Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) +\left(\frac{9}{6}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-6}{5}+ \frac{9}{6}-\frac{12}{4}\\=\frac{-6}{5}+\frac{3}{2}-\frac{3}{1}\\=\frac{-12}{10}+\frac{15}{10}-\frac{30}{10}\\=\frac{-12+15-30}{10}\\=\frac{-27}{10}\)
2. \(+\left(\frac{9}{-4}\right) +\left(\frac{-4}{6}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-9}{4}- \frac{4}{6}+\frac{4}{2}\\=\frac{-9}{4}-\frac{2}{3}+\frac{2}{1}\\=\frac{-27}{12}-\frac{8}{12}+\frac{24}{12}\\=\frac{-27-8+24}{12}\\=\frac{-11}{12}\)
3. \(-\left(\frac{-10}{3}\right) +\left(\frac{8}{5}\right) -\left(\frac{-3}{9}\right)\\= \frac{10}{3}+ \frac{8}{5}+\frac{3}{9}\\=\frac{10}{3}+\frac{8}{5}+\frac{1}{3}\\=\frac{50}{15}+\frac{24}{15}+\frac{5}{15}\\=\frac{50+24+5}{15}\\=\frac{79}{15}\)
4. \(+\left(\frac{9}{-4}\right) -\left(\frac{-10}{-9}\right) -\left(\frac{2}{-6}\right)\\= \frac{-9}{4}- \frac{10}{9}+\frac{2}{6}\\=\frac{-9}{4}-\frac{10}{9}+\frac{1}{3}\\=\frac{-81}{36}-\frac{40}{36}+\frac{12}{36}\\=\frac{-81-40+12}{36}\\=\frac{-109}{36}\)
5. \(-\left(\frac{3}{2}\right) +\left(\frac{5}{-3}\right) +\left(\frac{7}{8}\right)\\= \frac{-3}{2}- \frac{5}{3}+\frac{7}{8}\\=\frac{-36}{24}-\frac{40}{24}+\frac{21}{24}\\=\frac{-36-40+21}{24}\\=\frac{-55}{24}\)
6. \(-\left(\frac{3}{2}\right) +\left(\frac{-5}{2}\right) -\left(\frac{5}{12}\right)\\= \frac{-3}{2}- \frac{5}{2}-\frac{5}{12}\\=\frac{-18}{12}-\frac{30}{12}-\frac{5}{12}\\=\frac{-18-30-5}{12}\\=\frac{-53}{12}\)
7. \(+\left(\frac{9}{-4}\right) +\left(\frac{-6}{5}\right) -\left(\frac{3}{-2}\right)\\= \frac{-9}{4}- \frac{6}{5}+\frac{3}{2}\\=\frac{-45}{20}-\frac{24}{20}+\frac{30}{20}\\=\frac{-45-24+30}{20}\\=\frac{-39}{20}\)
8. \(-\left(\frac{-4}{3}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{3}{-11}\right)\\= \frac{4}{3}+ \frac{8}{3}-\frac{3}{11}\\=\frac{44}{33}+\frac{88}{33}-\frac{9}{33}\\=\frac{44+88-9}{33}\\=\frac{123}{33}\\=\frac{41}{11}\)
9. \(+\left(\frac{-9}{2}\right) +\left(\frac{-3}{-10}\right) -\left(\frac{-5}{9}\right)\\= \frac{-9}{2}+ \frac{3}{10}+\frac{5}{9}\\=\frac{-405}{90}+\frac{27}{90}+\frac{50}{90}\\=\frac{-405+27+50}{90}\\=\frac{-328}{90}\\=\frac{-164}{45}\)
10. \(-\left(\frac{2}{-5}\right) -\left(\frac{-2}{7}\right) +\left(\frac{10}{9}\right)\\= \frac{2}{5}+ \frac{2}{7}+\frac{10}{9}\\=\frac{126}{315}+\frac{90}{315}+\frac{350}{315}\\=\frac{126+90+350}{315}\\=\frac{566}{315}\)
11. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-5}{-3}\right) +\left(\frac{2}{-7}\right)\\= \frac{10}{9}- \frac{5}{3}-\frac{2}{7}\\=\frac{70}{63}-\frac{105}{63}-\frac{18}{63}\\=\frac{70-105-18}{63}\\=\frac{-53}{63}\)
12. \(+\left(\frac{6}{5}\right) -\left(\frac{-10}{2}\right) +\left(\frac{-11}{-6}\right)\\= \frac{6}{5}+ \frac{10}{2}+\frac{11}{6}\\=\frac{6}{5}+\frac{5}{1}+\frac{11}{6}\\=\frac{36}{30}+\frac{150}{30}+\frac{55}{30}\\=\frac{36+150+55}{30}\\=\frac{241}{30}\)