Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) -\left(\frac{6}{7}\right) -\left(\frac{9}{5}\right)\\= \frac{-6}{5}- \frac{6}{7}-\frac{9}{5}\\=\frac{-42}{35}-\frac{30}{35}-\frac{63}{35}\\=\frac{-42-30-63}{35}\\=\frac{-135}{35}\\=\frac{-27}{7}\)
2. \(+\left(\frac{5}{2}\right) +\left(\frac{5}{5}\right) -\left(\frac{-7}{3}\right)\\= \frac{5}{2}+ \frac{5}{5}+\frac{7}{3}\\=\frac{5}{2}+\frac{1}{1}+\frac{7}{3}\\=\frac{15}{6}+\frac{6}{6}+\frac{14}{6}\\=\frac{15+6+14}{6}\\=\frac{35}{6}\)
3. \(-\left(\frac{-6}{5}\right) +\left(\frac{5}{7}\right) +\left(\frac{4}{-3}\right)\\= \frac{6}{5}+ \frac{5}{7}-\frac{4}{3}\\=\frac{126}{105}+\frac{75}{105}-\frac{140}{105}\\=\frac{126+75-140}{105}\\=\frac{61}{105}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{2}{-6}\right) +\left(\frac{9}{-9}\right)\\= \frac{6}{5}+ \frac{2}{6}-\frac{9}{9}\\=\frac{6}{5}+\frac{1}{3}-\frac{1}{1}\\=\frac{18}{15}+\frac{5}{15}-\frac{15}{15}\\=\frac{18+5-15}{15}\\=\frac{8}{15}\)
5. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-3}{-6}\right) +\left(\frac{-3}{9}\right)\\= \frac{2}{5}+ \frac{3}{6}-\frac{3}{9}\\=\frac{2}{5}+\frac{1}{2}-\frac{1}{3}\\=\frac{12}{30}+\frac{15}{30}-\frac{10}{30}\\=\frac{12+15-10}{30}\\=\frac{17}{30}\)
6. \(+\left(\frac{-9}{-5}\right) -\left(\frac{-2}{10}\right) +\left(\frac{10}{-5}\right)\\= \frac{9}{5}+ \frac{2}{10}-\frac{10}{5}\\=\frac{9}{5}+\frac{1}{5}-\frac{2}{1}\\=\frac{9+1-2}{5}\\=\frac{8}{5}\)
7. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-10}{6}\right) +\left(\frac{4}{9}\right)\\= \frac{-8}{7}+ \frac{10}{6}+\frac{4}{9}\\=\frac{-8}{7}+\frac{5}{3}+\frac{4}{9}\\=\frac{-72}{63}+\frac{105}{63}+\frac{28}{63}\\=\frac{-72+105+28}{63}\\=\frac{61}{63}\)
8. \(+\left(\frac{-6}{5}\right) +\left(\frac{-3}{9}\right) -\left(\frac{-11}{7}\right)\\= \frac{-6}{5}- \frac{3}{9}+\frac{11}{7}\\=\frac{-6}{5}-\frac{1}{3}+\frac{11}{7}\\=\frac{-126}{105}-\frac{35}{105}+\frac{165}{105}\\=\frac{-126-35+165}{105}\\=\frac{4}{105}\)
9. \(+\left(\frac{8}{3}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-11}{3}\right)\\= \frac{8}{3}+ \frac{4}{8}-\frac{11}{3}\\=\frac{8}{3}+\frac{1}{2}-\frac{11}{3}\\=\frac{16}{6}+\frac{3}{6}-\frac{22}{6}\\=\frac{16+3-22}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
10. \(-\left(\frac{4}{9}\right) -\left(\frac{6}{10}\right) -\left(\frac{-7}{6}\right)\\= \frac{-4}{9}- \frac{6}{10}+\frac{7}{6}\\=\frac{-4}{9}-\frac{3}{5}+\frac{7}{6}\\=\frac{-40}{90}-\frac{54}{90}+\frac{105}{90}\\=\frac{-40-54+105}{90}\\=\frac{11}{90}\)
11. \(-\left(\frac{-2}{9}\right) -\left(\frac{-7}{-7}\right) -\left(\frac{-6}{4}\right)\\= \frac{2}{9}- \frac{7}{7}+\frac{6}{4}\\=\frac{2}{9}-\frac{1}{1}+\frac{3}{2}\\=\frac{4}{18}-\frac{18}{18}+\frac{27}{18}\\=\frac{4-18+27}{18}\\=\frac{13}{18}\)
12. \(-\left(\frac{9}{4}\right) -\left(\frac{-2}{4}\right) -\left(\frac{-6}{-4}\right)\\= \frac{-9}{4}+ \frac{2}{4}-\frac{6}{4}\\=\frac{-9}{4}+\frac{1}{2}-\frac{3}{2}\\=\frac{-9+1-3}{4}\\=\frac{-11}{4}\)