Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-7}\right) +\left(\frac{4}{4}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-6}{7}+ \frac{4}{4}-\frac{9}{10}\\=\frac{-6}{7}+\frac{1}{1}-\frac{9}{10}\\=\frac{-60}{70}+\frac{70}{70}-\frac{63}{70}\\=\frac{-60+70-63}{70}\\=\frac{-53}{70}\)
2. \(+\left(\frac{-4}{7}\right) +\left(\frac{8}{-4}\right) +\left(\frac{-8}{-6}\right)\\= \frac{-4}{7}- \frac{8}{4}+\frac{8}{6}\\=\frac{-4}{7}-\frac{2}{1}+\frac{4}{3}\\=\frac{-12}{21}-\frac{42}{21}+\frac{28}{21}\\=\frac{-12-42+28}{21}\\=\frac{-26}{21}\)
3. \(+\left(\frac{8}{9}\right) +\left(\frac{2}{-3}\right) +\left(\frac{4}{-3}\right)\\= \frac{8}{9}- \frac{2}{3}-\frac{4}{3}\\=\frac{8-2-4}{9}\\=\frac{2}{9}\)
4. \(+\left(\frac{-4}{-7}\right) +\left(\frac{8}{-10}\right) +\left(\frac{10}{-7}\right)\\= \frac{4}{7}- \frac{8}{10}-\frac{10}{7}\\=\frac{4}{7}-\frac{4}{5}-\frac{10}{7}\\=\frac{20}{35}-\frac{28}{35}-\frac{50}{35}\\=\frac{20-28-50}{35}\\=\frac{-58}{35}\)
5. \(-\left(\frac{-10}{9}\right) -\left(\frac{-8}{-2}\right) +\left(\frac{7}{8}\right)\\= \frac{10}{9}- \frac{8}{2}+\frac{7}{8}\\=\frac{10}{9}-\frac{4}{1}+\frac{7}{8}\\=\frac{80}{72}-\frac{288}{72}+\frac{63}{72}\\=\frac{80-288+63}{72}\\=\frac{-145}{72}\)
6. \(-\left(\frac{2}{7}\right) -\left(\frac{-9}{2}\right) +\left(\frac{6}{5}\right)\\= \frac{-2}{7}+ \frac{9}{2}+\frac{6}{5}\\=\frac{-20}{70}+\frac{315}{70}+\frac{84}{70}\\=\frac{-20+315+84}{70}\\=\frac{379}{70}\)
7. \(-\left(\frac{4}{-3}\right) +\left(\frac{5}{-4}\right) -\left(\frac{-5}{-9}\right)\\= \frac{4}{3}- \frac{5}{4}-\frac{5}{9}\\=\frac{48}{36}-\frac{45}{36}-\frac{20}{36}\\=\frac{48-45-20}{36}\\=\frac{-17}{36}\)
8. \(-\left(\frac{-10}{7}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{-7}{11}\right)\\= \frac{10}{7}+ \frac{2}{9}+\frac{7}{11}\\=\frac{990}{693}+\frac{154}{693}+\frac{441}{693}\\=\frac{990+154+441}{693}\\=\frac{1585}{693}\)
9. \(+\left(\frac{-4}{3}\right) +\left(\frac{-8}{-4}\right) +\left(\frac{-8}{-2}\right)\\= \frac{-4}{3}+ \frac{8}{4}+\frac{8}{2}\\=\frac{-4}{3}+\frac{2}{1}+\frac{4}{1}\\=\frac{-4+2+4}{3}\\=\frac{2}{3}\)
10. \(-\left(\frac{-3}{2}\right) -\left(\frac{4}{-10}\right) -\left(\frac{4}{-2}\right)\\= \frac{3}{2}+ \frac{4}{10}+\frac{4}{2}\\=\frac{3}{2}+\frac{2}{5}+\frac{2}{1}\\=\frac{15}{10}+\frac{4}{10}+\frac{20}{10}\\=\frac{15+4+20}{10}\\=\frac{39}{10}\)
11. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-2}{2}\right) -\left(\frac{-11}{8}\right)\\= \frac{-6}{7}+ \frac{2}{2}+\frac{11}{8}\\=\frac{-6}{7}+\frac{1}{1}+\frac{11}{8}\\=\frac{-48}{56}+\frac{56}{56}+\frac{77}{56}\\=\frac{-48+56+77}{56}\\=\frac{85}{56}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{9}{-3}\right) -\left(\frac{9}{6}\right)\\= \frac{-6}{5}+ \frac{9}{3}-\frac{9}{6}\\=\frac{-6}{5}+\frac{3}{1}-\frac{3}{2}\\=\frac{-12}{10}+\frac{30}{10}-\frac{15}{10}\\=\frac{-12+30-15}{10}\\=\frac{3}{10}\)