Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-3}\right) -\left(\frac{9}{10}\right) +\left(\frac{4}{11}\right)\\= \frac{-10}{3}- \frac{9}{10}+\frac{4}{11}\\=\frac{-1100}{330}-\frac{297}{330}+\frac{120}{330}\\=\frac{-1100-297+120}{330}\\=\frac{-1277}{330}\)
2. \(+\left(\frac{-4}{-5}\right) +\left(\frac{4}{9}\right) -\left(\frac{-12}{-11}\right)\\= \frac{4}{5}+ \frac{4}{9}-\frac{12}{11}\\=\frac{396}{495}+\frac{220}{495}-\frac{540}{495}\\=\frac{396+220-540}{495}\\=\frac{76}{495}\)
3. \(-\left(\frac{-8}{-3}\right) -\left(\frac{6}{-5}\right) -\left(\frac{9}{-12}\right)\\= \frac{-8}{3}+ \frac{6}{5}+\frac{9}{12}\\=\frac{-8}{3}+\frac{6}{5}+\frac{3}{4}\\=\frac{-160}{60}+\frac{72}{60}+\frac{45}{60}\\=\frac{-160+72+45}{60}\\=\frac{-43}{60}\)
4. \(+\left(\frac{9}{7}\right) +\left(\frac{-4}{-6}\right) +\left(\frac{9}{-12}\right)\\= \frac{9}{7}+ \frac{4}{6}-\frac{9}{12}\\=\frac{9}{7}+\frac{2}{3}-\frac{3}{4}\\=\frac{108}{84}+\frac{56}{84}-\frac{63}{84}\\=\frac{108+56-63}{84}\\=\frac{101}{84}\)
5. \(+\left(\frac{10}{3}\right) -\left(\frac{3}{-9}\right) +\left(\frac{8}{3}\right)\\= \frac{10}{3}+ \frac{3}{9}+\frac{8}{3}\\=\frac{10}{3}+\frac{1}{3}+\frac{8}{3}\\=\frac{10+1+8}{3}\\=\frac{19}{3}\)
6. \(-\left(\frac{-3}{7}\right) +\left(\frac{6}{2}\right) +\left(\frac{-11}{2}\right)\\= \frac{3}{7}+ \frac{6}{2}-\frac{11}{2}\\=\frac{3}{7}+\frac{3}{1}-\frac{11}{2}\\=\frac{6}{14}+\frac{42}{14}-\frac{77}{14}\\=\frac{6+42-77}{14}\\=\frac{-29}{14}\)
7. \(-\left(\frac{9}{7}\right) +\left(\frac{-3}{9}\right) +\left(\frac{5}{-7}\right)\\= \frac{-9}{7}- \frac{3}{9}-\frac{5}{7}\\=\frac{-9}{7}-\frac{1}{3}-\frac{5}{7}\\=\frac{-27}{21}-\frac{7}{21}-\frac{15}{21}\\=\frac{-27-7-15}{21}\\=\frac{-49}{21}\\=\frac{-7}{3}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{9}{8}\right)\\= \frac{6}{5}- \frac{2}{3}+\frac{9}{8}\\=\frac{144}{120}-\frac{80}{120}+\frac{135}{120}\\=\frac{144-80+135}{120}\\=\frac{199}{120}\)
9. \(+\left(\frac{4}{3}\right) +\left(\frac{3}{4}\right) -\left(\frac{8}{-10}\right)\\= \frac{4}{3}+ \frac{3}{4}+\frac{8}{10}\\=\frac{4}{3}+\frac{3}{4}+\frac{4}{5}\\=\frac{80}{60}+\frac{45}{60}+\frac{48}{60}\\=\frac{80+45+48}{60}\\=\frac{173}{60}\)
10. \(-\left(\frac{-10}{9}\right) -\left(\frac{6}{7}\right) -\left(\frac{4}{12}\right)\\= \frac{10}{9}- \frac{6}{7}-\frac{4}{12}\\=\frac{10}{9}-\frac{6}{7}-\frac{1}{3}\\=\frac{70}{63}-\frac{54}{63}-\frac{21}{63}\\=\frac{70-54-21}{63}\\=\frac{-5}{63}\)
11. \(+\left(\frac{5}{6}\right) +\left(\frac{3}{4}\right) +\left(\frac{12}{-10}\right)\\= \frac{5}{6}+ \frac{3}{4}-\frac{12}{10}\\=\frac{5}{6}+\frac{3}{4}-\frac{6}{5}\\=\frac{50}{60}+\frac{45}{60}-\frac{72}{60}\\=\frac{50+45-72}{60}\\=\frac{23}{60}\)
12. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-10}{-4}\right) -\left(\frac{8}{-5}\right)\\= \frac{3}{2}+ \frac{10}{4}+\frac{8}{5}\\=\frac{3}{2}+\frac{5}{2}+\frac{8}{5}\\=\frac{15}{10}+\frac{25}{10}+\frac{16}{10}\\=\frac{15+25+16}{10}\\=\frac{56}{10}\\=\frac{28}{5}\)