Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-5}\right) -\left(\frac{-4}{4}\right) +\left(\frac{-10}{4}\right)\\= \frac{8}{5}+ \frac{4}{4}-\frac{10}{4}\\=\frac{8}{5}+\frac{1}{1}-\frac{5}{2}\\=\frac{16}{10}+\frac{10}{10}-\frac{25}{10}\\=\frac{16+10-25}{10}\\=\frac{1}{10}\)
2. \(+\left(\frac{-3}{-5}\right) +\left(\frac{2}{4}\right) +\left(\frac{11}{8}\right)\\= \frac{3}{5}+ \frac{2}{4}+\frac{11}{8}\\=\frac{3}{5}+\frac{1}{2}+\frac{11}{8}\\=\frac{24}{40}+\frac{20}{40}+\frac{55}{40}\\=\frac{24+20+55}{40}\\=\frac{99}{40}\)
3. \(+\left(\frac{-9}{5}\right) +\left(\frac{3}{-5}\right) -\left(\frac{12}{12}\right)\\= \frac{-9}{5}- \frac{3}{5}-\frac{12}{12}\\=\frac{-9}{5}-\frac{3}{5}-\frac{1}{1}\\=\frac{-9-3-1}{5}\\=\frac{-13}{5}\)
4. \(-\left(\frac{5}{-9}\right) -\left(\frac{-4}{6}\right) -\left(\frac{-8}{-5}\right)\\= \frac{5}{9}+ \frac{4}{6}-\frac{8}{5}\\=\frac{5}{9}+\frac{2}{3}-\frac{8}{5}\\=\frac{25}{45}+\frac{30}{45}-\frac{72}{45}\\=\frac{25+30-72}{45}\\=\frac{-17}{45}\)
5. \(-\left(\frac{-4}{9}\right) -\left(\frac{3}{10}\right) -\left(\frac{8}{-5}\right)\\= \frac{4}{9}- \frac{3}{10}+\frac{8}{5}\\=\frac{40}{90}-\frac{27}{90}+\frac{144}{90}\\=\frac{40-27+144}{90}\\=\frac{157}{90}\)
6. \(+\left(\frac{6}{5}\right) +\left(\frac{-3}{10}\right) +\left(\frac{8}{8}\right)\\= \frac{6}{5}- \frac{3}{10}+\frac{8}{8}\\=\frac{6}{5}-\frac{3}{10}+\frac{1}{1}\\=\frac{12}{10}-\frac{3}{10}+\frac{10}{10}\\=\frac{12-3+10}{10}\\=\frac{19}{10}\)
7. \(+\left(\frac{7}{-9}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{-5}{-5}\right)\\= \frac{-7}{9}+ \frac{7}{8}-\frac{5}{5}\\=\frac{-7}{9}+\frac{7}{8}-\frac{1}{1}\\=\frac{-56}{72}+\frac{63}{72}-\frac{72}{72}\\=\frac{-56+63-72}{72}\\=\frac{-65}{72}\)
8. \(+\left(\frac{-10}{3}\right) +\left(\frac{4}{4}\right) -\left(\frac{-9}{8}\right)\\= \frac{-10}{3}+ \frac{4}{4}+\frac{9}{8}\\=\frac{-10}{3}+\frac{1}{1}+\frac{9}{8}\\=\frac{-80}{24}+\frac{24}{24}+\frac{27}{24}\\=\frac{-80+24+27}{24}\\=\frac{-29}{24}\)
9. \(+\left(\frac{10}{-7}\right) -\left(\frac{3}{-9}\right) +\left(\frac{-4}{2}\right)\\= \frac{-10}{7}+ \frac{3}{9}-\frac{4}{2}\\=\frac{-10}{7}+\frac{1}{3}-\frac{2}{1}\\=\frac{-30}{21}+\frac{7}{21}-\frac{42}{21}\\=\frac{-30+7-42}{21}\\=\frac{-65}{21}\)
10. \(+\left(\frac{-3}{-5}\right) -\left(\frac{3}{5}\right) +\left(\frac{-3}{-4}\right)\\= \frac{3}{5}- \frac{3}{5}+\frac{3}{4}\\=\frac{12}{20}-\frac{12}{20}+\frac{15}{20}\\=\frac{12-12+15}{20}\\=\frac{15}{20}\\=\frac{3}{4}\)
11. \(-\left(\frac{2}{-7}\right) +\left(\frac{-3}{6}\right) -\left(\frac{-8}{-7}\right)\\= \frac{2}{7}- \frac{3}{6}-\frac{8}{7}\\=\frac{2}{7}-\frac{1}{2}-\frac{8}{7}\\=\frac{4}{14}-\frac{7}{14}-\frac{16}{14}\\=\frac{4-7-16}{14}\\=\frac{-19}{14}\)
12. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-6}{5}\right) +\left(\frac{-8}{-5}\right)\\= \frac{10}{9}+ \frac{6}{5}+\frac{8}{5}\\=\frac{50}{45}+\frac{54}{45}+\frac{72}{45}\\=\frac{50+54+72}{45}\\=\frac{176}{45}\)