Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{5}\right) -\left(\frac{-4}{7}\right) +\left(\frac{-2}{3}\right)\\= \frac{9}{5}+ \frac{4}{7}-\frac{2}{3}\\=\frac{189}{105}+\frac{60}{105}-\frac{70}{105}\\=\frac{189+60-70}{105}\\=\frac{179}{105}\)
2. \(-\left(\frac{-9}{5}\right) +\left(\frac{-5}{7}\right) +\left(\frac{-4}{7}\right)\\= \frac{9}{5}- \frac{5}{7}-\frac{4}{7}\\=\frac{63}{35}-\frac{25}{35}-\frac{20}{35}\\=\frac{63-25-20}{35}\\=\frac{18}{35}\)
3. \(-\left(\frac{4}{3}\right) -\left(\frac{10}{-9}\right) +\left(\frac{4}{-11}\right)\\= \frac{-4}{3}+ \frac{10}{9}-\frac{4}{11}\\=\frac{-132}{99}+\frac{110}{99}-\frac{36}{99}\\=\frac{-132+110-36}{99}\\=\frac{-58}{99}\)
4. \(+\left(\frac{9}{-2}\right) -\left(\frac{10}{9}\right) -\left(\frac{-5}{12}\right)\\= \frac{-9}{2}- \frac{10}{9}+\frac{5}{12}\\=\frac{-162}{36}-\frac{40}{36}+\frac{15}{36}\\=\frac{-162-40+15}{36}\\=\frac{-187}{36}\)
5. \(-\left(\frac{-3}{-7}\right) -\left(\frac{10}{-6}\right) -\left(\frac{7}{4}\right)\\= \frac{-3}{7}+ \frac{10}{6}-\frac{7}{4}\\=\frac{-3}{7}+\frac{5}{3}-\frac{7}{4}\\=\frac{-36}{84}+\frac{140}{84}-\frac{147}{84}\\=\frac{-36+140-147}{84}\\=\frac{-43}{84}\)
6. \(-\left(\frac{5}{9}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{3}{-2}\right)\\= \frac{-5}{9}- \frac{7}{7}-\frac{3}{2}\\=\frac{-5}{9}-\frac{1}{1}-\frac{3}{2}\\=\frac{-10}{18}-\frac{18}{18}-\frac{27}{18}\\=\frac{-10-18-27}{18}\\=\frac{-55}{18}\)
7. \(+\left(\frac{2}{7}\right) -\left(\frac{4}{-6}\right) +\left(\frac{-5}{-5}\right)\\= \frac{2}{7}+ \frac{4}{6}+\frac{5}{5}\\=\frac{2}{7}+\frac{2}{3}+\frac{1}{1}\\=\frac{6}{21}+\frac{14}{21}+\frac{21}{21}\\=\frac{6+14+21}{21}\\=\frac{41}{21}\)
8. \(+\left(\frac{-7}{2}\right) -\left(\frac{5}{-4}\right) +\left(\frac{12}{-11}\right)\\= \frac{-7}{2}+ \frac{5}{4}-\frac{12}{11}\\=\frac{-154}{44}+\frac{55}{44}-\frac{48}{44}\\=\frac{-154+55-48}{44}\\=\frac{-147}{44}\)
9. \(+\left(\frac{10}{9}\right) -\left(\frac{7}{-3}\right) +\left(\frac{-4}{7}\right)\\= \frac{10}{9}+ \frac{7}{3}-\frac{4}{7}\\=\frac{70}{63}+\frac{147}{63}-\frac{36}{63}\\=\frac{70+147-36}{63}\\=\frac{181}{63}\)
10. \(-\left(\frac{-7}{-8}\right) +\left(\frac{9}{-3}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-7}{8}- \frac{9}{3}-\frac{2}{11}\\=\frac{-7}{8}-\frac{3}{1}-\frac{2}{11}\\=\frac{-77}{88}-\frac{264}{88}-\frac{16}{88}\\=\frac{-77-264-16}{88}\\=\frac{-357}{88}\)
11. \(+\left(\frac{-9}{-5}\right) -\left(\frac{9}{6}\right) +\left(\frac{-10}{3}\right)\\= \frac{9}{5}- \frac{9}{6}-\frac{10}{3}\\=\frac{9}{5}-\frac{3}{2}-\frac{10}{3}\\=\frac{54}{30}-\frac{45}{30}-\frac{100}{30}\\=\frac{54-45-100}{30}\\=\frac{-91}{30}\)
12. \(+\left(\frac{-4}{9}\right) -\left(\frac{5}{7}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-4}{9}- \frac{5}{7}-\frac{2}{5}\\=\frac{-140}{315}-\frac{225}{315}-\frac{126}{315}\\=\frac{-140-225-126}{315}\\=\frac{-491}{315}\)