Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{7}\right) +\left(\frac{4}{-7}\right) +\left(\frac{-8}{12}\right)\\= \frac{-2}{7}- \frac{4}{7}-\frac{8}{12}\\=\frac{-2}{7}-\frac{4}{7}-\frac{2}{3}\\=\frac{-6}{21}-\frac{12}{21}-\frac{14}{21}\\=\frac{-6-12-14}{21}\\=\frac{-32}{21}\)
2. \(-\left(\frac{-5}{3}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-9}{-10}\right)\\= \frac{5}{3}- \frac{10}{9}+\frac{9}{10}\\=\frac{150}{90}-\frac{100}{90}+\frac{81}{90}\\=\frac{150-100+81}{90}\\=\frac{131}{90}\)
3. \(+\left(\frac{4}{-9}\right) -\left(\frac{9}{-6}\right) -\left(\frac{9}{-2}\right)\\= \frac{-4}{9}+ \frac{9}{6}+\frac{9}{2}\\=\frac{-4}{9}+\frac{3}{2}+\frac{9}{2}\\=\frac{-8}{18}+\frac{27}{18}+\frac{81}{18}\\=\frac{-8+27+81}{18}\\=\frac{100}{18}\\=\frac{50}{9}\)
4. \(+\left(\frac{-7}{-2}\right) +\left(\frac{7}{-2}\right) -\left(\frac{-6}{-9}\right)\\= \frac{7}{2}- \frac{7}{2}-\frac{6}{9}\\=\frac{7}{2}-\frac{7}{2}-\frac{2}{3}\\=\frac{21}{6}-\frac{21}{6}-\frac{4}{6}\\=\frac{21-21-4}{6}\\=\frac{-4}{6}\\=\frac{-2}{3}\)
5. \(+\left(\frac{2}{3}\right) +\left(\frac{9}{-8}\right) -\left(\frac{6}{-5}\right)\\= \frac{2}{3}- \frac{9}{8}+\frac{6}{5}\\=\frac{80}{120}-\frac{135}{120}+\frac{144}{120}\\=\frac{80-135+144}{120}\\=\frac{89}{120}\)
6. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{-9}{-3}\right)\\= \frac{-6}{5}- \frac{9}{2}+\frac{9}{3}\\=\frac{-6}{5}-\frac{9}{2}+\frac{3}{1}\\=\frac{-12}{10}-\frac{45}{10}+\frac{30}{10}\\=\frac{-12-45+30}{10}\\=\frac{-27}{10}\)
7. \(+\left(\frac{6}{-5}\right) +\left(\frac{7}{3}\right) +\left(\frac{-12}{10}\right)\\= \frac{-6}{5}+ \frac{7}{3}-\frac{12}{10}\\=\frac{-6}{5}+\frac{7}{3}-\frac{6}{5}\\=\frac{-18}{15}+\frac{35}{15}-\frac{18}{15}\\=\frac{-18+35-18}{15}\\=\frac{-1}{15}\)
8. \(-\left(\frac{-7}{2}\right) -\left(\frac{-8}{7}\right) -\left(\frac{11}{5}\right)\\= \frac{7}{2}+ \frac{8}{7}-\frac{11}{5}\\=\frac{245}{70}+\frac{80}{70}-\frac{154}{70}\\=\frac{245+80-154}{70}\\=\frac{171}{70}\)
9. \(+\left(\frac{-4}{-3}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-7}{-3}\right)\\= \frac{4}{3}+ \frac{6}{3}-\frac{7}{3}\\=\frac{4}{3}+\frac{2}{1}-\frac{7}{3}\\=\frac{4+2-7}{3}\\=\frac{-1}{3}\)
10. \(-\left(\frac{6}{5}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{-4}{4}\right)\\= \frac{-6}{5}+ \frac{8}{8}+\frac{4}{4}\\=\frac{-6}{5}+\frac{1}{1}+\frac{1}{1}\\=\frac{-6+1+1}{5}\\=\frac{-4}{5}\)
11. \(-\left(\frac{10}{-3}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-10}{-4}\right)\\= \frac{10}{3}- \frac{7}{5}-\frac{10}{4}\\=\frac{10}{3}-\frac{7}{5}-\frac{5}{2}\\=\frac{100}{30}-\frac{42}{30}-\frac{75}{30}\\=\frac{100-42-75}{30}\\=\frac{-17}{30}\)
12. \(+\left(\frac{-5}{-9}\right) +\left(\frac{10}{-8}\right) +\left(\frac{-12}{-10}\right)\\= \frac{5}{9}- \frac{10}{8}+\frac{12}{10}\\=\frac{5}{9}-\frac{5}{4}+\frac{6}{5}\\=\frac{100}{180}-\frac{225}{180}+\frac{216}{180}\\=\frac{100-225+216}{180}\\=\frac{91}{180}\)