Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-3}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-9}{5}\right)\\= \frac{-4}{3}- \frac{9}{2}+\frac{9}{5}\\=\frac{-40}{30}-\frac{135}{30}+\frac{54}{30}\\=\frac{-40-135+54}{30}\\=\frac{-121}{30}\)
2. \(+\left(\frac{2}{9}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{5}{-2}\right)\\= \frac{2}{9}+ \frac{8}{5}+\frac{5}{2}\\=\frac{20}{90}+\frac{144}{90}+\frac{225}{90}\\=\frac{20+144+225}{90}\\=\frac{389}{90}\)
3. \(-\left(\frac{9}{2}\right) +\left(\frac{4}{4}\right) +\left(\frac{9}{-3}\right)\\= \frac{-9}{2}+ \frac{4}{4}-\frac{9}{3}\\=\frac{-9}{2}+\frac{1}{1}-\frac{3}{1}\\=\frac{-9+1-3}{2}\\=\frac{-11}{2}\)
4. \(-\left(\frac{6}{5}\right) -\left(\frac{3}{8}\right) +\left(\frac{10}{10}\right)\\= \frac{-6}{5}- \frac{3}{8}+\frac{10}{10}\\=\frac{-6}{5}-\frac{3}{8}+\frac{1}{1}\\=\frac{-48}{40}-\frac{15}{40}+\frac{40}{40}\\=\frac{-48-15+40}{40}\\=\frac{-23}{40}\)
5. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-2}{4}\right) -\left(\frac{-11}{5}\right)\\= \frac{9}{4}- \frac{2}{4}+\frac{11}{5}\\=\frac{9}{4}-\frac{1}{2}+\frac{11}{5}\\=\frac{45}{20}-\frac{10}{20}+\frac{44}{20}\\=\frac{45-10+44}{20}\\=\frac{79}{20}\)
6. \(-\left(\frac{-2}{7}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{-11}{5}\right)\\= \frac{2}{7}- \frac{10}{10}-\frac{11}{5}\\=\frac{2}{7}-\frac{1}{1}-\frac{11}{5}\\=\frac{10}{35}-\frac{35}{35}-\frac{77}{35}\\=\frac{10-35-77}{35}\\=\frac{-102}{35}\)
7. \(-\left(\frac{5}{-8}\right) -\left(\frac{5}{6}\right) +\left(\frac{3}{3}\right)\\= \frac{5}{8}- \frac{5}{6}+\frac{3}{3}\\=\frac{5}{8}-\frac{5}{6}+\frac{1}{1}\\=\frac{15}{24}-\frac{20}{24}+\frac{24}{24}\\=\frac{15-20+24}{24}\\=\frac{19}{24}\)
8. \(-\left(\frac{-5}{2}\right) +\left(\frac{-2}{2}\right) +\left(\frac{8}{-3}\right)\\= \frac{5}{2}- \frac{2}{2}-\frac{8}{3}\\=\frac{5}{2}-\frac{1}{1}-\frac{8}{3}\\=\frac{15}{6}-\frac{6}{6}-\frac{16}{6}\\=\frac{15-6-16}{6}\\=\frac{-7}{6}\)
9. \(-\left(\frac{6}{-7}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{12}{9}\right)\\= \frac{6}{7}- \frac{6}{10}+\frac{12}{9}\\=\frac{6}{7}-\frac{3}{5}+\frac{4}{3}\\=\frac{90}{105}-\frac{63}{105}+\frac{140}{105}\\=\frac{90-63+140}{105}\\=\frac{167}{105}\)
10. \(+\left(\frac{6}{5}\right) +\left(\frac{2}{2}\right) +\left(\frac{12}{-10}\right)\\= \frac{6}{5}+ \frac{2}{2}-\frac{12}{10}\\=\frac{6}{5}+\frac{1}{1}-\frac{6}{5}\\=\frac{6+1-6}{5}\\=\frac{1}{5}\)
11. \(-\left(\frac{-10}{7}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{5}{-7}\right)\\= \frac{10}{7}- \frac{2}{8}+\frac{5}{7}\\=\frac{10}{7}-\frac{1}{4}+\frac{5}{7}\\=\frac{40}{28}-\frac{7}{28}+\frac{20}{28}\\=\frac{40-7+20}{28}\\=\frac{53}{28}\)
12. \(-\left(\frac{2}{5}\right) +\left(\frac{-7}{6}\right) -\left(\frac{-10}{-5}\right)\\= \frac{-2}{5}- \frac{7}{6}-\frac{10}{5}\\=\frac{-2}{5}-\frac{7}{6}-\frac{2}{1}\\=\frac{-12}{30}-\frac{35}{30}-\frac{60}{30}\\=\frac{-12-35-60}{30}\\=\frac{-107}{30}\)