Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{9}\right) -\left(\frac{8}{-6}\right) -\left(\frac{7}{7}\right)\\= \frac{-10}{9}+ \frac{8}{6}-\frac{7}{7}\\=\frac{-10}{9}+\frac{4}{3}-\frac{1}{1}\\=\frac{-10+4-1}{9}\\=\frac{-7}{9}\)
2. \(+\left(\frac{8}{-3}\right) -\left(\frac{8}{9}\right) +\left(\frac{9}{-10}\right)\\= \frac{-8}{3}- \frac{8}{9}-\frac{9}{10}\\=\frac{-240}{90}-\frac{80}{90}-\frac{81}{90}\\=\frac{-240-80-81}{90}\\=\frac{-401}{90}\)
3. \(+\left(\frac{-2}{-5}\right) -\left(\frac{2}{5}\right) -\left(\frac{2}{-8}\right)\\= \frac{2}{5}- \frac{2}{5}+\frac{2}{8}\\=\frac{2}{5}-\frac{2}{5}+\frac{1}{4}\\=\frac{8}{20}-\frac{8}{20}+\frac{5}{20}\\=\frac{8-8+5}{20}\\=\frac{5}{20}\\=\frac{1}{4}\)
4. \(+\left(\frac{8}{9}\right) +\left(\frac{8}{-4}\right) -\left(\frac{10}{-12}\right)\\= \frac{8}{9}- \frac{8}{4}+\frac{10}{12}\\=\frac{8}{9}-\frac{2}{1}+\frac{5}{6}\\=\frac{16}{18}-\frac{36}{18}+\frac{15}{18}\\=\frac{16-36+15}{18}\\=\frac{-5}{18}\)
5. \(+\left(\frac{2}{7}\right) -\left(\frac{9}{8}\right) -\left(\frac{-11}{4}\right)\\= \frac{2}{7}- \frac{9}{8}+\frac{11}{4}\\=\frac{16}{56}-\frac{63}{56}+\frac{154}{56}\\=\frac{16-63+154}{56}\\=\frac{107}{56}\)
6. \(-\left(\frac{9}{-2}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{-7}{-12}\right)\\= \frac{9}{2}+ \frac{6}{7}-\frac{7}{12}\\=\frac{378}{84}+\frac{72}{84}-\frac{49}{84}\\=\frac{378+72-49}{84}\\=\frac{401}{84}\)
7. \(+\left(\frac{2}{9}\right) -\left(\frac{4}{2}\right) -\left(\frac{-8}{-11}\right)\\= \frac{2}{9}- \frac{4}{2}-\frac{8}{11}\\=\frac{2}{9}-\frac{2}{1}-\frac{8}{11}\\=\frac{22}{99}-\frac{198}{99}-\frac{72}{99}\\=\frac{22-198-72}{99}\\=\frac{-248}{99}\)
8. \(+\left(\frac{3}{-2}\right) +\left(\frac{7}{6}\right) -\left(\frac{-12}{10}\right)\\= \frac{-3}{2}+ \frac{7}{6}+\frac{12}{10}\\=\frac{-3}{2}+\frac{7}{6}+\frac{6}{5}\\=\frac{-45}{30}+\frac{35}{30}+\frac{36}{30}\\=\frac{-45+35+36}{30}\\=\frac{26}{30}\\=\frac{13}{15}\)
9. \(+\left(\frac{9}{5}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-2}{-7}\right)\\= \frac{9}{5}- \frac{3}{7}+\frac{2}{7}\\=\frac{63}{35}-\frac{15}{35}+\frac{10}{35}\\=\frac{63-15+10}{35}\\=\frac{58}{35}\)
10. \(-\left(\frac{7}{-8}\right) +\left(\frac{-5}{5}\right) -\left(\frac{3}{7}\right)\\= \frac{7}{8}- \frac{5}{5}-\frac{3}{7}\\=\frac{7}{8}-\frac{1}{1}-\frac{3}{7}\\=\frac{49}{56}-\frac{56}{56}-\frac{24}{56}\\=\frac{49-56-24}{56}\\=\frac{-31}{56}\)
11. \(-\left(\frac{4}{-7}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{11}{-12}\right)\\= \frac{4}{7}+ \frac{3}{6}+\frac{11}{12}\\=\frac{4}{7}+\frac{1}{2}+\frac{11}{12}\\=\frac{48}{84}+\frac{42}{84}+\frac{77}{84}\\=\frac{48+42+77}{84}\\=\frac{167}{84}\)
12. \(-\left(\frac{7}{5}\right) +\left(\frac{5}{5}\right) -\left(\frac{-9}{3}\right)\\= \frac{-7}{5}+ \frac{5}{5}+\frac{9}{3}\\=\frac{-7}{5}+\frac{1}{1}+\frac{3}{1}\\=\frac{-7+1+3}{5}\\=\frac{-3}{5}\)