Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-5}\right) +\left(\frac{9}{7}\right) -\left(\frac{5}{7}\right)\\= \frac{4}{5}+ \frac{9}{7}-\frac{5}{7}\\=\frac{28}{35}+\frac{45}{35}-\frac{25}{35}\\=\frac{28+45-25}{35}\\=\frac{48}{35}\)
2. \(+\left(\frac{10}{-9}\right) -\left(\frac{-4}{6}\right) +\left(\frac{7}{2}\right)\\= \frac{-10}{9}+ \frac{4}{6}+\frac{7}{2}\\=\frac{-10}{9}+\frac{2}{3}+\frac{7}{2}\\=\frac{-20}{18}+\frac{12}{18}+\frac{63}{18}\\=\frac{-20+12+63}{18}\\=\frac{55}{18}\)
3. \(-\left(\frac{6}{5}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{-5}{-2}\right)\\= \frac{-6}{5}- \frac{7}{10}+\frac{5}{2}\\=\frac{-12}{10}-\frac{7}{10}+\frac{25}{10}\\=\frac{-12-7+25}{10}\\=\frac{6}{10}\\=\frac{3}{5}\)
4. \(-\left(\frac{2}{9}\right) -\left(\frac{-7}{4}\right) -\left(\frac{-5}{-8}\right)\\= \frac{-2}{9}+ \frac{7}{4}-\frac{5}{8}\\=\frac{-16}{72}+\frac{126}{72}-\frac{45}{72}\\=\frac{-16+126-45}{72}\\=\frac{65}{72}\)
5. \(-\left(\frac{7}{8}\right) +\left(\frac{6}{9}\right) +\left(\frac{-6}{-7}\right)\\= \frac{-7}{8}+ \frac{6}{9}+\frac{6}{7}\\=\frac{-7}{8}+\frac{2}{3}+\frac{6}{7}\\=\frac{-147}{168}+\frac{112}{168}+\frac{144}{168}\\=\frac{-147+112+144}{168}\\=\frac{109}{168}\)
6. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-2}{5}\right) +\left(\frac{-5}{5}\right)\\= \frac{6}{5}- \frac{2}{5}-\frac{5}{5}\\=\frac{6}{5}-\frac{2}{5}-\frac{1}{1}\\=\frac{6-2-1}{5}\\=\frac{3}{5}\)
7. \(+\left(\frac{5}{4}\right) -\left(\frac{5}{10}\right) +\left(\frac{-4}{-3}\right)\\= \frac{5}{4}- \frac{5}{10}+\frac{4}{3}\\=\frac{5}{4}-\frac{1}{2}+\frac{4}{3}\\=\frac{15}{12}-\frac{6}{12}+\frac{16}{12}\\=\frac{15-6+16}{12}\\=\frac{25}{12}\)
8. \(+\left(\frac{-5}{-2}\right) +\left(\frac{-6}{6}\right) -\left(\frac{-8}{6}\right)\\= \frac{5}{2}- \frac{6}{6}+\frac{8}{6}\\=\frac{5}{2}-\frac{1}{1}+\frac{4}{3}\\=\frac{15}{6}-\frac{6}{6}+\frac{8}{6}\\=\frac{15-6+8}{6}\\=\frac{17}{6}\)
9. \(+\left(\frac{-3}{4}\right) +\left(\frac{3}{4}\right) +\left(\frac{-9}{-11}\right)\\= \frac{-3}{4}+ \frac{3}{4}+\frac{9}{11}\\=\frac{-33}{44}+\frac{33}{44}+\frac{36}{44}\\=\frac{-33+33+36}{44}\\=\frac{36}{44}\\=\frac{9}{11}\)
10. \(-\left(\frac{-2}{-7}\right) +\left(\frac{10}{-8}\right) -\left(\frac{12}{5}\right)\\= \frac{-2}{7}- \frac{10}{8}-\frac{12}{5}\\=\frac{-2}{7}-\frac{5}{4}-\frac{12}{5}\\=\frac{-40}{140}-\frac{175}{140}-\frac{336}{140}\\=\frac{-40-175-336}{140}\\=\frac{-551}{140}\)
11. \(+\left(\frac{4}{-5}\right) +\left(\frac{-10}{-7}\right) -\left(\frac{7}{-5}\right)\\= \frac{-4}{5}+ \frac{10}{7}+\frac{7}{5}\\=\frac{-28}{35}+\frac{50}{35}+\frac{49}{35}\\=\frac{-28+50+49}{35}\\=\frac{71}{35}\)
12. \(+\left(\frac{4}{-5}\right) +\left(\frac{7}{-9}\right) +\left(\frac{-4}{9}\right)\\= \frac{-4}{5}- \frac{7}{9}-\frac{4}{9}\\=\frac{-36}{45}-\frac{35}{45}-\frac{20}{45}\\=\frac{-36-35-20}{45}\\=\frac{-91}{45}\)