Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-4}{2}\right) -\left(\frac{-10}{-3}\right)\\= \frac{-3}{2}- \frac{4}{2}-\frac{10}{3}\\=\frac{-3}{2}-\frac{2}{1}-\frac{10}{3}\\=\frac{-9}{6}-\frac{12}{6}-\frac{20}{6}\\=\frac{-9-12-20}{6}\\=\frac{-41}{6}\)
2. \(+\left(\frac{3}{4}\right) -\left(\frac{6}{-9}\right) +\left(\frac{7}{-10}\right)\\= \frac{3}{4}+ \frac{6}{9}-\frac{7}{10}\\=\frac{3}{4}+\frac{2}{3}-\frac{7}{10}\\=\frac{45}{60}+\frac{40}{60}-\frac{42}{60}\\=\frac{45+40-42}{60}\\=\frac{43}{60}\)
3. \(-\left(\frac{-4}{-7}\right) -\left(\frac{5}{-10}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-4}{7}+ \frac{5}{10}+\frac{5}{9}\\=\frac{-4}{7}+\frac{1}{2}+\frac{5}{9}\\=\frac{-72}{126}+\frac{63}{126}+\frac{70}{126}\\=\frac{-72+63+70}{126}\\=\frac{61}{126}\)
4. \(-\left(\frac{-6}{5}\right) -\left(\frac{-7}{2}\right) +\left(\frac{-6}{-9}\right)\\= \frac{6}{5}+ \frac{7}{2}+\frac{6}{9}\\=\frac{6}{5}+\frac{7}{2}+\frac{2}{3}\\=\frac{36}{30}+\frac{105}{30}+\frac{20}{30}\\=\frac{36+105+20}{30}\\=\frac{161}{30}\)
5. \(-\left(\frac{4}{-3}\right) -\left(\frac{8}{-7}\right) +\left(\frac{-4}{7}\right)\\= \frac{4}{3}+ \frac{8}{7}-\frac{4}{7}\\=\frac{28}{21}+\frac{24}{21}-\frac{12}{21}\\=\frac{28+24-12}{21}\\=\frac{40}{21}\)
6. \(-\left(\frac{-5}{9}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-5}{-10}\right)\\= \frac{5}{9}+ \frac{6}{10}+\frac{5}{10}\\=\frac{5}{9}+\frac{3}{5}+\frac{1}{2}\\=\frac{50}{90}+\frac{54}{90}+\frac{45}{90}\\=\frac{50+54+45}{90}\\=\frac{149}{90}\)
7. \(+\left(\frac{-5}{6}\right) +\left(\frac{9}{-3}\right) -\left(\frac{12}{9}\right)\\= \frac{-5}{6}- \frac{9}{3}-\frac{12}{9}\\=\frac{-5}{6}-\frac{3}{1}-\frac{4}{3}\\=\frac{-5-3-4}{6}\\=\frac{-12}{6}\\=\frac{-2}{1}\)
8. \(+\left(\frac{7}{-2}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{4}{-6}\right)\\= \frac{-7}{2}+ \frac{8}{10}-\frac{4}{6}\\=\frac{-7}{2}+\frac{4}{5}-\frac{2}{3}\\=\frac{-105}{30}+\frac{24}{30}-\frac{20}{30}\\=\frac{-105+24-20}{30}\\=\frac{-101}{30}\)
9. \(-\left(\frac{4}{3}\right) -\left(\frac{8}{4}\right) -\left(\frac{10}{10}\right)\\= \frac{-4}{3}- \frac{8}{4}-\frac{10}{10}\\=\frac{-4}{3}-\frac{2}{1}-\frac{1}{1}\\=\frac{-4-2-1}{3}\\=\frac{-7}{3}\)
10. \(-\left(\frac{6}{7}\right) +\left(\frac{-5}{5}\right) -\left(\frac{-6}{11}\right)\\= \frac{-6}{7}- \frac{5}{5}+\frac{6}{11}\\=\frac{-6}{7}-\frac{1}{1}+\frac{6}{11}\\=\frac{-66}{77}-\frac{77}{77}+\frac{42}{77}\\=\frac{-66-77+42}{77}\\=\frac{-101}{77}\)
11. \(-\left(\frac{3}{7}\right) -\left(\frac{-2}{9}\right) -\left(\frac{4}{-4}\right)\\= \frac{-3}{7}+ \frac{2}{9}+\frac{4}{4}\\=\frac{-3}{7}+\frac{2}{9}+\frac{1}{1}\\=\frac{-27}{63}+\frac{14}{63}+\frac{63}{63}\\=\frac{-27+14+63}{63}\\=\frac{50}{63}\)
12. \(-\left(\frac{4}{3}\right) -\left(\frac{4}{6}\right) +\left(\frac{-10}{-9}\right)\\= \frac{-4}{3}- \frac{4}{6}+\frac{10}{9}\\=\frac{-4}{3}-\frac{2}{3}+\frac{10}{9}\\=\frac{-12}{9}-\frac{6}{9}+\frac{10}{9}\\=\frac{-12-6+10}{9}\\=\frac{-8}{9}\)