Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{9}\right) -\left(\frac{-10}{4}\right) +\left(\frac{-11}{10}\right)\\= \frac{-4}{9}+ \frac{10}{4}-\frac{11}{10}\\=\frac{-4}{9}+\frac{5}{2}-\frac{11}{10}\\=\frac{-40}{90}+\frac{225}{90}-\frac{99}{90}\\=\frac{-40+225-99}{90}\\=\frac{86}{90}\\=\frac{43}{45}\)
2. \(+\left(\frac{7}{8}\right) -\left(\frac{-10}{8}\right) -\left(\frac{3}{-6}\right)\\= \frac{7}{8}+ \frac{10}{8}+\frac{3}{6}\\=\frac{7}{8}+\frac{5}{4}+\frac{1}{2}\\=\frac{7+5+1}{8}\\=\frac{13}{8}\)
3. \(+\left(\frac{-7}{-9}\right) -\left(\frac{-5}{-10}\right) -\left(\frac{-6}{2}\right)\\= \frac{7}{9}- \frac{5}{10}+\frac{6}{2}\\=\frac{7}{9}-\frac{1}{2}+\frac{3}{1}\\=\frac{14}{18}-\frac{9}{18}+\frac{54}{18}\\=\frac{14-9+54}{18}\\=\frac{59}{18}\)
4. \(+\left(\frac{-3}{2}\right) -\left(\frac{-3}{-6}\right) +\left(\frac{9}{4}\right)\\= \frac{-3}{2}- \frac{3}{6}+\frac{9}{4}\\=\frac{-3}{2}-\frac{1}{2}+\frac{9}{4}\\=\frac{-6}{4}-\frac{2}{4}+\frac{9}{4}\\=\frac{-6-2+9}{4}\\=\frac{1}{4}\)
5. \(+\left(\frac{5}{8}\right) -\left(\frac{-4}{5}\right) -\left(\frac{7}{6}\right)\\= \frac{5}{8}+ \frac{4}{5}-\frac{7}{6}\\=\frac{75}{120}+\frac{96}{120}-\frac{140}{120}\\=\frac{75+96-140}{120}\\=\frac{31}{120}\)
6. \(-\left(\frac{-8}{9}\right) +\left(\frac{-6}{10}\right) +\left(\frac{-12}{-9}\right)\\= \frac{8}{9}- \frac{6}{10}+\frac{12}{9}\\=\frac{8}{9}-\frac{3}{5}+\frac{4}{3}\\=\frac{40}{45}-\frac{27}{45}+\frac{60}{45}\\=\frac{40-27+60}{45}\\=\frac{73}{45}\)
7. \(-\left(\frac{-7}{-4}\right) -\left(\frac{9}{-7}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-7}{4}+ \frac{9}{7}-\frac{12}{4}\\=\frac{-7}{4}+\frac{9}{7}-\frac{3}{1}\\=\frac{-49}{28}+\frac{36}{28}-\frac{84}{28}\\=\frac{-49+36-84}{28}\\=\frac{-97}{28}\)
8. \(+\left(\frac{4}{5}\right) -\left(\frac{-2}{2}\right) +\left(\frac{3}{7}\right)\\= \frac{4}{5}+ \frac{2}{2}+\frac{3}{7}\\=\frac{4}{5}+\frac{1}{1}+\frac{3}{7}\\=\frac{28}{35}+\frac{35}{35}+\frac{15}{35}\\=\frac{28+35+15}{35}\\=\frac{78}{35}\)
9. \(+\left(\frac{-3}{-5}\right) +\left(\frac{10}{-10}\right) -\left(\frac{-9}{-10}\right)\\= \frac{3}{5}- \frac{10}{10}-\frac{9}{10}\\=\frac{3}{5}-\frac{1}{1}-\frac{9}{10}\\=\frac{6}{10}-\frac{10}{10}-\frac{9}{10}\\=\frac{6-10-9}{10}\\=\frac{-13}{10}\)
10. \(-\left(\frac{-2}{3}\right) +\left(\frac{4}{10}\right) +\left(\frac{10}{7}\right)\\= \frac{2}{3}+ \frac{4}{10}+\frac{10}{7}\\=\frac{2}{3}+\frac{2}{5}+\frac{10}{7}\\=\frac{70}{105}+\frac{42}{105}+\frac{150}{105}\\=\frac{70+42+150}{105}\\=\frac{262}{105}\)
11. \(-\left(\frac{9}{2}\right) -\left(\frac{-8}{3}\right) +\left(\frac{-4}{-4}\right)\\= \frac{-9}{2}+ \frac{8}{3}+\frac{4}{4}\\=\frac{-9}{2}+\frac{8}{3}+\frac{1}{1}\\=\frac{-27}{6}+\frac{16}{6}+\frac{6}{6}\\=\frac{-27+16+6}{6}\\=\frac{-5}{6}\)
12. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-2}{3}\right) -\left(\frac{-4}{-12}\right)\\= \frac{3}{2}- \frac{2}{3}-\frac{4}{12}\\=\frac{3}{2}-\frac{2}{3}-\frac{1}{3}\\=\frac{9}{6}-\frac{4}{6}-\frac{2}{6}\\=\frac{9-4-2}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)