Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-3}\right) -\left(\frac{9}{2}\right) +\left(\frac{11}{8}\right)\\= \frac{-2}{3}- \frac{9}{2}+\frac{11}{8}\\=\frac{-16}{24}-\frac{108}{24}+\frac{33}{24}\\=\frac{-16-108+33}{24}\\=\frac{-91}{24}\)
2. \(+\left(\frac{-3}{7}\right) -\left(\frac{9}{-5}\right) +\left(\frac{11}{-9}\right)\\= \frac{-3}{7}+ \frac{9}{5}-\frac{11}{9}\\=\frac{-135}{315}+\frac{567}{315}-\frac{385}{315}\\=\frac{-135+567-385}{315}\\=\frac{47}{315}\)
3. \(+\left(\frac{9}{7}\right) -\left(\frac{-5}{3}\right) -\left(\frac{2}{9}\right)\\= \frac{9}{7}+ \frac{5}{3}-\frac{2}{9}\\=\frac{81}{63}+\frac{105}{63}-\frac{14}{63}\\=\frac{81+105-14}{63}\\=\frac{172}{63}\)
4. \(+\left(\frac{3}{7}\right) -\left(\frac{7}{2}\right) +\left(\frac{-11}{-5}\right)\\= \frac{3}{7}- \frac{7}{2}+\frac{11}{5}\\=\frac{30}{70}-\frac{245}{70}+\frac{154}{70}\\=\frac{30-245+154}{70}\\=\frac{-61}{70}\)
5. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-6}{10}\right) +\left(\frac{-11}{-2}\right)\\= \frac{3}{2}+ \frac{6}{10}+\frac{11}{2}\\=\frac{3}{2}+\frac{3}{5}+\frac{11}{2}\\=\frac{15}{10}+\frac{6}{10}+\frac{55}{10}\\=\frac{15+6+55}{10}\\=\frac{76}{10}\\=\frac{38}{5}\)
6. \(+\left(\frac{3}{-2}\right) -\left(\frac{9}{8}\right) +\left(\frac{3}{-4}\right)\\= \frac{-3}{2}- \frac{9}{8}-\frac{3}{4}\\=\frac{-12}{8}-\frac{9}{8}-\frac{6}{8}\\=\frac{-12-9-6}{8}\\=\frac{-27}{8}\)
7. \(-\left(\frac{4}{-5}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{-4}{-3}\right)\\= \frac{4}{5}- \frac{5}{3}-\frac{4}{3}\\=\frac{12}{15}-\frac{25}{15}-\frac{20}{15}\\=\frac{12-25-20}{15}\\=\frac{-33}{15}\\=\frac{-11}{5}\)
8. \(+\left(\frac{7}{-2}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-11}{-9}\right)\\= \frac{-7}{2}+ \frac{5}{8}-\frac{11}{9}\\=\frac{-252}{72}+\frac{45}{72}-\frac{88}{72}\\=\frac{-252+45-88}{72}\\=\frac{-295}{72}\)
9. \(+\left(\frac{-9}{-8}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{10}{-6}\right)\\= \frac{9}{8}- \frac{9}{6}-\frac{10}{6}\\=\frac{9}{8}-\frac{3}{2}-\frac{5}{3}\\=\frac{27}{24}-\frac{36}{24}-\frac{40}{24}\\=\frac{27-36-40}{24}\\=\frac{-49}{24}\)
10. \(-\left(\frac{5}{8}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{-8}{-3}\right)\\= \frac{-5}{8}- \frac{9}{9}+\frac{8}{3}\\=\frac{-5}{8}-\frac{1}{1}+\frac{8}{3}\\=\frac{-15}{24}-\frac{24}{24}+\frac{64}{24}\\=\frac{-15-24+64}{24}\\=\frac{25}{24}\)
11. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{4}{4}\right)\\= \frac{9}{2}- \frac{3}{3}+\frac{4}{4}\\=\frac{9}{2}-\frac{1}{1}+\frac{1}{1}\\=\frac{9-1+1}{2}\\=\frac{9}{2}\)
12. \(+\left(\frac{6}{-5}\right) +\left(\frac{-7}{3}\right) -\left(\frac{12}{6}\right)\\= \frac{-6}{5}- \frac{7}{3}-\frac{12}{6}\\=\frac{-6}{5}-\frac{7}{3}-\frac{2}{1}\\=\frac{-18}{15}-\frac{35}{15}-\frac{30}{15}\\=\frac{-18-35-30}{15}\\=\frac{-83}{15}\)