Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-3}\right) +\left(\frac{-6}{9}\right) +\left(\frac{-7}{-2}\right)\\= \frac{8}{3}- \frac{6}{9}+\frac{7}{2}\\=\frac{8}{3}-\frac{2}{3}+\frac{7}{2}\\=\frac{16}{6}-\frac{4}{6}+\frac{21}{6}\\=\frac{16-4+21}{6}\\=\frac{33}{6}\\=\frac{11}{2}\)
2. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-8}{9}+ \frac{9}{3}-\frac{6}{3}\\=\frac{-8}{9}+\frac{3}{1}-\frac{2}{1}\\=\frac{-8+3-2}{9}\\=\frac{-7}{9}\)
3. \(+\left(\frac{-3}{7}\right) +\left(\frac{8}{-8}\right) +\left(\frac{3}{-10}\right)\\= \frac{-3}{7}- \frac{8}{8}-\frac{3}{10}\\=\frac{-3}{7}-\frac{1}{1}-\frac{3}{10}\\=\frac{-30}{70}-\frac{70}{70}-\frac{21}{70}\\=\frac{-30-70-21}{70}\\=\frac{-121}{70}\)
4. \(-\left(\frac{2}{-5}\right) -\left(\frac{10}{6}\right) -\left(\frac{4}{3}\right)\\= \frac{2}{5}- \frac{10}{6}-\frac{4}{3}\\=\frac{2}{5}-\frac{5}{3}-\frac{4}{3}\\=\frac{6}{15}-\frac{25}{15}-\frac{20}{15}\\=\frac{6-25-20}{15}\\=\frac{-39}{15}\\=\frac{-13}{5}\)
5. \(+\left(\frac{-7}{4}\right) +\left(\frac{-5}{2}\right) +\left(\frac{7}{-4}\right)\\= \frac{-7}{4}- \frac{5}{2}-\frac{7}{4}\\=\frac{-7-5-7}{4}\\=\frac{-19}{4}\)
6. \(-\left(\frac{5}{-9}\right) +\left(\frac{-4}{2}\right) -\left(\frac{-4}{12}\right)\\= \frac{5}{9}- \frac{4}{2}+\frac{4}{12}\\=\frac{5}{9}-\frac{2}{1}+\frac{1}{3}\\=\frac{5-2+1}{9}\\=\frac{4}{9}\)
7. \(-\left(\frac{-7}{4}\right) +\left(\frac{9}{-6}\right) -\left(\frac{8}{4}\right)\\= \frac{7}{4}- \frac{9}{6}-\frac{8}{4}\\=\frac{7}{4}-\frac{3}{2}-\frac{2}{1}\\=\frac{7-3-2}{4}\\=\frac{2}{4}\\=\frac{1}{2}\)
8. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{-3}{10}\right)\\= \frac{2}{9}+ \frac{10}{5}-\frac{3}{10}\\=\frac{2}{9}+\frac{2}{1}-\frac{3}{10}\\=\frac{20}{90}+\frac{180}{90}-\frac{27}{90}\\=\frac{20+180-27}{90}\\=\frac{173}{90}\)
9. \(-\left(\frac{7}{9}\right) -\left(\frac{-8}{9}\right) +\left(\frac{5}{5}\right)\\= \frac{-7}{9}+ \frac{8}{9}+\frac{5}{5}\\=\frac{-7}{9}+\frac{8}{9}+\frac{1}{1}\\=\frac{-7+8+1}{9}\\=\frac{2}{9}\)
10. \(-\left(\frac{-2}{3}\right) -\left(\frac{4}{-3}\right) +\left(\frac{8}{7}\right)\\= \frac{2}{3}+ \frac{4}{3}+\frac{8}{7}\\=\frac{14}{21}+\frac{28}{21}+\frac{24}{21}\\=\frac{14+28+24}{21}\\=\frac{66}{21}\\=\frac{22}{7}\)
11. \(-\left(\frac{3}{-4}\right) -\left(\frac{-7}{7}\right) -\left(\frac{12}{12}\right)\\= \frac{3}{4}+ \frac{7}{7}-\frac{12}{12}\\=\frac{3}{4}+\frac{1}{1}-\frac{1}{1}\\=\frac{3+1-1}{4}\\=\frac{3}{4}\)
12. \(+\left(\frac{7}{-9}\right) +\left(\frac{10}{10}\right) -\left(\frac{3}{4}\right)\\= \frac{-7}{9}+ \frac{10}{10}-\frac{3}{4}\\=\frac{-7}{9}+\frac{1}{1}-\frac{3}{4}\\=\frac{-28}{36}+\frac{36}{36}-\frac{27}{36}\\=\frac{-28+36-27}{36}\\=\frac{-19}{36}\)