Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{3}\right) +\left(\frac{4}{-8}\right) -\left(\frac{3}{-9}\right)\\= \frac{-8}{3}- \frac{4}{8}+\frac{3}{9}\\=\frac{-8}{3}-\frac{1}{2}+\frac{1}{3}\\=\frac{-16}{6}-\frac{3}{6}+\frac{2}{6}\\=\frac{-16-3+2}{6}\\=\frac{-17}{6}\)
2. \(+\left(\frac{-5}{7}\right) +\left(\frac{6}{5}\right) -\left(\frac{-12}{2}\right)\\= \frac{-5}{7}+ \frac{6}{5}+\frac{12}{2}\\=\frac{-5}{7}+\frac{6}{5}+\frac{6}{1}\\=\frac{-25}{35}+\frac{42}{35}+\frac{210}{35}\\=\frac{-25+42+210}{35}\\=\frac{227}{35}\)
3. \(+\left(\frac{-5}{-3}\right) +\left(\frac{-4}{5}\right) -\left(\frac{5}{-7}\right)\\= \frac{5}{3}- \frac{4}{5}+\frac{5}{7}\\=\frac{175}{105}-\frac{84}{105}+\frac{75}{105}\\=\frac{175-84+75}{105}\\=\frac{166}{105}\)
4. \(+\left(\frac{-9}{5}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-4}{-4}\right)\\= \frac{-9}{5}+ \frac{5}{4}+\frac{4}{4}\\=\frac{-9}{5}+\frac{5}{4}+\frac{1}{1}\\=\frac{-36}{20}+\frac{25}{20}+\frac{20}{20}\\=\frac{-36+25+20}{20}\\=\frac{9}{20}\)
5. \(-\left(\frac{5}{-6}\right) +\left(\frac{-8}{6}\right) +\left(\frac{-4}{-7}\right)\\= \frac{5}{6}- \frac{8}{6}+\frac{4}{7}\\=\frac{5}{6}-\frac{4}{3}+\frac{4}{7}\\=\frac{35}{42}-\frac{56}{42}+\frac{24}{42}\\=\frac{35-56+24}{42}\\=\frac{3}{42}\\=\frac{1}{14}\)
6. \(-\left(\frac{-4}{7}\right) +\left(\frac{-7}{4}\right) +\left(\frac{7}{8}\right)\\= \frac{4}{7}- \frac{7}{4}+\frac{7}{8}\\=\frac{32}{56}-\frac{98}{56}+\frac{49}{56}\\=\frac{32-98+49}{56}\\=\frac{-17}{56}\)
7. \(-\left(\frac{-8}{9}\right) +\left(\frac{5}{-9}\right) -\left(\frac{-9}{-5}\right)\\= \frac{8}{9}- \frac{5}{9}-\frac{9}{5}\\=\frac{40}{45}-\frac{25}{45}-\frac{81}{45}\\=\frac{40-25-81}{45}\\=\frac{-66}{45}\\=\frac{-22}{15}\)
8. \(-\left(\frac{9}{8}\right) -\left(\frac{-3}{7}\right) +\left(\frac{6}{-11}\right)\\= \frac{-9}{8}+ \frac{3}{7}-\frac{6}{11}\\=\frac{-693}{616}+\frac{264}{616}-\frac{336}{616}\\=\frac{-693+264-336}{616}\\=\frac{-765}{616}\)
9. \(-\left(\frac{2}{-3}\right) -\left(\frac{7}{4}\right) +\left(\frac{2}{-5}\right)\\= \frac{2}{3}- \frac{7}{4}-\frac{2}{5}\\=\frac{40}{60}-\frac{105}{60}-\frac{24}{60}\\=\frac{40-105-24}{60}\\=\frac{-89}{60}\)
10. \(-\left(\frac{-3}{-4}\right) +\left(\frac{7}{9}\right) -\left(\frac{-4}{-8}\right)\\= \frac{-3}{4}+ \frac{7}{9}-\frac{4}{8}\\=\frac{-3}{4}+\frac{7}{9}-\frac{1}{2}\\=\frac{-27}{36}+\frac{28}{36}-\frac{18}{36}\\=\frac{-27+28-18}{36}\\=\frac{-17}{36}\)
11. \(-\left(\frac{-5}{-9}\right) -\left(\frac{10}{7}\right) -\left(\frac{-6}{-7}\right)\\= \frac{-5}{9}- \frac{10}{7}-\frac{6}{7}\\=\frac{-35}{63}-\frac{90}{63}-\frac{54}{63}\\=\frac{-35-90-54}{63}\\=\frac{-179}{63}\)
12. \(-\left(\frac{2}{-7}\right) +\left(\frac{4}{-7}\right) -\left(\frac{-11}{10}\right)\\= \frac{2}{7}- \frac{4}{7}+\frac{11}{10}\\=\frac{20}{70}-\frac{40}{70}+\frac{77}{70}\\=\frac{20-40+77}{70}\\=\frac{57}{70}\)