Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{-5}\right) +\left(\frac{2}{-10}\right) -\left(\frac{11}{4}\right)\\= \frac{-9}{5}- \frac{2}{10}-\frac{11}{4}\\=\frac{-9}{5}-\frac{1}{5}-\frac{11}{4}\\=\frac{-36}{20}-\frac{4}{20}-\frac{55}{20}\\=\frac{-36-4-55}{20}\\=\frac{-95}{20}\\=\frac{-19}{4}\)
2. \(+\left(\frac{8}{3}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{-6}{-9}\right)\\= \frac{8}{3}+ \frac{2}{8}+\frac{6}{9}\\=\frac{8}{3}+\frac{1}{4}+\frac{2}{3}\\=\frac{32}{12}+\frac{3}{12}+\frac{8}{12}\\=\frac{32+3+8}{12}\\=\frac{43}{12}\)
3. \(+\left(\frac{9}{-5}\right) +\left(\frac{7}{-2}\right) -\left(\frac{3}{-5}\right)\\= \frac{-9}{5}- \frac{7}{2}+\frac{3}{5}\\=\frac{-18}{10}-\frac{35}{10}+\frac{6}{10}\\=\frac{-18-35+6}{10}\\=\frac{-47}{10}\)
4. \(-\left(\frac{3}{-2}\right) -\left(\frac{-8}{-2}\right) +\left(\frac{-9}{-7}\right)\\= \frac{3}{2}- \frac{8}{2}+\frac{9}{7}\\=\frac{3}{2}-\frac{4}{1}+\frac{9}{7}\\=\frac{21}{14}-\frac{56}{14}+\frac{18}{14}\\=\frac{21-56+18}{14}\\=\frac{-17}{14}\)
5. \(+\left(\frac{6}{5}\right) -\left(\frac{-4}{5}\right) +\left(\frac{3}{-12}\right)\\= \frac{6}{5}+ \frac{4}{5}-\frac{3}{12}\\=\frac{6}{5}+\frac{4}{5}-\frac{1}{4}\\=\frac{24}{20}+\frac{16}{20}-\frac{5}{20}\\=\frac{24+16-5}{20}\\=\frac{35}{20}\\=\frac{7}{4}\)
6. \(+\left(\frac{-3}{2}\right) +\left(\frac{-5}{8}\right) -\left(\frac{7}{3}\right)\\= \frac{-3}{2}- \frac{5}{8}-\frac{7}{3}\\=\frac{-36}{24}-\frac{15}{24}-\frac{56}{24}\\=\frac{-36-15-56}{24}\\=\frac{-107}{24}\)
7. \(-\left(\frac{10}{-9}\right) -\left(\frac{-10}{4}\right) -\left(\frac{6}{9}\right)\\= \frac{10}{9}+ \frac{10}{4}-\frac{6}{9}\\=\frac{10}{9}+\frac{5}{2}-\frac{2}{3}\\=\frac{20}{18}+\frac{45}{18}-\frac{12}{18}\\=\frac{20+45-12}{18}\\=\frac{53}{18}\)
8. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-3}{5}\right) -\left(\frac{8}{8}\right)\\= \frac{-6}{5}- \frac{3}{5}-\frac{8}{8}\\=\frac{-6}{5}-\frac{3}{5}-\frac{1}{1}\\=\frac{-6-3-1}{5}\\=\frac{-10}{5}\\=\frac{-2}{1}\)
9. \(+\left(\frac{10}{9}\right) -\left(\frac{5}{6}\right) -\left(\frac{-2}{-5}\right)\\= \frac{10}{9}- \frac{5}{6}-\frac{2}{5}\\=\frac{100}{90}-\frac{75}{90}-\frac{36}{90}\\=\frac{100-75-36}{90}\\=\frac{-11}{90}\)
10. \(-\left(\frac{-6}{5}\right) +\left(\frac{-6}{5}\right) +\left(\frac{-6}{7}\right)\\= \frac{6}{5}- \frac{6}{5}-\frac{6}{7}\\=\frac{42}{35}-\frac{42}{35}-\frac{30}{35}\\=\frac{42-42-30}{35}\\=\frac{-30}{35}\\=\frac{-6}{7}\)
11. \(+\left(\frac{6}{-7}\right) +\left(\frac{-6}{2}\right) +\left(\frac{7}{-10}\right)\\= \frac{-6}{7}- \frac{6}{2}-\frac{7}{10}\\=\frac{-6}{7}-\frac{3}{1}-\frac{7}{10}\\=\frac{-60}{70}-\frac{210}{70}-\frac{49}{70}\\=\frac{-60-210-49}{70}\\=\frac{-319}{70}\)
12. \(-\left(\frac{-6}{7}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-11}{4}\right)\\= \frac{6}{7}+ \frac{8}{10}+\frac{11}{4}\\=\frac{6}{7}+\frac{4}{5}+\frac{11}{4}\\=\frac{120}{140}+\frac{112}{140}+\frac{385}{140}\\=\frac{120+112+385}{140}\\=\frac{617}{140}\)