Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{2}\right) -\left(\frac{6}{-8}\right) -\left(\frac{8}{-7}\right)\\= \frac{-7}{2}+ \frac{6}{8}+\frac{8}{7}\\=\frac{-7}{2}+\frac{3}{4}+\frac{8}{7}\\=\frac{-98}{28}+\frac{21}{28}+\frac{32}{28}\\=\frac{-98+21+32}{28}\\=\frac{-45}{28}\)
2. \(+\left(\frac{-3}{4}\right) -\left(\frac{-6}{-4}\right) +\left(\frac{2}{-10}\right)\\= \frac{-3}{4}- \frac{6}{4}-\frac{2}{10}\\=\frac{-3}{4}-\frac{3}{2}-\frac{1}{5}\\=\frac{-15}{20}-\frac{30}{20}-\frac{4}{20}\\=\frac{-15-30-4}{20}\\=\frac{-49}{20}\)
3. \(-\left(\frac{-10}{9}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{11}{10}\right)\\= \frac{10}{9}- \frac{3}{6}-\frac{11}{10}\\=\frac{10}{9}-\frac{1}{2}-\frac{11}{10}\\=\frac{100}{90}-\frac{45}{90}-\frac{99}{90}\\=\frac{100-45-99}{90}\\=\frac{-44}{90}\\=\frac{-22}{45}\)
4. \(+\left(\frac{-5}{7}\right) +\left(\frac{3}{3}\right) -\left(\frac{7}{-10}\right)\\= \frac{-5}{7}+ \frac{3}{3}+\frac{7}{10}\\=\frac{-5}{7}+\frac{1}{1}+\frac{7}{10}\\=\frac{-50}{70}+\frac{70}{70}+\frac{49}{70}\\=\frac{-50+70+49}{70}\\=\frac{69}{70}\)
5. \(+\left(\frac{9}{7}\right) +\left(\frac{9}{-10}\right) -\left(\frac{12}{-9}\right)\\= \frac{9}{7}- \frac{9}{10}+\frac{12}{9}\\=\frac{9}{7}-\frac{9}{10}+\frac{4}{3}\\=\frac{270}{210}-\frac{189}{210}+\frac{280}{210}\\=\frac{270-189+280}{210}\\=\frac{361}{210}\)
6. \(-\left(\frac{-3}{5}\right) -\left(\frac{4}{-10}\right) +\left(\frac{2}{-9}\right)\\= \frac{3}{5}+ \frac{4}{10}-\frac{2}{9}\\=\frac{3}{5}+\frac{2}{5}-\frac{2}{9}\\=\frac{27}{45}+\frac{18}{45}-\frac{10}{45}\\=\frac{27+18-10}{45}\\=\frac{35}{45}\\=\frac{7}{9}\)
7. \(+\left(\frac{-2}{7}\right) +\left(\frac{4}{6}\right) +\left(\frac{6}{-2}\right)\\= \frac{-2}{7}+ \frac{4}{6}-\frac{6}{2}\\=\frac{-2}{7}+\frac{2}{3}-\frac{3}{1}\\=\frac{-6}{21}+\frac{14}{21}-\frac{63}{21}\\=\frac{-6+14-63}{21}\\=\frac{-55}{21}\)
8. \(+\left(\frac{7}{-2}\right) +\left(\frac{9}{2}\right) -\left(\frac{-6}{3}\right)\\= \frac{-7}{2}+ \frac{9}{2}+\frac{6}{3}\\=\frac{-7}{2}+\frac{9}{2}+\frac{2}{1}\\=\frac{-7+9+2}{2}\\=\frac{4}{2}\\=\frac{2}{1}\)
9. \(-\left(\frac{6}{-5}\right) -\left(\frac{10}{-9}\right) -\left(\frac{3}{-3}\right)\\= \frac{6}{5}+ \frac{10}{9}+\frac{3}{3}\\=\frac{6}{5}+\frac{10}{9}+\frac{1}{1}\\=\frac{54}{45}+\frac{50}{45}+\frac{45}{45}\\=\frac{54+50+45}{45}\\=\frac{149}{45}\)
10. \(-\left(\frac{-6}{7}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-10}{-5}\right)\\= \frac{6}{7}- \frac{10}{3}+\frac{10}{5}\\=\frac{6}{7}-\frac{10}{3}+\frac{2}{1}\\=\frac{18}{21}-\frac{70}{21}+\frac{42}{21}\\=\frac{18-70+42}{21}\\=\frac{-10}{21}\)
11. \(+\left(\frac{-4}{-9}\right) +\left(\frac{10}{9}\right) +\left(\frac{-3}{-10}\right)\\= \frac{4}{9}+ \frac{10}{9}+\frac{3}{10}\\=\frac{40}{90}+\frac{100}{90}+\frac{27}{90}\\=\frac{40+100+27}{90}\\=\frac{167}{90}\)
12. \(+\left(\frac{-6}{-5}\right) -\left(\frac{4}{-10}\right) +\left(\frac{11}{-10}\right)\\= \frac{6}{5}+ \frac{4}{10}-\frac{11}{10}\\=\frac{6}{5}+\frac{2}{5}-\frac{11}{10}\\=\frac{12}{10}+\frac{4}{10}-\frac{11}{10}\\=\frac{12+4-11}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)