Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{3}\right) +\left(\frac{10}{-4}\right) +\left(\frac{8}{6}\right)\\= \frac{-4}{3}- \frac{10}{4}+\frac{8}{6}\\=\frac{-4}{3}-\frac{5}{2}+\frac{4}{3}\\=\frac{-8}{6}-\frac{15}{6}+\frac{8}{6}\\=\frac{-8-15+8}{6}\\=\frac{-15}{6}\\=\frac{-5}{2}\)
2. \(-\left(\frac{3}{-4}\right) +\left(\frac{6}{-6}\right) +\left(\frac{9}{5}\right)\\= \frac{3}{4}- \frac{6}{6}+\frac{9}{5}\\=\frac{3}{4}-\frac{1}{1}+\frac{9}{5}\\=\frac{15}{20}-\frac{20}{20}+\frac{36}{20}\\=\frac{15-20+36}{20}\\=\frac{31}{20}\)
3. \(+\left(\frac{-3}{-7}\right) +\left(\frac{6}{-9}\right) -\left(\frac{-8}{-2}\right)\\= \frac{3}{7}- \frac{6}{9}-\frac{8}{2}\\=\frac{3}{7}-\frac{2}{3}-\frac{4}{1}\\=\frac{9}{21}-\frac{14}{21}-\frac{84}{21}\\=\frac{9-14-84}{21}\\=\frac{-89}{21}\)
4. \(+\left(\frac{7}{-2}\right) -\left(\frac{-8}{3}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-7}{2}+ \frac{8}{3}+\frac{10}{4}\\=\frac{-7}{2}+\frac{8}{3}+\frac{5}{2}\\=\frac{-21}{6}+\frac{16}{6}+\frac{15}{6}\\=\frac{-21+16+15}{6}\\=\frac{10}{6}\\=\frac{5}{3}\)
5. \(-\left(\frac{3}{4}\right) +\left(\frac{-8}{4}\right) +\left(\frac{11}{12}\right)\\= \frac{-3}{4}- \frac{8}{4}+\frac{11}{12}\\=\frac{-3}{4}-\frac{2}{1}+\frac{11}{12}\\=\frac{-9}{12}-\frac{24}{12}+\frac{11}{12}\\=\frac{-9-24+11}{12}\\=\frac{-22}{12}\\=\frac{-11}{6}\)
6. \(+\left(\frac{7}{-8}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{6}{-9}\right)\\= \frac{-7}{8}- \frac{5}{7}+\frac{6}{9}\\=\frac{-7}{8}-\frac{5}{7}+\frac{2}{3}\\=\frac{-147}{168}-\frac{120}{168}+\frac{112}{168}\\=\frac{-147-120+112}{168}\\=\frac{-155}{168}\)
7. \(+\left(\frac{-5}{-8}\right) +\left(\frac{-8}{-9}\right) -\left(\frac{12}{12}\right)\\= \frac{5}{8}+ \frac{8}{9}-\frac{12}{12}\\=\frac{5}{8}+\frac{8}{9}-\frac{1}{1}\\=\frac{45}{72}+\frac{64}{72}-\frac{72}{72}\\=\frac{45+64-72}{72}\\=\frac{37}{72}\)
8. \(-\left(\frac{-9}{2}\right) -\left(\frac{7}{10}\right) -\left(\frac{-7}{-9}\right)\\= \frac{9}{2}- \frac{7}{10}-\frac{7}{9}\\=\frac{405}{90}-\frac{63}{90}-\frac{70}{90}\\=\frac{405-63-70}{90}\\=\frac{272}{90}\\=\frac{136}{45}\)
9. \(+\left(\frac{-3}{4}\right) -\left(\frac{-10}{2}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-3}{4}+ \frac{10}{2}-\frac{3}{5}\\=\frac{-3}{4}+\frac{5}{1}-\frac{3}{5}\\=\frac{-15}{20}+\frac{100}{20}-\frac{12}{20}\\=\frac{-15+100-12}{20}\\=\frac{73}{20}\)
10. \(+\left(\frac{-4}{-7}\right) +\left(\frac{6}{7}\right) +\left(\frac{-10}{2}\right)\\= \frac{4}{7}+ \frac{6}{7}-\frac{10}{2}\\=\frac{4}{7}+\frac{6}{7}-\frac{5}{1}\\=\frac{4+6-5}{7}\\=\frac{5}{7}\)
11. \(+\left(\frac{-9}{2}\right) -\left(\frac{-8}{4}\right) -\left(\frac{-9}{8}\right)\\= \frac{-9}{2}+ \frac{8}{4}+\frac{9}{8}\\=\frac{-9}{2}+\frac{2}{1}+\frac{9}{8}\\=\frac{-36}{8}+\frac{16}{8}+\frac{9}{8}\\=\frac{-36+16+9}{8}\\=\frac{-11}{8}\)
12. \(-\left(\frac{5}{3}\right) +\left(\frac{5}{-5}\right) -\left(\frac{2}{2}\right)\\= \frac{-5}{3}- \frac{5}{5}-\frac{2}{2}\\=\frac{-5}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{-5-1-1}{3}\\=\frac{-7}{3}\)