Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) +\left(\frac{5}{9}\right) -\left(\frac{12}{-3}\right)\\= \frac{-6}{5}+ \frac{5}{9}+\frac{12}{3}\\=\frac{-6}{5}+\frac{5}{9}+\frac{4}{1}\\=\frac{-54}{45}+\frac{25}{45}+\frac{180}{45}\\=\frac{-54+25+180}{45}\\=\frac{151}{45}\)
2. \(-\left(\frac{2}{9}\right) +\left(\frac{8}{8}\right) -\left(\frac{-3}{-10}\right)\\= \frac{-2}{9}+ \frac{8}{8}-\frac{3}{10}\\=\frac{-2}{9}+\frac{1}{1}-\frac{3}{10}\\=\frac{-20}{90}+\frac{90}{90}-\frac{27}{90}\\=\frac{-20+90-27}{90}\\=\frac{43}{90}\)
3. \(-\left(\frac{6}{-5}\right) -\left(\frac{-5}{9}\right) -\left(\frac{3}{8}\right)\\= \frac{6}{5}+ \frac{5}{9}-\frac{3}{8}\\=\frac{432}{360}+\frac{200}{360}-\frac{135}{360}\\=\frac{432+200-135}{360}\\=\frac{497}{360}\)
4. \(-\left(\frac{-7}{-8}\right) +\left(\frac{-4}{-6}\right) +\left(\frac{-11}{8}\right)\\= \frac{-7}{8}+ \frac{4}{6}-\frac{11}{8}\\=\frac{-7}{8}+\frac{2}{3}-\frac{11}{8}\\=\frac{-21}{24}+\frac{16}{24}-\frac{33}{24}\\=\frac{-21+16-33}{24}\\=\frac{-38}{24}\\=\frac{-19}{12}\)
5. \(-\left(\frac{-5}{6}\right) -\left(\frac{10}{10}\right) -\left(\frac{-4}{-11}\right)\\= \frac{5}{6}- \frac{10}{10}-\frac{4}{11}\\=\frac{5}{6}-\frac{1}{1}-\frac{4}{11}\\=\frac{55}{66}-\frac{66}{66}-\frac{24}{66}\\=\frac{55-66-24}{66}\\=\frac{-35}{66}\)
6. \(+\left(\frac{-2}{-5}\right) +\left(\frac{9}{3}\right) +\left(\frac{-9}{10}\right)\\= \frac{2}{5}+ \frac{9}{3}-\frac{9}{10}\\=\frac{2}{5}+\frac{3}{1}-\frac{9}{10}\\=\frac{4}{10}+\frac{30}{10}-\frac{9}{10}\\=\frac{4+30-9}{10}\\=\frac{25}{10}\\=\frac{5}{2}\)
7. \(+\left(\frac{3}{5}\right) -\left(\frac{4}{7}\right) +\left(\frac{-4}{8}\right)\\= \frac{3}{5}- \frac{4}{7}-\frac{4}{8}\\=\frac{3}{5}-\frac{4}{7}-\frac{1}{2}\\=\frac{42}{70}-\frac{40}{70}-\frac{35}{70}\\=\frac{42-40-35}{70}\\=\frac{-33}{70}\)
8. \(+\left(\frac{-4}{5}\right) +\left(\frac{-4}{6}\right) -\left(\frac{7}{-3}\right)\\= \frac{-4}{5}- \frac{4}{6}+\frac{7}{3}\\=\frac{-4}{5}-\frac{2}{3}+\frac{7}{3}\\=\frac{-12}{15}-\frac{10}{15}+\frac{35}{15}\\=\frac{-12-10+35}{15}\\=\frac{13}{15}\)
9. \(+\left(\frac{3}{5}\right) -\left(\frac{-6}{5}\right) +\left(\frac{4}{2}\right)\\= \frac{3}{5}+ \frac{6}{5}+\frac{4}{2}\\=\frac{3}{5}+\frac{6}{5}+\frac{2}{1}\\=\frac{3+6+2}{5}\\=\frac{11}{5}\)
10. \(+\left(\frac{2}{-5}\right) +\left(\frac{9}{-3}\right) +\left(\frac{11}{-2}\right)\\= \frac{-2}{5}- \frac{9}{3}-\frac{11}{2}\\=\frac{-2}{5}-\frac{3}{1}-\frac{11}{2}\\=\frac{-4}{10}-\frac{30}{10}-\frac{55}{10}\\=\frac{-4-30-55}{10}\\=\frac{-89}{10}\)
11. \(-\left(\frac{-4}{-5}\right) -\left(\frac{7}{8}\right) -\left(\frac{3}{5}\right)\\= \frac{-4}{5}- \frac{7}{8}-\frac{3}{5}\\=\frac{-32}{40}-\frac{35}{40}-\frac{24}{40}\\=\frac{-32-35-24}{40}\\=\frac{-91}{40}\)
12. \(-\left(\frac{3}{-4}\right) +\left(\frac{4}{-10}\right) +\left(\frac{7}{-2}\right)\\= \frac{3}{4}- \frac{4}{10}-\frac{7}{2}\\=\frac{3}{4}-\frac{2}{5}-\frac{7}{2}\\=\frac{15}{20}-\frac{8}{20}-\frac{70}{20}\\=\frac{15-8-70}{20}\\=\frac{-63}{20}\)