Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{7}\right) -\left(\frac{10}{-5}\right) +\left(\frac{-10}{-3}\right)\\= \frac{5}{7}+ \frac{10}{5}+\frac{10}{3}\\=\frac{5}{7}+\frac{2}{1}+\frac{10}{3}\\=\frac{15}{21}+\frac{42}{21}+\frac{70}{21}\\=\frac{15+42+70}{21}\\=\frac{127}{21}\)
2. \(-\left(\frac{4}{7}\right) -\left(\frac{-3}{4}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-4}{7}+ \frac{3}{4}-\frac{2}{3}\\=\frac{-48}{84}+\frac{63}{84}-\frac{56}{84}\\=\frac{-48+63-56}{84}\\=\frac{-41}{84}\)
3. \(-\left(\frac{3}{-4}\right) +\left(\frac{-9}{2}\right) +\left(\frac{4}{3}\right)\\= \frac{3}{4}- \frac{9}{2}+\frac{4}{3}\\=\frac{9}{12}-\frac{54}{12}+\frac{16}{12}\\=\frac{9-54+16}{12}\\=\frac{-29}{12}\)
4. \(-\left(\frac{6}{5}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{7}{10}\right)\\= \frac{-6}{5}- \frac{4}{6}-\frac{7}{10}\\=\frac{-6}{5}-\frac{2}{3}-\frac{7}{10}\\=\frac{-36}{30}-\frac{20}{30}-\frac{21}{30}\\=\frac{-36-20-21}{30}\\=\frac{-77}{30}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{2}{3}\right) +\left(\frac{-11}{-8}\right)\\= \frac{-6}{5}+ \frac{2}{3}+\frac{11}{8}\\=\frac{-144}{120}+\frac{80}{120}+\frac{165}{120}\\=\frac{-144+80+165}{120}\\=\frac{101}{120}\)
6. \(-\left(\frac{-10}{9}\right) +\left(\frac{6}{10}\right) -\left(\frac{9}{-11}\right)\\= \frac{10}{9}+ \frac{6}{10}+\frac{9}{11}\\=\frac{10}{9}+\frac{3}{5}+\frac{9}{11}\\=\frac{550}{495}+\frac{297}{495}+\frac{405}{495}\\=\frac{550+297+405}{495}\\=\frac{1252}{495}\)
7. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{2}\right) -\left(\frac{7}{4}\right)\\= \frac{-6}{5}+ \frac{3}{2}-\frac{7}{4}\\=\frac{-24}{20}+\frac{30}{20}-\frac{35}{20}\\=\frac{-24+30-35}{20}\\=\frac{-29}{20}\)
8. \(-\left(\frac{2}{5}\right) -\left(\frac{-5}{8}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-2}{5}+ \frac{5}{8}-\frac{8}{12}\\=\frac{-2}{5}+\frac{5}{8}-\frac{2}{3}\\=\frac{-48}{120}+\frac{75}{120}-\frac{80}{120}\\=\frac{-48+75-80}{120}\\=\frac{-53}{120}\)
9. \(-\left(\frac{5}{-3}\right) -\left(\frac{10}{-4}\right) -\left(\frac{-11}{11}\right)\\= \frac{5}{3}+ \frac{10}{4}+\frac{11}{11}\\=\frac{5}{3}+\frac{5}{2}+\frac{1}{1}\\=\frac{10}{6}+\frac{15}{6}+\frac{6}{6}\\=\frac{10+15+6}{6}\\=\frac{31}{6}\)
10. \(+\left(\frac{3}{7}\right) -\left(\frac{10}{-4}\right) -\left(\frac{4}{4}\right)\\= \frac{3}{7}+ \frac{10}{4}-\frac{4}{4}\\=\frac{3}{7}+\frac{5}{2}-\frac{1}{1}\\=\frac{6}{14}+\frac{35}{14}-\frac{14}{14}\\=\frac{6+35-14}{14}\\=\frac{27}{14}\)
11. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-6}{6}\right) +\left(\frac{10}{6}\right)\\= \frac{-8}{3}- \frac{6}{6}+\frac{10}{6}\\=\frac{-8}{3}-\frac{1}{1}+\frac{5}{3}\\=\frac{-8-1+5}{3}\\=\frac{-4}{3}\)
12. \(+\left(\frac{-2}{7}\right) +\left(\frac{10}{6}\right) +\left(\frac{-10}{4}\right)\\= \frac{-2}{7}+ \frac{10}{6}-\frac{10}{4}\\=\frac{-2}{7}+\frac{5}{3}-\frac{5}{2}\\=\frac{-12}{42}+\frac{70}{42}-\frac{105}{42}\\=\frac{-12+70-105}{42}\\=\frac{-47}{42}\)