Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-3}\right) +\left(\frac{2}{9}\right) -\left(\frac{-12}{12}\right)\\= \frac{-8}{3}+ \frac{2}{9}+\frac{12}{12}\\=\frac{-8}{3}+\frac{2}{9}+\frac{1}{1}\\=\frac{-24}{9}+\frac{2}{9}+\frac{9}{9}\\=\frac{-24+2+9}{9}\\=\frac{-13}{9}\)
2. \(+\left(\frac{-4}{3}\right) +\left(\frac{-8}{4}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-4}{3}- \frac{8}{4}-\frac{5}{3}\\=\frac{-4}{3}-\frac{2}{1}-\frac{5}{3}\\=\frac{-4-2-5}{3}\\=\frac{-11}{3}\)
3. \(+\left(\frac{3}{7}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{5}{-4}\right)\\= \frac{3}{7}+ \frac{7}{8}-\frac{5}{4}\\=\frac{24}{56}+\frac{49}{56}-\frac{70}{56}\\=\frac{24+49-70}{56}\\=\frac{3}{56}\)
4. \(+\left(\frac{4}{-3}\right) -\left(\frac{4}{8}\right) -\left(\frac{-7}{4}\right)\\= \frac{-4}{3}- \frac{4}{8}+\frac{7}{4}\\=\frac{-4}{3}-\frac{1}{2}+\frac{7}{4}\\=\frac{-16}{12}-\frac{6}{12}+\frac{21}{12}\\=\frac{-16-6+21}{12}\\=\frac{-1}{12}\)
5. \(+\left(\frac{6}{-7}\right) +\left(\frac{-4}{-10}\right) -\left(\frac{-12}{-10}\right)\\= \frac{-6}{7}+ \frac{4}{10}-\frac{12}{10}\\=\frac{-6}{7}+\frac{2}{5}-\frac{6}{5}\\=\frac{-30}{35}+\frac{14}{35}-\frac{42}{35}\\=\frac{-30+14-42}{35}\\=\frac{-58}{35}\)
6. \(-\left(\frac{-4}{7}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{-7}{2}\right)\\= \frac{4}{7}- \frac{6}{7}-\frac{7}{2}\\=\frac{8}{14}-\frac{12}{14}-\frac{49}{14}\\=\frac{8-12-49}{14}\\=\frac{-53}{14}\)
7. \(+\left(\frac{-6}{5}\right) +\left(\frac{4}{-4}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-6}{5}- \frac{4}{4}+\frac{9}{2}\\=\frac{-6}{5}-\frac{1}{1}+\frac{9}{2}\\=\frac{-12}{10}-\frac{10}{10}+\frac{45}{10}\\=\frac{-12-10+45}{10}\\=\frac{23}{10}\)
8. \(-\left(\frac{10}{7}\right) -\left(\frac{9}{-7}\right) -\left(\frac{-7}{12}\right)\\= \frac{-10}{7}+ \frac{9}{7}+\frac{7}{12}\\=\frac{-120}{84}+\frac{108}{84}+\frac{49}{84}\\=\frac{-120+108+49}{84}\\=\frac{37}{84}\)
9. \(+\left(\frac{-7}{9}\right) +\left(\frac{-9}{7}\right) -\left(\frac{-10}{-11}\right)\\= \frac{-7}{9}- \frac{9}{7}-\frac{10}{11}\\=\frac{-539}{693}-\frac{891}{693}-\frac{630}{693}\\=\frac{-539-891-630}{693}\\=\frac{-2060}{693}\)
10. \(+\left(\frac{4}{3}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{-9}{11}\right)\\= \frac{4}{3}+ \frac{10}{8}-\frac{9}{11}\\=\frac{4}{3}+\frac{5}{4}-\frac{9}{11}\\=\frac{176}{132}+\frac{165}{132}-\frac{108}{132}\\=\frac{176+165-108}{132}\\=\frac{233}{132}\)
11. \(+\left(\frac{4}{-9}\right) +\left(\frac{-8}{2}\right) +\left(\frac{12}{7}\right)\\= \frac{-4}{9}- \frac{8}{2}+\frac{12}{7}\\=\frac{-4}{9}-\frac{4}{1}+\frac{12}{7}\\=\frac{-28}{63}-\frac{252}{63}+\frac{108}{63}\\=\frac{-28-252+108}{63}\\=\frac{-172}{63}\)
12. \(+\left(\frac{8}{5}\right) +\left(\frac{4}{2}\right) +\left(\frac{-12}{-12}\right)\\= \frac{8}{5}+ \frac{4}{2}+\frac{12}{12}\\=\frac{8}{5}+\frac{2}{1}+\frac{1}{1}\\=\frac{8+2+1}{5}\\=\frac{11}{5}\)