Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{9}\right) +\left(\frac{-9}{10}\right) +\left(\frac{-11}{9}\right)\\= \frac{-2}{9}- \frac{9}{10}-\frac{11}{9}\\=\frac{-20}{90}-\frac{81}{90}-\frac{110}{90}\\=\frac{-20-81-110}{90}\\=\frac{-211}{90}\)
2. \(+\left(\frac{5}{-6}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{-7}{5}\right)\\= \frac{-5}{6}+ \frac{6}{3}+\frac{7}{5}\\=\frac{-5}{6}+\frac{2}{1}+\frac{7}{5}\\=\frac{-25}{30}+\frac{60}{30}+\frac{42}{30}\\=\frac{-25+60+42}{30}\\=\frac{77}{30}\)
3. \(-\left(\frac{-4}{-7}\right) -\left(\frac{-9}{-4}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-4}{7}- \frac{9}{4}-\frac{3}{5}\\=\frac{-80}{140}-\frac{315}{140}-\frac{84}{140}\\=\frac{-80-315-84}{140}\\=\frac{-479}{140}\)
4. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{10}\right) +\left(\frac{-12}{-5}\right)\\= \frac{6}{5}- \frac{4}{10}+\frac{12}{5}\\=\frac{6}{5}-\frac{2}{5}+\frac{12}{5}\\=\frac{6-2+12}{5}\\=\frac{16}{5}\)
5. \(+\left(\frac{8}{-9}\right) -\left(\frac{9}{-9}\right) -\left(\frac{-8}{8}\right)\\= \frac{-8}{9}+ \frac{9}{9}+\frac{8}{8}\\=\frac{-8}{9}+\frac{1}{1}+\frac{1}{1}\\=\frac{-8+1+1}{9}\\=\frac{-6}{9}\\=\frac{-2}{3}\)
6. \(-\left(\frac{5}{7}\right) -\left(\frac{8}{4}\right) +\left(\frac{2}{-11}\right)\\= \frac{-5}{7}- \frac{8}{4}-\frac{2}{11}\\=\frac{-5}{7}-\frac{2}{1}-\frac{2}{11}\\=\frac{-55}{77}-\frac{154}{77}-\frac{14}{77}\\=\frac{-55-154-14}{77}\\=\frac{-223}{77}\)
7. \(-\left(\frac{9}{5}\right) +\left(\frac{6}{10}\right) -\left(\frac{2}{-11}\right)\\= \frac{-9}{5}+ \frac{6}{10}+\frac{2}{11}\\=\frac{-9}{5}+\frac{3}{5}+\frac{2}{11}\\=\frac{-99}{55}+\frac{33}{55}+\frac{10}{55}\\=\frac{-99+33+10}{55}\\=\frac{-56}{55}\)
8. \(+\left(\frac{7}{8}\right) -\left(\frac{-5}{7}\right) +\left(\frac{8}{-7}\right)\\= \frac{7}{8}+ \frac{5}{7}-\frac{8}{7}\\=\frac{49}{56}+\frac{40}{56}-\frac{64}{56}\\=\frac{49+40-64}{56}\\=\frac{25}{56}\)
9. \(+\left(\frac{-3}{2}\right) +\left(\frac{5}{4}\right) +\left(\frac{-5}{8}\right)\\= \frac{-3}{2}+ \frac{5}{4}-\frac{5}{8}\\=\frac{-12}{8}+\frac{10}{8}-\frac{5}{8}\\=\frac{-12+10-5}{8}\\=\frac{-7}{8}\)
10. \(+\left(\frac{8}{-5}\right) -\left(\frac{-5}{-4}\right) +\left(\frac{12}{-11}\right)\\= \frac{-8}{5}- \frac{5}{4}-\frac{12}{11}\\=\frac{-352}{220}-\frac{275}{220}-\frac{240}{220}\\=\frac{-352-275-240}{220}\\=\frac{-867}{220}\)
11. \(+\left(\frac{-6}{-5}\right) +\left(\frac{4}{5}\right) -\left(\frac{-6}{11}\right)\\= \frac{6}{5}+ \frac{4}{5}+\frac{6}{11}\\=\frac{66}{55}+\frac{44}{55}+\frac{30}{55}\\=\frac{66+44+30}{55}\\=\frac{140}{55}\\=\frac{28}{11}\)
12. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{9}{10}\right)\\= \frac{3}{7}+ \frac{3}{8}+\frac{9}{10}\\=\frac{120}{280}+\frac{105}{280}+\frac{252}{280}\\=\frac{120+105+252}{280}\\=\frac{477}{280}\)