Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) +\left(\frac{10}{4}\right) +\left(\frac{9}{-3}\right)\\= \frac{6}{5}+ \frac{10}{4}-\frac{9}{3}\\=\frac{6}{5}+\frac{5}{2}-\frac{3}{1}\\=\frac{12}{10}+\frac{25}{10}-\frac{30}{10}\\=\frac{12+25-30}{10}\\=\frac{7}{10}\)
2. \(+\left(\frac{4}{-3}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{4}{-2}\right)\\= \frac{-4}{3}+ \frac{2}{8}-\frac{4}{2}\\=\frac{-4}{3}+\frac{1}{4}-\frac{2}{1}\\=\frac{-16}{12}+\frac{3}{12}-\frac{24}{12}\\=\frac{-16+3-24}{12}\\=\frac{-37}{12}\)
3. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-5}{4}\right) +\left(\frac{11}{-7}\right)\\= \frac{9}{2}+ \frac{5}{4}-\frac{11}{7}\\=\frac{126}{28}+\frac{35}{28}-\frac{44}{28}\\=\frac{126+35-44}{28}\\=\frac{117}{28}\)
4. \(+\left(\frac{-2}{-7}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{-9}{-2}\right)\\= \frac{2}{7}+ \frac{4}{10}+\frac{9}{2}\\=\frac{2}{7}+\frac{2}{5}+\frac{9}{2}\\=\frac{20}{70}+\frac{28}{70}+\frac{315}{70}\\=\frac{20+28+315}{70}\\=\frac{363}{70}\)
5. \(-\left(\frac{4}{3}\right) -\left(\frac{-5}{9}\right) +\left(\frac{5}{5}\right)\\= \frac{-4}{3}+ \frac{5}{9}+\frac{5}{5}\\=\frac{-4}{3}+\frac{5}{9}+\frac{1}{1}\\=\frac{-12}{9}+\frac{5}{9}+\frac{9}{9}\\=\frac{-12+5+9}{9}\\=\frac{2}{9}\)
6. \(-\left(\frac{2}{9}\right) +\left(\frac{10}{10}\right) +\left(\frac{-4}{11}\right)\\= \frac{-2}{9}+ \frac{10}{10}-\frac{4}{11}\\=\frac{-2}{9}+\frac{1}{1}-\frac{4}{11}\\=\frac{-22}{99}+\frac{99}{99}-\frac{36}{99}\\=\frac{-22+99-36}{99}\\=\frac{41}{99}\)
7. \(+\left(\frac{8}{3}\right) +\left(\frac{8}{9}\right) +\left(\frac{11}{-4}\right)\\= \frac{8}{3}+ \frac{8}{9}-\frac{11}{4}\\=\frac{96}{36}+\frac{32}{36}-\frac{99}{36}\\=\frac{96+32-99}{36}\\=\frac{29}{36}\)
8. \(+\left(\frac{-5}{2}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-5}{2}+ \frac{6}{8}+\frac{10}{8}\\=\frac{-5}{2}+\frac{3}{4}+\frac{5}{4}\\=\frac{-10}{4}+\frac{3}{4}+\frac{5}{4}\\=\frac{-10+3+5}{4}\\=\frac{-2}{4}\\=\frac{-1}{2}\)
9. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{-8}{6}\right)\\= \frac{-10}{9}- \frac{9}{7}+\frac{8}{6}\\=\frac{-10}{9}-\frac{9}{7}+\frac{4}{3}\\=\frac{-70}{63}-\frac{81}{63}+\frac{84}{63}\\=\frac{-70-81+84}{63}\\=\frac{-67}{63}\)
10. \(-\left(\frac{3}{-4}\right) -\left(\frac{-8}{7}\right) +\left(\frac{-8}{-11}\right)\\= \frac{3}{4}+ \frac{8}{7}+\frac{8}{11}\\=\frac{231}{308}+\frac{352}{308}+\frac{224}{308}\\=\frac{231+352+224}{308}\\=\frac{807}{308}\)
11. \(-\left(\frac{7}{9}\right) +\left(\frac{3}{-5}\right) +\left(\frac{8}{5}\right)\\= \frac{-7}{9}- \frac{3}{5}+\frac{8}{5}\\=\frac{-35}{45}-\frac{27}{45}+\frac{72}{45}\\=\frac{-35-27+72}{45}\\=\frac{10}{45}\\=\frac{2}{9}\)
12. \(-\left(\frac{-6}{-7}\right) +\left(\frac{2}{6}\right) +\left(\frac{-9}{11}\right)\\= \frac{-6}{7}+ \frac{2}{6}-\frac{9}{11}\\=\frac{-6}{7}+\frac{1}{3}-\frac{9}{11}\\=\frac{-198}{231}+\frac{77}{231}-\frac{189}{231}\\=\frac{-198+77-189}{231}\\=\frac{-310}{231}\)