Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) +\left(\frac{7}{2}\right) -\left(\frac{4}{12}\right)\\= \frac{6}{5}+ \frac{7}{2}-\frac{4}{12}\\=\frac{6}{5}+\frac{7}{2}-\frac{1}{3}\\=\frac{36}{30}+\frac{105}{30}-\frac{10}{30}\\=\frac{36+105-10}{30}\\=\frac{131}{30}\)
2. \(+\left(\frac{8}{-7}\right) +\left(\frac{4}{-2}\right) -\left(\frac{12}{-9}\right)\\= \frac{-8}{7}- \frac{4}{2}+\frac{12}{9}\\=\frac{-8}{7}-\frac{2}{1}+\frac{4}{3}\\=\frac{-24}{21}-\frac{42}{21}+\frac{28}{21}\\=\frac{-24-42+28}{21}\\=\frac{-38}{21}\)
3. \(+\left(\frac{-8}{3}\right) -\left(\frac{9}{8}\right) -\left(\frac{6}{12}\right)\\= \frac{-8}{3}- \frac{9}{8}-\frac{6}{12}\\=\frac{-8}{3}-\frac{9}{8}-\frac{1}{2}\\=\frac{-64}{24}-\frac{27}{24}-\frac{12}{24}\\=\frac{-64-27-12}{24}\\=\frac{-103}{24}\)
4. \(+\left(\frac{6}{7}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-5}{-11}\right)\\= \frac{6}{7}+ \frac{3}{5}-\frac{5}{11}\\=\frac{330}{385}+\frac{231}{385}-\frac{175}{385}\\=\frac{330+231-175}{385}\\=\frac{386}{385}\)
5. \(-\left(\frac{-2}{3}\right) +\left(\frac{9}{5}\right) -\left(\frac{10}{5}\right)\\= \frac{2}{3}+ \frac{9}{5}-\frac{10}{5}\\=\frac{2}{3}+\frac{9}{5}-\frac{2}{1}\\=\frac{10}{15}+\frac{27}{15}-\frac{30}{15}\\=\frac{10+27-30}{15}\\=\frac{7}{15}\)
6. \(-\left(\frac{-4}{-5}\right) -\left(\frac{-3}{-9}\right) +\left(\frac{7}{-7}\right)\\= \frac{-4}{5}- \frac{3}{9}-\frac{7}{7}\\=\frac{-4}{5}-\frac{1}{3}-\frac{1}{1}\\=\frac{-12}{15}-\frac{5}{15}-\frac{15}{15}\\=\frac{-12-5-15}{15}\\=\frac{-32}{15}\)
7. \(-\left(\frac{8}{9}\right) +\left(\frac{6}{6}\right) +\left(\frac{7}{12}\right)\\= \frac{-8}{9}+ \frac{6}{6}+\frac{7}{12}\\=\frac{-8}{9}+\frac{1}{1}+\frac{7}{12}\\=\frac{-32}{36}+\frac{36}{36}+\frac{21}{36}\\=\frac{-32+36+21}{36}\\=\frac{25}{36}\)
8. \(+\left(\frac{8}{-9}\right) +\left(\frac{9}{10}\right) -\left(\frac{4}{-12}\right)\\= \frac{-8}{9}+ \frac{9}{10}+\frac{4}{12}\\=\frac{-8}{9}+\frac{9}{10}+\frac{1}{3}\\=\frac{-80}{90}+\frac{81}{90}+\frac{30}{90}\\=\frac{-80+81+30}{90}\\=\frac{31}{90}\)
9. \(-\left(\frac{-9}{4}\right) -\left(\frac{-8}{6}\right) +\left(\frac{7}{-11}\right)\\= \frac{9}{4}+ \frac{8}{6}-\frac{7}{11}\\=\frac{9}{4}+\frac{4}{3}-\frac{7}{11}\\=\frac{297}{132}+\frac{176}{132}-\frac{84}{132}\\=\frac{297+176-84}{132}\\=\frac{389}{132}\)
10. \(-\left(\frac{10}{3}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{11}{11}\right)\\= \frac{-10}{3}- \frac{4}{4}+\frac{11}{11}\\=\frac{-10}{3}-\frac{1}{1}+\frac{1}{1}\\=\frac{-10-1+1}{3}\\=\frac{-10}{3}\)
11. \(+\left(\frac{5}{-9}\right) +\left(\frac{-10}{-2}\right) -\left(\frac{-10}{8}\right)\\= \frac{-5}{9}+ \frac{10}{2}+\frac{10}{8}\\=\frac{-5}{9}+\frac{5}{1}+\frac{5}{4}\\=\frac{-20}{36}+\frac{180}{36}+\frac{45}{36}\\=\frac{-20+180+45}{36}\\=\frac{205}{36}\)
12. \(+\left(\frac{10}{-7}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{-5}{12}\right)\\= \frac{-10}{7}+ \frac{8}{2}+\frac{5}{12}\\=\frac{-10}{7}+\frac{4}{1}+\frac{5}{12}\\=\frac{-120}{84}+\frac{336}{84}+\frac{35}{84}\\=\frac{-120+336+35}{84}\\=\frac{251}{84}\)