Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-7}\right) -\left(\frac{9}{3}\right) -\left(\frac{-3}{-3}\right)\\= \frac{3}{7}- \frac{9}{3}-\frac{3}{3}\\=\frac{3}{7}-\frac{3}{1}-\frac{1}{1}\\=\frac{3-3-1}{7}\\=\frac{-1}{7}\)
2. \(+\left(\frac{2}{7}\right) -\left(\frac{7}{4}\right) -\left(\frac{11}{12}\right)\\= \frac{2}{7}- \frac{7}{4}-\frac{11}{12}\\=\frac{24}{84}-\frac{147}{84}-\frac{77}{84}\\=\frac{24-147-77}{84}\\=\frac{-200}{84}\\=\frac{-50}{21}\)
3. \(-\left(\frac{-10}{9}\right) -\left(\frac{4}{9}\right) -\left(\frac{-8}{-10}\right)\\= \frac{10}{9}- \frac{4}{9}-\frac{8}{10}\\=\frac{10}{9}-\frac{4}{9}-\frac{4}{5}\\=\frac{50}{45}-\frac{20}{45}-\frac{36}{45}\\=\frac{50-20-36}{45}\\=\frac{-6}{45}\\=\frac{-2}{15}\)
4. \(+\left(\frac{-2}{-3}\right) -\left(\frac{7}{-5}\right) +\left(\frac{7}{2}\right)\\= \frac{2}{3}+ \frac{7}{5}+\frac{7}{2}\\=\frac{20}{30}+\frac{42}{30}+\frac{105}{30}\\=\frac{20+42+105}{30}\\=\frac{167}{30}\)
5. \(-\left(\frac{-2}{7}\right) -\left(\frac{-2}{3}\right) +\left(\frac{7}{4}\right)\\= \frac{2}{7}+ \frac{2}{3}+\frac{7}{4}\\=\frac{24}{84}+\frac{56}{84}+\frac{147}{84}\\=\frac{24+56+147}{84}\\=\frac{227}{84}\)
6. \(-\left(\frac{8}{3}\right) +\left(\frac{7}{8}\right) +\left(\frac{11}{5}\right)\\= \frac{-8}{3}+ \frac{7}{8}+\frac{11}{5}\\=\frac{-320}{120}+\frac{105}{120}+\frac{264}{120}\\=\frac{-320+105+264}{120}\\=\frac{49}{120}\)
7. \(+\left(\frac{-10}{3}\right) -\left(\frac{10}{9}\right) +\left(\frac{5}{-8}\right)\\= \frac{-10}{3}- \frac{10}{9}-\frac{5}{8}\\=\frac{-240}{72}-\frac{80}{72}-\frac{45}{72}\\=\frac{-240-80-45}{72}\\=\frac{-365}{72}\)
8. \(+\left(\frac{-7}{9}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{5}{-2}\right)\\= \frac{-7}{9}+ \frac{7}{4}-\frac{5}{2}\\=\frac{-28}{36}+\frac{63}{36}-\frac{90}{36}\\=\frac{-28+63-90}{36}\\=\frac{-55}{36}\)
9. \(-\left(\frac{9}{7}\right) +\left(\frac{-9}{2}\right) -\left(\frac{10}{8}\right)\\= \frac{-9}{7}- \frac{9}{2}-\frac{10}{8}\\=\frac{-9}{7}-\frac{9}{2}-\frac{5}{4}\\=\frac{-36}{28}-\frac{126}{28}-\frac{35}{28}\\=\frac{-36-126-35}{28}\\=\frac{-197}{28}\)
10. \(-\left(\frac{8}{3}\right) -\left(\frac{7}{2}\right) +\left(\frac{4}{-12}\right)\\= \frac{-8}{3}- \frac{7}{2}-\frac{4}{12}\\=\frac{-8}{3}-\frac{7}{2}-\frac{1}{3}\\=\frac{-16}{6}-\frac{21}{6}-\frac{2}{6}\\=\frac{-16-21-2}{6}\\=\frac{-39}{6}\\=\frac{-13}{2}\)
11. \(-\left(\frac{-2}{-5}\right) +\left(\frac{4}{7}\right) +\left(\frac{7}{-8}\right)\\= \frac{-2}{5}+ \frac{4}{7}-\frac{7}{8}\\=\frac{-112}{280}+\frac{160}{280}-\frac{245}{280}\\=\frac{-112+160-245}{280}\\=\frac{-197}{280}\)
12. \(+\left(\frac{3}{-8}\right) +\left(\frac{7}{9}\right) +\left(\frac{-10}{7}\right)\\= \frac{-3}{8}+ \frac{7}{9}-\frac{10}{7}\\=\frac{-189}{504}+\frac{392}{504}-\frac{720}{504}\\=\frac{-189+392-720}{504}\\=\frac{-517}{504}\)