Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{4}\right) +\left(\frac{3}{8}\right) +\left(\frac{-2}{11}\right)\\= \frac{9}{4}+ \frac{3}{8}-\frac{2}{11}\\=\frac{198}{88}+\frac{33}{88}-\frac{16}{88}\\=\frac{198+33-16}{88}\\=\frac{215}{88}\)
2. \(+\left(\frac{8}{-7}\right) +\left(\frac{-8}{-3}\right) -\left(\frac{2}{7}\right)\\= \frac{-8}{7}+ \frac{8}{3}-\frac{2}{7}\\=\frac{-24}{21}+\frac{56}{21}-\frac{6}{21}\\=\frac{-24+56-6}{21}\\=\frac{26}{21}\)
3. \(-\left(\frac{5}{-6}\right) -\left(\frac{9}{10}\right) -\left(\frac{7}{10}\right)\\= \frac{5}{6}- \frac{9}{10}-\frac{7}{10}\\=\frac{25}{30}-\frac{27}{30}-\frac{21}{30}\\=\frac{25-27-21}{30}\\=\frac{-23}{30}\)
4. \(-\left(\frac{10}{-7}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{5}{-11}\right)\\= \frac{10}{7}+ \frac{6}{9}-\frac{5}{11}\\=\frac{10}{7}+\frac{2}{3}-\frac{5}{11}\\=\frac{330}{231}+\frac{154}{231}-\frac{105}{231}\\=\frac{330+154-105}{231}\\=\frac{379}{231}\)
5. \(+\left(\frac{10}{7}\right) -\left(\frac{4}{6}\right) -\left(\frac{6}{8}\right)\\= \frac{10}{7}- \frac{4}{6}-\frac{6}{8}\\=\frac{10}{7}-\frac{2}{3}-\frac{3}{4}\\=\frac{120}{84}-\frac{56}{84}-\frac{63}{84}\\=\frac{120-56-63}{84}\\=\frac{1}{84}\)
6. \(+\left(\frac{-7}{8}\right) +\left(\frac{6}{-4}\right) -\left(\frac{-3}{10}\right)\\= \frac{-7}{8}- \frac{6}{4}+\frac{3}{10}\\=\frac{-7}{8}-\frac{3}{2}+\frac{3}{10}\\=\frac{-35}{40}-\frac{60}{40}+\frac{12}{40}\\=\frac{-35-60+12}{40}\\=\frac{-83}{40}\)
7. \(+\left(\frac{4}{3}\right) -\left(\frac{8}{2}\right) +\left(\frac{-4}{5}\right)\\= \frac{4}{3}- \frac{8}{2}-\frac{4}{5}\\=\frac{4}{3}-\frac{4}{1}-\frac{4}{5}\\=\frac{20}{15}-\frac{60}{15}-\frac{12}{15}\\=\frac{20-60-12}{15}\\=\frac{-52}{15}\)
8. \(+\left(\frac{6}{7}\right) +\left(\frac{7}{3}\right) +\left(\frac{11}{2}\right)\\= \frac{6}{7}+ \frac{7}{3}+\frac{11}{2}\\=\frac{36}{42}+\frac{98}{42}+\frac{231}{42}\\=\frac{36+98+231}{42}\\=\frac{365}{42}\)
9. \(+\left(\frac{10}{9}\right) +\left(\frac{-7}{4}\right) -\left(\frac{-9}{-6}\right)\\= \frac{10}{9}- \frac{7}{4}-\frac{9}{6}\\=\frac{10}{9}-\frac{7}{4}-\frac{3}{2}\\=\frac{40}{36}-\frac{63}{36}-\frac{54}{36}\\=\frac{40-63-54}{36}\\=\frac{-77}{36}\)
10. \(-\left(\frac{7}{-2}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{-6}{-4}\right)\\= \frac{7}{2}- \frac{4}{5}+\frac{6}{4}\\=\frac{7}{2}-\frac{4}{5}+\frac{3}{2}\\=\frac{35}{10}-\frac{8}{10}+\frac{15}{10}\\=\frac{35-8+15}{10}\\=\frac{42}{10}\\=\frac{21}{5}\)
11. \(+\left(\frac{-7}{6}\right) +\left(\frac{-6}{10}\right) -\left(\frac{-3}{9}\right)\\= \frac{-7}{6}- \frac{6}{10}+\frac{3}{9}\\=\frac{-7}{6}-\frac{3}{5}+\frac{1}{3}\\=\frac{-35}{30}-\frac{18}{30}+\frac{10}{30}\\=\frac{-35-18+10}{30}\\=\frac{-43}{30}\)
12. \(+\left(\frac{-5}{8}\right) -\left(\frac{8}{7}\right) -\left(\frac{-12}{9}\right)\\= \frac{-5}{8}- \frac{8}{7}+\frac{12}{9}\\=\frac{-5}{8}-\frac{8}{7}+\frac{4}{3}\\=\frac{-105}{168}-\frac{192}{168}+\frac{224}{168}\\=\frac{-105-192+224}{168}\\=\frac{-73}{168}\)