Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{7}\right) -\left(\frac{4}{4}\right) -\left(\frac{-6}{-2}\right)\\= \frac{-4}{7}- \frac{4}{4}-\frac{6}{2}\\=\frac{-4}{7}-\frac{1}{1}-\frac{3}{1}\\=\frac{-4-1-3}{7}\\=\frac{-8}{7}\)
2. \(-\left(\frac{3}{2}\right) +\left(\frac{8}{-8}\right) +\left(\frac{8}{-12}\right)\\= \frac{-3}{2}- \frac{8}{8}-\frac{8}{12}\\=\frac{-3}{2}-\frac{1}{1}-\frac{2}{3}\\=\frac{-9}{6}-\frac{6}{6}-\frac{4}{6}\\=\frac{-9-6-4}{6}\\=\frac{-19}{6}\)
3. \(-\left(\frac{-7}{-9}\right) +\left(\frac{8}{4}\right) +\left(\frac{-12}{11}\right)\\= \frac{-7}{9}+ \frac{8}{4}-\frac{12}{11}\\=\frac{-7}{9}+\frac{2}{1}-\frac{12}{11}\\=\frac{-77}{99}+\frac{198}{99}-\frac{108}{99}\\=\frac{-77+198-108}{99}\\=\frac{13}{99}\)
4. \(+\left(\frac{3}{4}\right) +\left(\frac{3}{9}\right) -\left(\frac{11}{-8}\right)\\= \frac{3}{4}+ \frac{3}{9}+\frac{11}{8}\\=\frac{3}{4}+\frac{1}{3}+\frac{11}{8}\\=\frac{18}{24}+\frac{8}{24}+\frac{33}{24}\\=\frac{18+8+33}{24}\\=\frac{59}{24}\)
5. \(+\left(\frac{2}{9}\right) +\left(\frac{-5}{9}\right) -\left(\frac{3}{6}\right)\\= \frac{2}{9}- \frac{5}{9}-\frac{3}{6}\\=\frac{2}{9}-\frac{5}{9}-\frac{1}{2}\\=\frac{4}{18}-\frac{10}{18}-\frac{9}{18}\\=\frac{4-10-9}{18}\\=\frac{-15}{18}\\=\frac{-5}{6}\)
6. \(+\left(\frac{10}{-7}\right) +\left(\frac{6}{8}\right) +\left(\frac{12}{-10}\right)\\= \frac{-10}{7}+ \frac{6}{8}-\frac{12}{10}\\=\frac{-10}{7}+\frac{3}{4}-\frac{6}{5}\\=\frac{-200}{140}+\frac{105}{140}-\frac{168}{140}\\=\frac{-200+105-168}{140}\\=\frac{-263}{140}\)
7. \(+\left(\frac{4}{-9}\right) +\left(\frac{8}{10}\right) -\left(\frac{10}{-3}\right)\\= \frac{-4}{9}+ \frac{8}{10}+\frac{10}{3}\\=\frac{-4}{9}+\frac{4}{5}+\frac{10}{3}\\=\frac{-20}{45}+\frac{36}{45}+\frac{150}{45}\\=\frac{-20+36+150}{45}\\=\frac{166}{45}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{9}{-3}\right) -\left(\frac{-4}{9}\right)\\= \frac{-6}{5}+ \frac{9}{3}+\frac{4}{9}\\=\frac{-6}{5}+\frac{3}{1}+\frac{4}{9}\\=\frac{-54}{45}+\frac{135}{45}+\frac{20}{45}\\=\frac{-54+135+20}{45}\\=\frac{101}{45}\)
9. \(+\left(\frac{10}{3}\right) -\left(\frac{8}{-8}\right) -\left(\frac{4}{5}\right)\\= \frac{10}{3}+ \frac{8}{8}-\frac{4}{5}\\=\frac{10}{3}+\frac{1}{1}-\frac{4}{5}\\=\frac{50}{15}+\frac{15}{15}-\frac{12}{15}\\=\frac{50+15-12}{15}\\=\frac{53}{15}\)
10. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-4}{-6}\right) -\left(\frac{9}{9}\right)\\= \frac{2}{3}+ \frac{4}{6}-\frac{9}{9}\\=\frac{2}{3}+\frac{2}{3}-\frac{1}{1}\\=\frac{2+2-1}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
11. \(+\left(\frac{-8}{3}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{-12}{2}\right)\\= \frac{-8}{3}- \frac{7}{9}-\frac{12}{2}\\=\frac{-8}{3}-\frac{7}{9}-\frac{6}{1}\\=\frac{-24}{9}-\frac{7}{9}-\frac{54}{9}\\=\frac{-24-7-54}{9}\\=\frac{-85}{9}\)
12. \(+\left(\frac{10}{-3}\right) -\left(\frac{4}{-3}\right) +\left(\frac{6}{2}\right)\\= \frac{-10}{3}+ \frac{4}{3}+\frac{6}{2}\\=\frac{-10}{3}+\frac{4}{3}+\frac{3}{1}\\=\frac{-10+4+3}{3}\\=\frac{-3}{3}\\=\frac{-1}{1}\)