Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{5}\right) -\left(\frac{9}{6}\right) +\left(\frac{8}{-6}\right)\\= \frac{4}{5}- \frac{9}{6}-\frac{8}{6}\\=\frac{4}{5}-\frac{3}{2}-\frac{4}{3}\\=\frac{24}{30}-\frac{45}{30}-\frac{40}{30}\\=\frac{24-45-40}{30}\\=\frac{-61}{30}\)
2. \(-\left(\frac{5}{6}\right) -\left(\frac{-5}{2}\right) +\left(\frac{6}{-5}\right)\\= \frac{-5}{6}+ \frac{5}{2}-\frac{6}{5}\\=\frac{-25}{30}+\frac{75}{30}-\frac{36}{30}\\=\frac{-25+75-36}{30}\\=\frac{14}{30}\\=\frac{7}{15}\)
3. \(-\left(\frac{8}{-3}\right) -\left(\frac{-5}{10}\right) +\left(\frac{4}{3}\right)\\= \frac{8}{3}+ \frac{5}{10}+\frac{4}{3}\\=\frac{8}{3}+\frac{1}{2}+\frac{4}{3}\\=\frac{16}{6}+\frac{3}{6}+\frac{8}{6}\\=\frac{16+3+8}{6}\\=\frac{27}{6}\\=\frac{9}{2}\)
4. \(+\left(\frac{4}{-7}\right) -\left(\frac{4}{-2}\right) +\left(\frac{3}{-11}\right)\\= \frac{-4}{7}+ \frac{4}{2}-\frac{3}{11}\\=\frac{-4}{7}+\frac{2}{1}-\frac{3}{11}\\=\frac{-44}{77}+\frac{154}{77}-\frac{21}{77}\\=\frac{-44+154-21}{77}\\=\frac{89}{77}\)
5. \(-\left(\frac{4}{-7}\right) -\left(\frac{3}{-9}\right) -\left(\frac{11}{-4}\right)\\= \frac{4}{7}+ \frac{3}{9}+\frac{11}{4}\\=\frac{4}{7}+\frac{1}{3}+\frac{11}{4}\\=\frac{48}{84}+\frac{28}{84}+\frac{231}{84}\\=\frac{48+28+231}{84}\\=\frac{307}{84}\)
6. \(-\left(\frac{-5}{-2}\right) -\left(\frac{10}{10}\right) -\left(\frac{-6}{11}\right)\\= \frac{-5}{2}- \frac{10}{10}+\frac{6}{11}\\=\frac{-5}{2}-\frac{1}{1}+\frac{6}{11}\\=\frac{-55}{22}-\frac{22}{22}+\frac{12}{22}\\=\frac{-55-22+12}{22}\\=\frac{-65}{22}\)
7. \(-\left(\frac{-8}{-5}\right) -\left(\frac{3}{-8}\right) -\left(\frac{-5}{-10}\right)\\= \frac{-8}{5}+ \frac{3}{8}-\frac{5}{10}\\=\frac{-8}{5}+\frac{3}{8}-\frac{1}{2}\\=\frac{-64}{40}+\frac{15}{40}-\frac{20}{40}\\=\frac{-64+15-20}{40}\\=\frac{-69}{40}\)
8. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-8}{-9}\right) +\left(\frac{3}{8}\right)\\= \frac{-8}{3}+ \frac{8}{9}+\frac{3}{8}\\=\frac{-192}{72}+\frac{64}{72}+\frac{27}{72}\\=\frac{-192+64+27}{72}\\=\frac{-101}{72}\)
9. \(-\left(\frac{6}{7}\right) +\left(\frac{6}{-9}\right) -\left(\frac{10}{-11}\right)\\= \frac{-6}{7}- \frac{6}{9}+\frac{10}{11}\\=\frac{-6}{7}-\frac{2}{3}+\frac{10}{11}\\=\frac{-198}{231}-\frac{154}{231}+\frac{210}{231}\\=\frac{-198-154+210}{231}\\=\frac{-142}{231}\)
10. \(+\left(\frac{-5}{4}\right) +\left(\frac{-9}{3}\right) -\left(\frac{12}{12}\right)\\= \frac{-5}{4}- \frac{9}{3}-\frac{12}{12}\\=\frac{-5}{4}-\frac{3}{1}-\frac{1}{1}\\=\frac{-5-3-1}{4}\\=\frac{-9}{4}\)
11. \(-\left(\frac{-5}{6}\right) -\left(\frac{-9}{8}\right) -\left(\frac{12}{7}\right)\\= \frac{5}{6}+ \frac{9}{8}-\frac{12}{7}\\=\frac{140}{168}+\frac{189}{168}-\frac{288}{168}\\=\frac{140+189-288}{168}\\=\frac{41}{168}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{-8}{6}\right) +\left(\frac{4}{11}\right)\\= \frac{-6}{5}+ \frac{8}{6}+\frac{4}{11}\\=\frac{-6}{5}+\frac{4}{3}+\frac{4}{11}\\=\frac{-198}{165}+\frac{220}{165}+\frac{60}{165}\\=\frac{-198+220+60}{165}\\=\frac{82}{165}\)