Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-4}\right) +\left(\frac{4}{4}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-9}{4}+ \frac{4}{4}-\frac{5}{3}\\=\frac{-9}{4}+\frac{1}{1}-\frac{5}{3}\\=\frac{-27}{12}+\frac{12}{12}-\frac{20}{12}\\=\frac{-27+12-20}{12}\\=\frac{-35}{12}\)
2. \(+\left(\frac{7}{2}\right) +\left(\frac{-7}{8}\right) -\left(\frac{2}{-2}\right)\\= \frac{7}{2}- \frac{7}{8}+\frac{2}{2}\\=\frac{7}{2}-\frac{7}{8}+\frac{1}{1}\\=\frac{28}{8}-\frac{7}{8}+\frac{8}{8}\\=\frac{28-7+8}{8}\\=\frac{29}{8}\)
3. \(-\left(\frac{-10}{9}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{-8}{10}\right)\\= \frac{10}{9}+ \frac{2}{2}-\frac{8}{10}\\=\frac{10}{9}+\frac{1}{1}-\frac{4}{5}\\=\frac{50}{45}+\frac{45}{45}-\frac{36}{45}\\=\frac{50+45-36}{45}\\=\frac{59}{45}\)
4. \(-\left(\frac{-3}{-7}\right) +\left(\frac{-8}{-6}\right) -\left(\frac{-2}{11}\right)\\= \frac{-3}{7}+ \frac{8}{6}+\frac{2}{11}\\=\frac{-3}{7}+\frac{4}{3}+\frac{2}{11}\\=\frac{-99}{231}+\frac{308}{231}+\frac{42}{231}\\=\frac{-99+308+42}{231}\\=\frac{251}{231}\)
5. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-2}{5}\right) +\left(\frac{-11}{-10}\right)\\= \frac{2}{9}- \frac{2}{5}+\frac{11}{10}\\=\frac{20}{90}-\frac{36}{90}+\frac{99}{90}\\=\frac{20-36+99}{90}\\=\frac{83}{90}\)
6. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{4}{-8}\right)\\= \frac{6}{5}- \frac{8}{6}-\frac{4}{8}\\=\frac{6}{5}-\frac{4}{3}-\frac{1}{2}\\=\frac{36}{30}-\frac{40}{30}-\frac{15}{30}\\=\frac{36-40-15}{30}\\=\frac{-19}{30}\)
7. \(+\left(\frac{-4}{7}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{12}{-12}\right)\\= \frac{-4}{7}+ \frac{8}{5}-\frac{12}{12}\\=\frac{-4}{7}+\frac{8}{5}-\frac{1}{1}\\=\frac{-20}{35}+\frac{56}{35}-\frac{35}{35}\\=\frac{-20+56-35}{35}\\=\frac{1}{35}\)
8. \(-\left(\frac{7}{-2}\right) +\left(\frac{7}{6}\right) +\left(\frac{3}{-12}\right)\\= \frac{7}{2}+ \frac{7}{6}-\frac{3}{12}\\=\frac{7}{2}+\frac{7}{6}-\frac{1}{4}\\=\frac{42}{12}+\frac{14}{12}-\frac{3}{12}\\=\frac{42+14-3}{12}\\=\frac{53}{12}\)
9. \(+\left(\frac{3}{4}\right) +\left(\frac{8}{7}\right) -\left(\frac{-4}{-10}\right)\\= \frac{3}{4}+ \frac{8}{7}-\frac{4}{10}\\=\frac{3}{4}+\frac{8}{7}-\frac{2}{5}\\=\frac{105}{140}+\frac{160}{140}-\frac{56}{140}\\=\frac{105+160-56}{140}\\=\frac{209}{140}\)
10. \(+\left(\frac{-2}{7}\right) -\left(\frac{-10}{-6}\right) -\left(\frac{8}{5}\right)\\= \frac{-2}{7}- \frac{10}{6}-\frac{8}{5}\\=\frac{-2}{7}-\frac{5}{3}-\frac{8}{5}\\=\frac{-30}{105}-\frac{175}{105}-\frac{168}{105}\\=\frac{-30-175-168}{105}\\=\frac{-373}{105}\)
11. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-7}{10}\right) +\left(\frac{9}{5}\right)\\= \frac{-3}{7}+ \frac{7}{10}+\frac{9}{5}\\=\frac{-30}{70}+\frac{49}{70}+\frac{126}{70}\\=\frac{-30+49+126}{70}\\=\frac{145}{70}\\=\frac{29}{14}\)
12. \(-\left(\frac{-3}{4}\right) -\left(\frac{2}{-9}\right) +\left(\frac{-6}{11}\right)\\= \frac{3}{4}+ \frac{2}{9}-\frac{6}{11}\\=\frac{297}{396}+\frac{88}{396}-\frac{216}{396}\\=\frac{297+88-216}{396}\\=\frac{169}{396}\)