Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-8}\right) +\left(\frac{9}{4}\right) +\left(\frac{8}{5}\right)\\= \frac{7}{8}+ \frac{9}{4}+\frac{8}{5}\\=\frac{35}{40}+\frac{90}{40}+\frac{64}{40}\\=\frac{35+90+64}{40}\\=\frac{189}{40}\)
2. \(+\left(\frac{-9}{2}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{5}{5}\right)\\= \frac{-9}{2}+ \frac{9}{8}+\frac{5}{5}\\=\frac{-9}{2}+\frac{9}{8}+\frac{1}{1}\\=\frac{-36}{8}+\frac{9}{8}+\frac{8}{8}\\=\frac{-36+9+8}{8}\\=\frac{-19}{8}\)
3. \(+\left(\frac{8}{3}\right) +\left(\frac{-4}{6}\right) -\left(\frac{3}{11}\right)\\= \frac{8}{3}- \frac{4}{6}-\frac{3}{11}\\=\frac{8}{3}-\frac{2}{3}-\frac{3}{11}\\=\frac{88}{33}-\frac{22}{33}-\frac{9}{33}\\=\frac{88-22-9}{33}\\=\frac{57}{33}\\=\frac{19}{11}\)
4. \(-\left(\frac{-9}{-2}\right) -\left(\frac{-3}{-7}\right) +\left(\frac{9}{-7}\right)\\= \frac{-9}{2}- \frac{3}{7}-\frac{9}{7}\\=\frac{-63}{14}-\frac{6}{14}-\frac{18}{14}\\=\frac{-63-6-18}{14}\\=\frac{-87}{14}\)
5. \(-\left(\frac{9}{2}\right) +\left(\frac{4}{6}\right) +\left(\frac{3}{5}\right)\\= \frac{-9}{2}+ \frac{4}{6}+\frac{3}{5}\\=\frac{-9}{2}+\frac{2}{3}+\frac{3}{5}\\=\frac{-135}{30}+\frac{20}{30}+\frac{18}{30}\\=\frac{-135+20+18}{30}\\=\frac{-97}{30}\)
6. \(-\left(\frac{4}{9}\right) +\left(\frac{-2}{-10}\right) -\left(\frac{7}{4}\right)\\= \frac{-4}{9}+ \frac{2}{10}-\frac{7}{4}\\=\frac{-4}{9}+\frac{1}{5}-\frac{7}{4}\\=\frac{-80}{180}+\frac{36}{180}-\frac{315}{180}\\=\frac{-80+36-315}{180}\\=\frac{-359}{180}\)
7. \(+\left(\frac{2}{-5}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{5}{-6}\right)\\= \frac{-2}{5}+ \frac{4}{9}-\frac{5}{6}\\=\frac{-36}{90}+\frac{40}{90}-\frac{75}{90}\\=\frac{-36+40-75}{90}\\=\frac{-71}{90}\)
8. \(+\left(\frac{-7}{-8}\right) -\left(\frac{6}{-8}\right) -\left(\frac{-7}{6}\right)\\= \frac{7}{8}+ \frac{6}{8}+\frac{7}{6}\\=\frac{7}{8}+\frac{3}{4}+\frac{7}{6}\\=\frac{21}{24}+\frac{18}{24}+\frac{28}{24}\\=\frac{21+18+28}{24}\\=\frac{67}{24}\)
9. \(+\left(\frac{-4}{9}\right) +\left(\frac{2}{4}\right) +\left(\frac{11}{7}\right)\\= \frac{-4}{9}+ \frac{2}{4}+\frac{11}{7}\\=\frac{-4}{9}+\frac{1}{2}+\frac{11}{7}\\=\frac{-56}{126}+\frac{63}{126}+\frac{198}{126}\\=\frac{-56+63+198}{126}\\=\frac{205}{126}\)
10. \(-\left(\frac{4}{-5}\right) +\left(\frac{2}{2}\right) -\left(\frac{12}{9}\right)\\= \frac{4}{5}+ \frac{2}{2}-\frac{12}{9}\\=\frac{4}{5}+\frac{1}{1}-\frac{4}{3}\\=\frac{12}{15}+\frac{15}{15}-\frac{20}{15}\\=\frac{12+15-20}{15}\\=\frac{7}{15}\)
11. \(-\left(\frac{9}{4}\right) +\left(\frac{10}{-9}\right) -\left(\frac{-5}{-12}\right)\\= \frac{-9}{4}- \frac{10}{9}-\frac{5}{12}\\=\frac{-81}{36}-\frac{40}{36}-\frac{15}{36}\\=\frac{-81-40-15}{36}\\=\frac{-136}{36}\\=\frac{-34}{9}\)
12. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-7}{-2}\right) -\left(\frac{-2}{5}\right)\\= \frac{-10}{3}- \frac{7}{2}+\frac{2}{5}\\=\frac{-100}{30}-\frac{105}{30}+\frac{12}{30}\\=\frac{-100-105+12}{30}\\=\frac{-193}{30}\)