Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{5}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{-11}{-11}\right)\\= \frac{-6}{5}+ \frac{5}{9}+\frac{11}{11}\\=\frac{-6}{5}+\frac{5}{9}+\frac{1}{1}\\=\frac{-54}{45}+\frac{25}{45}+\frac{45}{45}\\=\frac{-54+25+45}{45}\\=\frac{16}{45}\)
2. \(+\left(\frac{3}{-4}\right) +\left(\frac{-8}{7}\right) -\left(\frac{9}{10}\right)\\= \frac{-3}{4}- \frac{8}{7}-\frac{9}{10}\\=\frac{-105}{140}-\frac{160}{140}-\frac{126}{140}\\=\frac{-105-160-126}{140}\\=\frac{-391}{140}\)
3. \(+\left(\frac{8}{7}\right) -\left(\frac{8}{-6}\right) +\left(\frac{-11}{-9}\right)\\= \frac{8}{7}+ \frac{8}{6}+\frac{11}{9}\\=\frac{8}{7}+\frac{4}{3}+\frac{11}{9}\\=\frac{72}{63}+\frac{84}{63}+\frac{77}{63}\\=\frac{72+84+77}{63}\\=\frac{233}{63}\)
4. \(+\left(\frac{-6}{7}\right) -\left(\frac{7}{-5}\right) -\left(\frac{11}{12}\right)\\= \frac{-6}{7}+ \frac{7}{5}-\frac{11}{12}\\=\frac{-360}{420}+\frac{588}{420}-\frac{385}{420}\\=\frac{-360+588-385}{420}\\=\frac{-157}{420}\)
5. \(-\left(\frac{9}{-7}\right) +\left(\frac{-4}{10}\right) +\left(\frac{-3}{4}\right)\\= \frac{9}{7}- \frac{4}{10}-\frac{3}{4}\\=\frac{9}{7}-\frac{2}{5}-\frac{3}{4}\\=\frac{180}{140}-\frac{56}{140}-\frac{105}{140}\\=\frac{180-56-105}{140}\\=\frac{19}{140}\)
6. \(-\left(\frac{-5}{-6}\right) +\left(\frac{8}{-10}\right) +\left(\frac{-5}{-3}\right)\\= \frac{-5}{6}- \frac{8}{10}+\frac{5}{3}\\=\frac{-5}{6}-\frac{4}{5}+\frac{5}{3}\\=\frac{-25}{30}-\frac{24}{30}+\frac{50}{30}\\=\frac{-25-24+50}{30}\\=\frac{1}{30}\)
7. \(-\left(\frac{7}{-8}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{4}{-8}\right)\\= \frac{7}{8}- \frac{4}{6}+\frac{4}{8}\\=\frac{7}{8}-\frac{2}{3}+\frac{1}{2}\\=\frac{21}{24}-\frac{16}{24}+\frac{12}{24}\\=\frac{21-16+12}{24}\\=\frac{17}{24}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{-3}\right) +\left(\frac{11}{-6}\right)\\= \frac{6}{5}+ \frac{6}{3}-\frac{11}{6}\\=\frac{6}{5}+\frac{2}{1}-\frac{11}{6}\\=\frac{36}{30}+\frac{60}{30}-\frac{55}{30}\\=\frac{36+60-55}{30}\\=\frac{41}{30}\)
9. \(-\left(\frac{3}{-5}\right) +\left(\frac{-6}{3}\right) +\left(\frac{-6}{7}\right)\\= \frac{3}{5}- \frac{6}{3}-\frac{6}{7}\\=\frac{3}{5}-\frac{2}{1}-\frac{6}{7}\\=\frac{21}{35}-\frac{70}{35}-\frac{30}{35}\\=\frac{21-70-30}{35}\\=\frac{-79}{35}\)
10. \(+\left(\frac{-5}{6}\right) +\left(\frac{4}{-4}\right) -\left(\frac{-3}{-10}\right)\\= \frac{-5}{6}- \frac{4}{4}-\frac{3}{10}\\=\frac{-5}{6}-\frac{1}{1}-\frac{3}{10}\\=\frac{-25}{30}-\frac{30}{30}-\frac{9}{30}\\=\frac{-25-30-9}{30}\\=\frac{-64}{30}\\=\frac{-32}{15}\)
11. \(+\left(\frac{-9}{-7}\right) +\left(\frac{9}{-2}\right) -\left(\frac{-2}{-10}\right)\\= \frac{9}{7}- \frac{9}{2}-\frac{2}{10}\\=\frac{9}{7}-\frac{9}{2}-\frac{1}{5}\\=\frac{90}{70}-\frac{315}{70}-\frac{14}{70}\\=\frac{90-315-14}{70}\\=\frac{-239}{70}\)
12. \(+\left(\frac{5}{-9}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{-4}{4}\right)\\= \frac{-5}{9}- \frac{3}{3}-\frac{4}{4}\\=\frac{-5}{9}-\frac{1}{1}-\frac{1}{1}\\=\frac{-5-1-1}{9}\\=\frac{-7}{9}\)