Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{5}{2}\right) -\left(\frac{-4}{8}\right) -\left(\frac{-9}{6}\right)\\= \frac{5}{2}+ \frac{4}{8}+\frac{9}{6}\\=\frac{5}{2}+\frac{1}{2}+\frac{3}{2}\\=\frac{5+1+3}{2}\\=\frac{9}{2}\)
2. \(+\left(\frac{6}{-5}\right) +\left(\frac{3}{10}\right) +\left(\frac{-6}{8}\right)\\= \frac{-6}{5}+ \frac{3}{10}-\frac{6}{8}\\=\frac{-6}{5}+\frac{3}{10}-\frac{3}{4}\\=\frac{-24}{20}+\frac{6}{20}-\frac{15}{20}\\=\frac{-24+6-15}{20}\\=\frac{-33}{20}\)
3. \(-\left(\frac{10}{3}\right) +\left(\frac{-7}{10}\right) -\left(\frac{-6}{-6}\right)\\= \frac{-10}{3}- \frac{7}{10}-\frac{6}{6}\\=\frac{-10}{3}-\frac{7}{10}-\frac{1}{1}\\=\frac{-100}{30}-\frac{21}{30}-\frac{30}{30}\\=\frac{-100-21-30}{30}\\=\frac{-151}{30}\)
4. \(+\left(\frac{4}{-7}\right) +\left(\frac{-6}{-3}\right) +\left(\frac{11}{12}\right)\\= \frac{-4}{7}+ \frac{6}{3}+\frac{11}{12}\\=\frac{-4}{7}+\frac{2}{1}+\frac{11}{12}\\=\frac{-48}{84}+\frac{168}{84}+\frac{77}{84}\\=\frac{-48+168+77}{84}\\=\frac{197}{84}\)
5. \(+\left(\frac{4}{-3}\right) +\left(\frac{5}{-5}\right) -\left(\frac{-5}{6}\right)\\= \frac{-4}{3}- \frac{5}{5}+\frac{5}{6}\\=\frac{-4}{3}-\frac{1}{1}+\frac{5}{6}\\=\frac{-8}{6}-\frac{6}{6}+\frac{5}{6}\\=\frac{-8-6+5}{6}\\=\frac{-9}{6}\\=\frac{-3}{2}\)
6. \(-\left(\frac{4}{7}\right) +\left(\frac{-4}{5}\right) +\left(\frac{11}{9}\right)\\= \frac{-4}{7}- \frac{4}{5}+\frac{11}{9}\\=\frac{-180}{315}-\frac{252}{315}+\frac{385}{315}\\=\frac{-180-252+385}{315}\\=\frac{-47}{315}\)
7. \(+\left(\frac{5}{4}\right) -\left(\frac{7}{-3}\right) +\left(\frac{-11}{-10}\right)\\= \frac{5}{4}+ \frac{7}{3}+\frac{11}{10}\\=\frac{75}{60}+\frac{140}{60}+\frac{66}{60}\\=\frac{75+140+66}{60}\\=\frac{281}{60}\)
8. \(+\left(\frac{-4}{5}\right) -\left(\frac{-9}{-4}\right) -\left(\frac{-10}{11}\right)\\= \frac{-4}{5}- \frac{9}{4}+\frac{10}{11}\\=\frac{-176}{220}-\frac{495}{220}+\frac{200}{220}\\=\frac{-176-495+200}{220}\\=\frac{-471}{220}\)
9. \(-\left(\frac{-10}{9}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{-11}{-8}\right)\\= \frac{10}{9}- \frac{3}{3}-\frac{11}{8}\\=\frac{10}{9}-\frac{1}{1}-\frac{11}{8}\\=\frac{80}{72}-\frac{72}{72}-\frac{99}{72}\\=\frac{80-72-99}{72}\\=\frac{-91}{72}\)
10. \(+\left(\frac{8}{3}\right) +\left(\frac{-4}{8}\right) -\left(\frac{-2}{-4}\right)\\= \frac{8}{3}- \frac{4}{8}-\frac{2}{4}\\=\frac{8}{3}-\frac{1}{2}-\frac{1}{2}\\=\frac{16}{6}-\frac{3}{6}-\frac{3}{6}\\=\frac{16-3-3}{6}\\=\frac{10}{6}\\=\frac{5}{3}\)
11. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{-9}{9}\right)\\= \frac{8}{7}+ \frac{9}{3}+\frac{9}{9}\\=\frac{8}{7}+\frac{3}{1}+\frac{1}{1}\\=\frac{8+3+1}{7}\\=\frac{12}{7}\)
12. \(+\left(\frac{10}{-9}\right) +\left(\frac{2}{-4}\right) -\left(\frac{9}{9}\right)\\= \frac{-10}{9}- \frac{2}{4}-\frac{9}{9}\\=\frac{-10}{9}-\frac{1}{2}-\frac{1}{1}\\=\frac{-20}{18}-\frac{9}{18}-\frac{18}{18}\\=\frac{-20-9-18}{18}\\=\frac{-47}{18}\)