Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{2}\right) -\left(\frac{3}{-9}\right) -\left(\frac{-7}{-5}\right)\\= \frac{5}{2}+ \frac{3}{9}-\frac{7}{5}\\=\frac{5}{2}+\frac{1}{3}-\frac{7}{5}\\=\frac{75}{30}+\frac{10}{30}-\frac{42}{30}\\=\frac{75+10-42}{30}\\=\frac{43}{30}\)
2. \(-\left(\frac{8}{9}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-11}{9}\right)\\= \frac{-8}{9}- \frac{3}{7}-\frac{11}{9}\\=\frac{-56}{63}-\frac{27}{63}-\frac{77}{63}\\=\frac{-56-27-77}{63}\\=\frac{-160}{63}\)
3. \(-\left(\frac{-5}{-2}\right) -\left(\frac{5}{8}\right) +\left(\frac{-4}{-6}\right)\\= \frac{-5}{2}- \frac{5}{8}+\frac{4}{6}\\=\frac{-5}{2}-\frac{5}{8}+\frac{2}{3}\\=\frac{-60}{24}-\frac{15}{24}+\frac{16}{24}\\=\frac{-60-15+16}{24}\\=\frac{-59}{24}\)
4. \(-\left(\frac{-2}{-7}\right) -\left(\frac{-10}{4}\right) -\left(\frac{4}{-3}\right)\\= \frac{-2}{7}+ \frac{10}{4}+\frac{4}{3}\\=\frac{-2}{7}+\frac{5}{2}+\frac{4}{3}\\=\frac{-12}{42}+\frac{105}{42}+\frac{56}{42}\\=\frac{-12+105+56}{42}\\=\frac{149}{42}\)
5. \(-\left(\frac{-5}{6}\right) +\left(\frac{-10}{2}\right) -\left(\frac{9}{11}\right)\\= \frac{5}{6}- \frac{10}{2}-\frac{9}{11}\\=\frac{5}{6}-\frac{5}{1}-\frac{9}{11}\\=\frac{55}{66}-\frac{330}{66}-\frac{54}{66}\\=\frac{55-330-54}{66}\\=\frac{-329}{66}\)
6. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{9}{12}\right)\\= \frac{2}{5}+ \frac{9}{9}+\frac{9}{12}\\=\frac{2}{5}+\frac{1}{1}+\frac{3}{4}\\=\frac{8}{20}+\frac{20}{20}+\frac{15}{20}\\=\frac{8+20+15}{20}\\=\frac{43}{20}\)
7. \(+\left(\frac{5}{7}\right) +\left(\frac{-6}{5}\right) +\left(\frac{-6}{-5}\right)\\= \frac{5}{7}- \frac{6}{5}+\frac{6}{5}\\=\frac{25}{35}-\frac{42}{35}+\frac{42}{35}\\=\frac{25-42+42}{35}\\=\frac{25}{35}\\=\frac{5}{7}\)
8. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{-7}{9}\right)\\= \frac{-3}{2}- \frac{4}{10}+\frac{7}{9}\\=\frac{-3}{2}-\frac{2}{5}+\frac{7}{9}\\=\frac{-135}{90}-\frac{36}{90}+\frac{70}{90}\\=\frac{-135-36+70}{90}\\=\frac{-101}{90}\)
9. \(+\left(\frac{-10}{-7}\right) +\left(\frac{7}{-9}\right) +\left(\frac{-7}{-5}\right)\\= \frac{10}{7}- \frac{7}{9}+\frac{7}{5}\\=\frac{450}{315}-\frac{245}{315}+\frac{441}{315}\\=\frac{450-245+441}{315}\\=\frac{646}{315}\)
10. \(-\left(\frac{6}{-7}\right) +\left(\frac{-10}{-8}\right) -\left(\frac{11}{-4}\right)\\= \frac{6}{7}+ \frac{10}{8}+\frac{11}{4}\\=\frac{6}{7}+\frac{5}{4}+\frac{11}{4}\\=\frac{24}{28}+\frac{35}{28}+\frac{77}{28}\\=\frac{24+35+77}{28}\\=\frac{136}{28}\\=\frac{34}{7}\)
11. \(-\left(\frac{7}{3}\right) +\left(\frac{-8}{7}\right) +\left(\frac{12}{-2}\right)\\= \frac{-7}{3}- \frac{8}{7}-\frac{12}{2}\\=\frac{-7}{3}-\frac{8}{7}-\frac{6}{1}\\=\frac{-49}{21}-\frac{24}{21}-\frac{126}{21}\\=\frac{-49-24-126}{21}\\=\frac{-199}{21}\)
12. \(-\left(\frac{4}{-5}\right) -\left(\frac{-2}{-9}\right) +\left(\frac{-12}{-8}\right)\\= \frac{4}{5}- \frac{2}{9}+\frac{12}{8}\\=\frac{4}{5}-\frac{2}{9}+\frac{3}{2}\\=\frac{72}{90}-\frac{20}{90}+\frac{135}{90}\\=\frac{72-20+135}{90}\\=\frac{187}{90}\)