Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{2}\right) +\left(\frac{2}{-7}\right) +\left(\frac{11}{7}\right)\\= \frac{-3}{2}- \frac{2}{7}+\frac{11}{7}\\=\frac{-21}{14}-\frac{4}{14}+\frac{22}{14}\\=\frac{-21-4+22}{14}\\=\frac{-3}{14}\)
2. \(-\left(\frac{8}{5}\right) -\left(\frac{2}{-4}\right) -\left(\frac{-3}{-11}\right)\\= \frac{-8}{5}+ \frac{2}{4}-\frac{3}{11}\\=\frac{-8}{5}+\frac{1}{2}-\frac{3}{11}\\=\frac{-176}{110}+\frac{55}{110}-\frac{30}{110}\\=\frac{-176+55-30}{110}\\=\frac{-151}{110}\)
3. \(+\left(\frac{-5}{7}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{6}{8}\right)\\= \frac{-5}{7}- \frac{3}{5}+\frac{6}{8}\\=\frac{-5}{7}-\frac{3}{5}+\frac{3}{4}\\=\frac{-100}{140}-\frac{84}{140}+\frac{105}{140}\\=\frac{-100-84+105}{140}\\=\frac{-79}{140}\)
4. \(+\left(\frac{-4}{-3}\right) +\left(\frac{4}{-4}\right) -\left(\frac{-12}{12}\right)\\= \frac{4}{3}- \frac{4}{4}+\frac{12}{12}\\=\frac{4}{3}-\frac{1}{1}+\frac{1}{1}\\=\frac{4-1+1}{3}\\=\frac{4}{3}\)
5. \(-\left(\frac{2}{-3}\right) +\left(\frac{3}{5}\right) -\left(\frac{5}{-4}\right)\\= \frac{2}{3}+ \frac{3}{5}+\frac{5}{4}\\=\frac{40}{60}+\frac{36}{60}+\frac{75}{60}\\=\frac{40+36+75}{60}\\=\frac{151}{60}\)
6. \(-\left(\frac{-4}{3}\right) -\left(\frac{4}{7}\right) -\left(\frac{-11}{12}\right)\\= \frac{4}{3}- \frac{4}{7}+\frac{11}{12}\\=\frac{112}{84}-\frac{48}{84}+\frac{77}{84}\\=\frac{112-48+77}{84}\\=\frac{141}{84}\\=\frac{47}{28}\)
7. \(+\left(\frac{7}{-2}\right) -\left(\frac{-9}{8}\right) +\left(\frac{-2}{-10}\right)\\= \frac{-7}{2}+ \frac{9}{8}+\frac{2}{10}\\=\frac{-7}{2}+\frac{9}{8}+\frac{1}{5}\\=\frac{-140}{40}+\frac{45}{40}+\frac{8}{40}\\=\frac{-140+45+8}{40}\\=\frac{-87}{40}\)
8. \(-\left(\frac{-8}{-7}\right) +\left(\frac{9}{-5}\right) -\left(\frac{-9}{-12}\right)\\= \frac{-8}{7}- \frac{9}{5}-\frac{9}{12}\\=\frac{-8}{7}-\frac{9}{5}-\frac{3}{4}\\=\frac{-160}{140}-\frac{252}{140}-\frac{105}{140}\\=\frac{-160-252-105}{140}\\=\frac{-517}{140}\)
9. \(+\left(\frac{-4}{-5}\right) +\left(\frac{3}{6}\right) -\left(\frac{7}{7}\right)\\= \frac{4}{5}+ \frac{3}{6}-\frac{7}{7}\\=\frac{4}{5}+\frac{1}{2}-\frac{1}{1}\\=\frac{8}{10}+\frac{5}{10}-\frac{10}{10}\\=\frac{8+5-10}{10}\\=\frac{3}{10}\)
10. \(-\left(\frac{10}{3}\right) -\left(\frac{8}{4}\right) +\left(\frac{2}{-12}\right)\\= \frac{-10}{3}- \frac{8}{4}-\frac{2}{12}\\=\frac{-10}{3}-\frac{2}{1}-\frac{1}{6}\\=\frac{-20}{6}-\frac{12}{6}-\frac{1}{6}\\=\frac{-20-12-1}{6}\\=\frac{-33}{6}\\=\frac{-11}{2}\)
11. \(-\left(\frac{9}{8}\right) +\left(\frac{6}{10}\right) +\left(\frac{-10}{10}\right)\\= \frac{-9}{8}+ \frac{6}{10}-\frac{10}{10}\\=\frac{-9}{8}+\frac{3}{5}-\frac{1}{1}\\=\frac{-45}{40}+\frac{24}{40}-\frac{40}{40}\\=\frac{-45+24-40}{40}\\=\frac{-61}{40}\)
12. \(-\left(\frac{7}{-4}\right) +\left(\frac{-9}{6}\right) +\left(\frac{-10}{12}\right)\\= \frac{7}{4}- \frac{9}{6}-\frac{10}{12}\\=\frac{7}{4}-\frac{3}{2}-\frac{5}{6}\\=\frac{21}{12}-\frac{18}{12}-\frac{10}{12}\\=\frac{21-18-10}{12}\\=\frac{-7}{12}\)