Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{7}\right) -\left(\frac{4}{-9}\right) -\left(\frac{7}{-12}\right)\\= \frac{6}{7}+ \frac{4}{9}+\frac{7}{12}\\=\frac{216}{252}+\frac{112}{252}+\frac{147}{252}\\=\frac{216+112+147}{252}\\=\frac{475}{252}\)
2. \(-\left(\frac{2}{9}\right) +\left(\frac{5}{2}\right) +\left(\frac{11}{6}\right)\\= \frac{-2}{9}+ \frac{5}{2}+\frac{11}{6}\\=\frac{-4}{18}+\frac{45}{18}+\frac{33}{18}\\=\frac{-4+45+33}{18}\\=\frac{74}{18}\\=\frac{37}{9}\)
3. \(-\left(\frac{10}{-7}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{5}{-3}\right)\\= \frac{10}{7}+ \frac{9}{6}-\frac{5}{3}\\=\frac{10}{7}+\frac{3}{2}-\frac{5}{3}\\=\frac{60}{42}+\frac{63}{42}-\frac{70}{42}\\=\frac{60+63-70}{42}\\=\frac{53}{42}\)
4. \(+\left(\frac{2}{-9}\right) +\left(\frac{8}{4}\right) +\left(\frac{-5}{-8}\right)\\= \frac{-2}{9}+ \frac{8}{4}+\frac{5}{8}\\=\frac{-2}{9}+\frac{2}{1}+\frac{5}{8}\\=\frac{-16}{72}+\frac{144}{72}+\frac{45}{72}\\=\frac{-16+144+45}{72}\\=\frac{173}{72}\)
5. \(-\left(\frac{-2}{7}\right) -\left(\frac{8}{-3}\right) +\left(\frac{9}{-4}\right)\\= \frac{2}{7}+ \frac{8}{3}-\frac{9}{4}\\=\frac{24}{84}+\frac{224}{84}-\frac{189}{84}\\=\frac{24+224-189}{84}\\=\frac{59}{84}\)
6. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-3}{-3}\right) +\left(\frac{2}{-4}\right)\\= \frac{-10}{3}+ \frac{3}{3}-\frac{2}{4}\\=\frac{-10}{3}+\frac{1}{1}-\frac{1}{2}\\=\frac{-20}{6}+\frac{6}{6}-\frac{3}{6}\\=\frac{-20+6-3}{6}\\=\frac{-17}{6}\)
7. \(-\left(\frac{-2}{-5}\right) -\left(\frac{9}{9}\right) +\left(\frac{7}{11}\right)\\= \frac{-2}{5}- \frac{9}{9}+\frac{7}{11}\\=\frac{-2}{5}-\frac{1}{1}+\frac{7}{11}\\=\frac{-22}{55}-\frac{55}{55}+\frac{35}{55}\\=\frac{-22-55+35}{55}\\=\frac{-42}{55}\)
8. \(+\left(\frac{-5}{-7}\right) +\left(\frac{7}{-10}\right) +\left(\frac{5}{-10}\right)\\= \frac{5}{7}- \frac{7}{10}-\frac{5}{10}\\=\frac{5}{7}-\frac{7}{10}-\frac{1}{2}\\=\frac{50}{70}-\frac{49}{70}-\frac{35}{70}\\=\frac{50-49-35}{70}\\=\frac{-34}{70}\\=\frac{-17}{35}\)
9. \(-\left(\frac{-8}{3}\right) +\left(\frac{3}{-10}\right) -\left(\frac{3}{4}\right)\\= \frac{8}{3}- \frac{3}{10}-\frac{3}{4}\\=\frac{160}{60}-\frac{18}{60}-\frac{45}{60}\\=\frac{160-18-45}{60}\\=\frac{97}{60}\)
10. \(-\left(\frac{-10}{7}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{-12}{3}\right)\\= \frac{10}{7}+ \frac{3}{5}-\frac{12}{3}\\=\frac{10}{7}+\frac{3}{5}-\frac{4}{1}\\=\frac{50}{35}+\frac{21}{35}-\frac{140}{35}\\=\frac{50+21-140}{35}\\=\frac{-69}{35}\)
11. \(-\left(\frac{10}{-9}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{-3}{-9}\right)\\= \frac{10}{9}- \frac{2}{2}+\frac{3}{9}\\=\frac{10}{9}-\frac{1}{1}+\frac{1}{3}\\=\frac{10-1+1}{9}\\=\frac{10}{9}\)
12. \(-\left(\frac{3}{2}\right) -\left(\frac{-9}{2}\right) +\left(\frac{6}{2}\right)\\= \frac{-3}{2}+ \frac{9}{2}+\frac{6}{2}\\=\frac{-3}{2}+\frac{9}{2}+\frac{3}{1}\\=\frac{-3+9+3}{2}\\=\frac{9}{2}\)