Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{7}\right) -\left(\frac{-2}{10}\right) -\left(\frac{-5}{-10}\right)\\= \frac{9}{7}+ \frac{2}{10}-\frac{5}{10}\\=\frac{9}{7}+\frac{1}{5}-\frac{1}{2}\\=\frac{90}{70}+\frac{14}{70}-\frac{35}{70}\\=\frac{90+14-35}{70}\\=\frac{69}{70}\)
2. \(-\left(\frac{2}{5}\right) +\left(\frac{5}{-10}\right) +\left(\frac{-8}{4}\right)\\= \frac{-2}{5}- \frac{5}{10}-\frac{8}{4}\\=\frac{-2}{5}-\frac{1}{2}-\frac{2}{1}\\=\frac{-4}{10}-\frac{5}{10}-\frac{20}{10}\\=\frac{-4-5-20}{10}\\=\frac{-29}{10}\)
3. \(-\left(\frac{-4}{-7}\right) +\left(\frac{-9}{8}\right) +\left(\frac{12}{-12}\right)\\= \frac{-4}{7}- \frac{9}{8}-\frac{12}{12}\\=\frac{-4}{7}-\frac{9}{8}-\frac{1}{1}\\=\frac{-32}{56}-\frac{63}{56}-\frac{56}{56}\\=\frac{-32-63-56}{56}\\=\frac{-151}{56}\)
4. \(-\left(\frac{-4}{3}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{9}{-5}\right)\\= \frac{4}{3}+ \frac{3}{9}+\frac{9}{5}\\=\frac{4}{3}+\frac{1}{3}+\frac{9}{5}\\=\frac{20}{15}+\frac{5}{15}+\frac{27}{15}\\=\frac{20+5+27}{15}\\=\frac{52}{15}\)
5. \(-\left(\frac{8}{7}\right) -\left(\frac{3}{-6}\right) -\left(\frac{-8}{-11}\right)\\= \frac{-8}{7}+ \frac{3}{6}-\frac{8}{11}\\=\frac{-8}{7}+\frac{1}{2}-\frac{8}{11}\\=\frac{-176}{154}+\frac{77}{154}-\frac{112}{154}\\=\frac{-176+77-112}{154}\\=\frac{-211}{154}\)
6. \(+\left(\frac{-9}{7}\right) -\left(\frac{4}{7}\right) -\left(\frac{12}{-8}\right)\\= \frac{-9}{7}- \frac{4}{7}+\frac{12}{8}\\=\frac{-9}{7}-\frac{4}{7}+\frac{3}{2}\\=\frac{-18}{14}-\frac{8}{14}+\frac{21}{14}\\=\frac{-18-8+21}{14}\\=\frac{-5}{14}\)
7. \(+\left(\frac{-4}{3}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{-7}{3}\right)\\= \frac{-4}{3}- \frac{2}{6}+\frac{7}{3}\\=\frac{-4}{3}-\frac{1}{3}+\frac{7}{3}\\=\frac{-4-1+7}{3}\\=\frac{2}{3}\)
8. \(+\left(\frac{8}{-7}\right) +\left(\frac{-2}{9}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-8}{7}- \frac{2}{9}+\frac{8}{9}\\=\frac{-72}{63}-\frac{14}{63}+\frac{56}{63}\\=\frac{-72-14+56}{63}\\=\frac{-30}{63}\\=\frac{-10}{21}\)
9. \(+\left(\frac{4}{7}\right) -\left(\frac{-10}{5}\right) -\left(\frac{10}{3}\right)\\= \frac{4}{7}+ \frac{10}{5}-\frac{10}{3}\\=\frac{4}{7}+\frac{2}{1}-\frac{10}{3}\\=\frac{12}{21}+\frac{42}{21}-\frac{70}{21}\\=\frac{12+42-70}{21}\\=\frac{-16}{21}\)
10. \(-\left(\frac{-8}{7}\right) -\left(\frac{-5}{7}\right) -\left(\frac{-4}{5}\right)\\= \frac{8}{7}+ \frac{5}{7}+\frac{4}{5}\\=\frac{40}{35}+\frac{25}{35}+\frac{28}{35}\\=\frac{40+25+28}{35}\\=\frac{93}{35}\)
11. \(-\left(\frac{7}{4}\right) -\left(\frac{-4}{10}\right) +\left(\frac{9}{5}\right)\\= \frac{-7}{4}+ \frac{4}{10}+\frac{9}{5}\\=\frac{-7}{4}+\frac{2}{5}+\frac{9}{5}\\=\frac{-35}{20}+\frac{8}{20}+\frac{36}{20}\\=\frac{-35+8+36}{20}\\=\frac{9}{20}\)
12. \(+\left(\frac{10}{3}\right) -\left(\frac{6}{4}\right) +\left(\frac{7}{-7}\right)\\= \frac{10}{3}- \frac{6}{4}-\frac{7}{7}\\=\frac{10}{3}-\frac{3}{2}-\frac{1}{1}\\=\frac{20}{6}-\frac{9}{6}-\frac{6}{6}\\=\frac{20-9-6}{6}\\=\frac{5}{6}\)