Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-3}\right) -\left(\frac{-6}{-5}\right) +\left(\frac{3}{3}\right)\\= \frac{10}{3}- \frac{6}{5}+\frac{3}{3}\\=\frac{10}{3}-\frac{6}{5}+\frac{1}{1}\\=\frac{50}{15}-\frac{18}{15}+\frac{15}{15}\\=\frac{50-18+15}{15}\\=\frac{47}{15}\)
2. \(-\left(\frac{6}{5}\right) +\left(\frac{10}{-8}\right) +\left(\frac{7}{-10}\right)\\= \frac{-6}{5}- \frac{10}{8}-\frac{7}{10}\\=\frac{-6}{5}-\frac{5}{4}-\frac{7}{10}\\=\frac{-24}{20}-\frac{25}{20}-\frac{14}{20}\\=\frac{-24-25-14}{20}\\=\frac{-63}{20}\)
3. \(-\left(\frac{4}{-7}\right) -\left(\frac{2}{10}\right) -\left(\frac{-12}{4}\right)\\= \frac{4}{7}- \frac{2}{10}+\frac{12}{4}\\=\frac{4}{7}-\frac{1}{5}+\frac{3}{1}\\=\frac{20}{35}-\frac{7}{35}+\frac{105}{35}\\=\frac{20-7+105}{35}\\=\frac{118}{35}\)
4. \(+\left(\frac{-10}{7}\right) +\left(\frac{-8}{4}\right) +\left(\frac{12}{-11}\right)\\= \frac{-10}{7}- \frac{8}{4}-\frac{12}{11}\\=\frac{-10}{7}-\frac{2}{1}-\frac{12}{11}\\=\frac{-110}{77}-\frac{154}{77}-\frac{84}{77}\\=\frac{-110-154-84}{77}\\=\frac{-348}{77}\)
5. \(+\left(\frac{8}{-9}\right) +\left(\frac{9}{-9}\right) -\left(\frac{-12}{10}\right)\\= \frac{-8}{9}- \frac{9}{9}+\frac{12}{10}\\=\frac{-8}{9}-\frac{1}{1}+\frac{6}{5}\\=\frac{-40}{45}-\frac{45}{45}+\frac{54}{45}\\=\frac{-40-45+54}{45}\\=\frac{-31}{45}\)
6. \(-\left(\frac{6}{-7}\right) -\left(\frac{3}{-9}\right) +\left(\frac{4}{5}\right)\\= \frac{6}{7}+ \frac{3}{9}+\frac{4}{5}\\=\frac{6}{7}+\frac{1}{3}+\frac{4}{5}\\=\frac{90}{105}+\frac{35}{105}+\frac{84}{105}\\=\frac{90+35+84}{105}\\=\frac{209}{105}\)
7. \(+\left(\frac{-3}{-7}\right) +\left(\frac{9}{-10}\right) +\left(\frac{2}{-11}\right)\\= \frac{3}{7}- \frac{9}{10}-\frac{2}{11}\\=\frac{330}{770}-\frac{693}{770}-\frac{140}{770}\\=\frac{330-693-140}{770}\\=\frac{-503}{770}\)
8. \(-\left(\frac{-10}{-3}\right) +\left(\frac{3}{3}\right) -\left(\frac{-2}{5}\right)\\= \frac{-10}{3}+ \frac{3}{3}+\frac{2}{5}\\=\frac{-10}{3}+\frac{1}{1}+\frac{2}{5}\\=\frac{-50}{15}+\frac{15}{15}+\frac{6}{15}\\=\frac{-50+15+6}{15}\\=\frac{-29}{15}\)
9. \(+\left(\frac{7}{-6}\right) -\left(\frac{8}{7}\right) +\left(\frac{2}{-7}\right)\\= \frac{-7}{6}- \frac{8}{7}-\frac{2}{7}\\=\frac{-49}{42}-\frac{48}{42}-\frac{12}{42}\\=\frac{-49-48-12}{42}\\=\frac{-109}{42}\)
10. \(+\left(\frac{6}{7}\right) -\left(\frac{-8}{-8}\right) -\left(\frac{8}{10}\right)\\= \frac{6}{7}- \frac{8}{8}-\frac{8}{10}\\=\frac{6}{7}-\frac{1}{1}-\frac{4}{5}\\=\frac{30}{35}-\frac{35}{35}-\frac{28}{35}\\=\frac{30-35-28}{35}\\=\frac{-33}{35}\)
11. \(-\left(\frac{8}{7}\right) +\left(\frac{2}{-7}\right) +\left(\frac{11}{4}\right)\\= \frac{-8}{7}- \frac{2}{7}+\frac{11}{4}\\=\frac{-32}{28}-\frac{8}{28}+\frac{77}{28}\\=\frac{-32-8+77}{28}\\=\frac{37}{28}\)
12. \(+\left(\frac{2}{-5}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{6}{7}\right)\\= \frac{-2}{5}+ \frac{7}{8}-\frac{6}{7}\\=\frac{-112}{280}+\frac{245}{280}-\frac{240}{280}\\=\frac{-112+245-240}{280}\\=\frac{-107}{280}\)