12}{6}\\=\frac{4}{3}+\frac{3}{5}-\frac{2}{1}\\=\frac{20}{15}+\frac{9}{15}-\frac{30}{15}\\=\frac{20+9-30}{15}\\=\frac{-1}{15}\)
11. \(-\left(\frac{-8}{5}\right) -\left(\frac{9}{-6}\right) -\left(\frac{7}{3}\right)\\= \frac{8}{5}+ \frac{9}{6}-\frac{7}{3}\\=\frac{8}{5}+\frac{3}{2}-\frac{7}{3}\\=\frac{48}{30}+\frac{45}{30}-\frac{70}{30}\\=\frac{48+45-70}{30}\\=\frac{23}{30}\)
12. \(-\left(\frac{9}{2}\right) +\left(\frac{-2}{2}\right) +\left(\frac{-6}{-4}\right)\\= \frac{-9}{2}- \frac{2}{2}+\frac{6}{4}\\=\frac{-9}{2}-\frac{1}{1}+\frac{3}{2}\\=\frac{-9-1+3}{2}\\=\frac{-7}{2}\)