Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{2}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{5}{-9}\right)\\= \frac{-5}{2}+ \frac{8}{4}+\frac{5}{9}\\=\frac{-5}{2}+\frac{2}{1}+\frac{5}{9}\\=\frac{-45}{18}+\frac{36}{18}+\frac{10}{18}\\=\frac{-45+36+10}{18}\\=\frac{1}{18}\)
2. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{-8}\right) +\left(\frac{-2}{7}\right)\\= \frac{6}{5}+ \frac{6}{8}-\frac{2}{7}\\=\frac{6}{5}+\frac{3}{4}-\frac{2}{7}\\=\frac{168}{140}+\frac{105}{140}-\frac{40}{140}\\=\frac{168+105-40}{140}\\=\frac{233}{140}\)
3. \(-\left(\frac{4}{5}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{-11}{7}\right)\\= \frac{-4}{5}+ \frac{10}{4}-\frac{11}{7}\\=\frac{-4}{5}+\frac{5}{2}-\frac{11}{7}\\=\frac{-56}{70}+\frac{175}{70}-\frac{110}{70}\\=\frac{-56+175-110}{70}\\=\frac{9}{70}\)
4. \(-\left(\frac{-7}{9}\right) +\left(\frac{7}{-4}\right) -\left(\frac{4}{-11}\right)\\= \frac{7}{9}- \frac{7}{4}+\frac{4}{11}\\=\frac{308}{396}-\frac{693}{396}+\frac{144}{396}\\=\frac{308-693+144}{396}\\=\frac{-241}{396}\)
5. \(-\left(\frac{-4}{-5}\right) +\left(\frac{4}{-4}\right) -\left(\frac{-5}{5}\right)\\= \frac{-4}{5}- \frac{4}{4}+\frac{5}{5}\\=\frac{-4}{5}-\frac{1}{1}+\frac{1}{1}\\=\frac{-4-1+1}{5}\\=\frac{-4}{5}\)
6. \(+\left(\frac{-9}{-2}\right) -\left(\frac{4}{8}\right) +\left(\frac{12}{3}\right)\\= \frac{9}{2}- \frac{4}{8}+\frac{12}{3}\\=\frac{9}{2}-\frac{1}{2}+\frac{4}{1}\\=\frac{9-1+4}{2}\\=\frac{12}{2}\\=\frac{6}{1}\)
7. \(+\left(\frac{2}{-9}\right) +\left(\frac{10}{8}\right) -\left(\frac{12}{-9}\right)\\= \frac{-2}{9}+ \frac{10}{8}+\frac{12}{9}\\=\frac{-2}{9}+\frac{5}{4}+\frac{4}{3}\\=\frac{-8}{36}+\frac{45}{36}+\frac{48}{36}\\=\frac{-8+45+48}{36}\\=\frac{85}{36}\)
8. \(+\left(\frac{-3}{-7}\right) -\left(\frac{8}{-5}\right) +\left(\frac{9}{10}\right)\\= \frac{3}{7}+ \frac{8}{5}+\frac{9}{10}\\=\frac{30}{70}+\frac{112}{70}+\frac{63}{70}\\=\frac{30+112+63}{70}\\=\frac{205}{70}\\=\frac{41}{14}\)
9. \(+\left(\frac{-2}{9}\right) -\left(\frac{-5}{-3}\right) +\left(\frac{-10}{-7}\right)\\= \frac{-2}{9}- \frac{5}{3}+\frac{10}{7}\\=\frac{-14}{63}-\frac{105}{63}+\frac{90}{63}\\=\frac{-14-105+90}{63}\\=\frac{-29}{63}\)
10. \(-\left(\frac{-8}{-9}\right) -\left(\frac{10}{4}\right) +\left(\frac{-11}{-10}\right)\\= \frac{-8}{9}- \frac{10}{4}+\frac{11}{10}\\=\frac{-8}{9}-\frac{5}{2}+\frac{11}{10}\\=\frac{-80}{90}-\frac{225}{90}+\frac{99}{90}\\=\frac{-80-225+99}{90}\\=\frac{-206}{90}\\=\frac{-103}{45}\)
11. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{9}{-4}\right)\\= \frac{2}{3}- \frac{5}{3}+\frac{9}{4}\\=\frac{8}{12}-\frac{20}{12}+\frac{27}{12}\\=\frac{8-20+27}{12}\\=\frac{15}{12}\\=\frac{5}{4}\)
12. \(+\left(\frac{-6}{-7}\right) -\left(\frac{5}{-7}\right) -\left(\frac{7}{12}\right)\\= \frac{6}{7}+ \frac{5}{7}-\frac{7}{12}\\=\frac{72}{84}+\frac{60}{84}-\frac{49}{84}\\=\frac{72+60-49}{84}\\=\frac{83}{84}\)