Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{3}\right) +\left(\frac{6}{-3}\right) +\left(\frac{7}{11}\right)\\= \frac{-4}{3}- \frac{6}{3}+\frac{7}{11}\\=\frac{-4}{3}-\frac{2}{1}+\frac{7}{11}\\=\frac{-44}{33}-\frac{66}{33}+\frac{21}{33}\\=\frac{-44-66+21}{33}\\=\frac{-89}{33}\)
2. \(+\left(\frac{2}{-9}\right) -\left(\frac{8}{-5}\right) +\left(\frac{-3}{4}\right)\\= \frac{-2}{9}+ \frac{8}{5}-\frac{3}{4}\\=\frac{-40}{180}+\frac{288}{180}-\frac{135}{180}\\=\frac{-40+288-135}{180}\\=\frac{113}{180}\)
3. \(-\left(\frac{8}{9}\right) -\left(\frac{-3}{-9}\right) -\left(\frac{12}{8}\right)\\= \frac{-8}{9}- \frac{3}{9}-\frac{12}{8}\\=\frac{-8}{9}-\frac{1}{3}-\frac{3}{2}\\=\frac{-16}{18}-\frac{6}{18}-\frac{27}{18}\\=\frac{-16-6-27}{18}\\=\frac{-49}{18}\)
4. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-2}{-3}\right)\\= \frac{-6}{5}+ \frac{5}{7}+\frac{2}{3}\\=\frac{-126}{105}+\frac{75}{105}+\frac{70}{105}\\=\frac{-126+75+70}{105}\\=\frac{19}{105}\)
5. \(+\left(\frac{-9}{-7}\right) +\left(\frac{6}{-2}\right) +\left(\frac{3}{8}\right)\\= \frac{9}{7}- \frac{6}{2}+\frac{3}{8}\\=\frac{9}{7}-\frac{3}{1}+\frac{3}{8}\\=\frac{72}{56}-\frac{168}{56}+\frac{21}{56}\\=\frac{72-168+21}{56}\\=\frac{-75}{56}\)
6. \(-\left(\frac{-4}{-9}\right) -\left(\frac{10}{-2}\right) -\left(\frac{-10}{-7}\right)\\= \frac{-4}{9}+ \frac{10}{2}-\frac{10}{7}\\=\frac{-4}{9}+\frac{5}{1}-\frac{10}{7}\\=\frac{-28}{63}+\frac{315}{63}-\frac{90}{63}\\=\frac{-28+315-90}{63}\\=\frac{197}{63}\)
7. \(-\left(\frac{7}{2}\right) -\left(\frac{-9}{9}\right) -\left(\frac{8}{-11}\right)\\= \frac{-7}{2}+ \frac{9}{9}+\frac{8}{11}\\=\frac{-7}{2}+\frac{1}{1}+\frac{8}{11}\\=\frac{-77}{22}+\frac{22}{22}+\frac{16}{22}\\=\frac{-77+22+16}{22}\\=\frac{-39}{22}\)
8. \(+\left(\frac{-8}{7}\right) +\left(\frac{9}{3}\right) -\left(\frac{12}{-9}\right)\\= \frac{-8}{7}+ \frac{9}{3}+\frac{12}{9}\\=\frac{-8}{7}+\frac{3}{1}+\frac{4}{3}\\=\frac{-24}{21}+\frac{63}{21}+\frac{28}{21}\\=\frac{-24+63+28}{21}\\=\frac{67}{21}\)
9. \(-\left(\frac{5}{2}\right) +\left(\frac{3}{-6}\right) +\left(\frac{9}{-10}\right)\\= \frac{-5}{2}- \frac{3}{6}-\frac{9}{10}\\=\frac{-5}{2}-\frac{1}{2}-\frac{9}{10}\\=\frac{-25}{10}-\frac{5}{10}-\frac{9}{10}\\=\frac{-25-5-9}{10}\\=\frac{-39}{10}\)
10. \(-\left(\frac{-9}{-8}\right) +\left(\frac{-8}{5}\right) +\left(\frac{7}{12}\right)\\= \frac{-9}{8}- \frac{8}{5}+\frac{7}{12}\\=\frac{-135}{120}-\frac{192}{120}+\frac{70}{120}\\=\frac{-135-192+70}{120}\\=\frac{-257}{120}\)
11. \(-\left(\frac{5}{-2}\right) +\left(\frac{-6}{10}\right) +\left(\frac{-10}{-8}\right)\\= \frac{5}{2}- \frac{6}{10}+\frac{10}{8}\\=\frac{5}{2}-\frac{3}{5}+\frac{5}{4}\\=\frac{50}{20}-\frac{12}{20}+\frac{25}{20}\\=\frac{50-12+25}{20}\\=\frac{63}{20}\)
12. \(-\left(\frac{-2}{3}\right) -\left(\frac{2}{-2}\right) -\left(\frac{7}{-11}\right)\\= \frac{2}{3}+ \frac{2}{2}+\frac{7}{11}\\=\frac{2}{3}+\frac{1}{1}+\frac{7}{11}\\=\frac{22}{33}+\frac{33}{33}+\frac{21}{33}\\=\frac{22+33+21}{33}\\=\frac{76}{33}\)