Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-3}\right) -\left(\frac{-9}{10}\right) -\left(\frac{2}{-11}\right)\\= \frac{7}{3}+ \frac{9}{10}+\frac{2}{11}\\=\frac{770}{330}+\frac{297}{330}+\frac{60}{330}\\=\frac{770+297+60}{330}\\=\frac{1127}{330}\)
2. \(-\left(\frac{2}{-3}\right) +\left(\frac{2}{8}\right) -\left(\frac{-12}{11}\right)\\= \frac{2}{3}+ \frac{2}{8}+\frac{12}{11}\\=\frac{2}{3}+\frac{1}{4}+\frac{12}{11}\\=\frac{88}{132}+\frac{33}{132}+\frac{144}{132}\\=\frac{88+33+144}{132}\\=\frac{265}{132}\)
3. \(+\left(\frac{-5}{-7}\right) -\left(\frac{4}{-3}\right) +\left(\frac{-7}{-5}\right)\\= \frac{5}{7}+ \frac{4}{3}+\frac{7}{5}\\=\frac{75}{105}+\frac{140}{105}+\frac{147}{105}\\=\frac{75+140+147}{105}\\=\frac{362}{105}\)
4. \(-\left(\frac{3}{2}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{-3}{12}\right)\\= \frac{-3}{2}- \frac{10}{2}+\frac{3}{12}\\=\frac{-3}{2}-\frac{5}{1}+\frac{1}{4}\\=\frac{-6}{4}-\frac{20}{4}+\frac{1}{4}\\=\frac{-6-20+1}{4}\\=\frac{-25}{4}\)
5. \(+\left(\frac{2}{-5}\right) -\left(\frac{4}{-3}\right) -\left(\frac{7}{5}\right)\\= \frac{-2}{5}+ \frac{4}{3}-\frac{7}{5}\\=\frac{-6}{15}+\frac{20}{15}-\frac{21}{15}\\=\frac{-6+20-21}{15}\\=\frac{-7}{15}\)
6. \(-\left(\frac{-3}{7}\right) -\left(\frac{-9}{8}\right) -\left(\frac{4}{-9}\right)\\= \frac{3}{7}+ \frac{9}{8}+\frac{4}{9}\\=\frac{216}{504}+\frac{567}{504}+\frac{224}{504}\\=\frac{216+567+224}{504}\\=\frac{1007}{504}\)
7. \(+\left(\frac{7}{-2}\right) +\left(\frac{7}{3}\right) -\left(\frac{7}{-9}\right)\\= \frac{-7}{2}+ \frac{7}{3}+\frac{7}{9}\\=\frac{-63}{18}+\frac{42}{18}+\frac{14}{18}\\=\frac{-63+42+14}{18}\\=\frac{-7}{18}\)
8. \(-\left(\frac{-9}{-8}\right) -\left(\frac{3}{-7}\right) -\left(\frac{-4}{4}\right)\\= \frac{-9}{8}+ \frac{3}{7}+\frac{4}{4}\\=\frac{-9}{8}+\frac{3}{7}+\frac{1}{1}\\=\frac{-63}{56}+\frac{24}{56}+\frac{56}{56}\\=\frac{-63+24+56}{56}\\=\frac{17}{56}\)
9. \(-\left(\frac{-6}{-5}\right) -\left(\frac{8}{2}\right) +\left(\frac{-10}{-7}\right)\\= \frac{-6}{5}- \frac{8}{2}+\frac{10}{7}\\=\frac{-6}{5}-\frac{4}{1}+\frac{10}{7}\\=\frac{-42}{35}-\frac{140}{35}+\frac{50}{35}\\=\frac{-42-140+50}{35}\\=\frac{-132}{35}\)
10. \(+\left(\frac{-3}{7}\right) -\left(\frac{-9}{10}\right) -\left(\frac{2}{3}\right)\\= \frac{-3}{7}+ \frac{9}{10}-\frac{2}{3}\\=\frac{-90}{210}+\frac{189}{210}-\frac{140}{210}\\=\frac{-90+189-140}{210}\\=\frac{-41}{210}\)
11. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-6}{8}\right) +\left(\frac{7}{-9}\right)\\= \frac{-10}{3}- \frac{6}{8}-\frac{7}{9}\\=\frac{-10}{3}-\frac{3}{4}-\frac{7}{9}\\=\frac{-120}{36}-\frac{27}{36}-\frac{28}{36}\\=\frac{-120-27-28}{36}\\=\frac{-175}{36}\)
12. \(-\left(\frac{-4}{7}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{-3}{-7}\right)\\= \frac{4}{7}- \frac{7}{9}+\frac{3}{7}\\=\frac{36}{63}-\frac{49}{63}+\frac{27}{63}\\=\frac{36-49+27}{63}\\=\frac{14}{63}\\=\frac{2}{9}\)