Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{2}\right) -\left(\frac{10}{-8}\right) +\left(\frac{-2}{-3}\right)\\= \frac{-9}{2}+ \frac{10}{8}+\frac{2}{3}\\=\frac{-9}{2}+\frac{5}{4}+\frac{2}{3}\\=\frac{-54}{12}+\frac{15}{12}+\frac{8}{12}\\=\frac{-54+15+8}{12}\\=\frac{-31}{12}\)
2. \(-\left(\frac{9}{4}\right) -\left(\frac{8}{5}\right) -\left(\frac{-12}{2}\right)\\= \frac{-9}{4}- \frac{8}{5}+\frac{12}{2}\\=\frac{-9}{4}-\frac{8}{5}+\frac{6}{1}\\=\frac{-45}{20}-\frac{32}{20}+\frac{120}{20}\\=\frac{-45-32+120}{20}\\=\frac{43}{20}\)
3. \(+\left(\frac{10}{-7}\right) -\left(\frac{-10}{8}\right) -\left(\frac{-5}{5}\right)\\= \frac{-10}{7}+ \frac{10}{8}+\frac{5}{5}\\=\frac{-10}{7}+\frac{5}{4}+\frac{1}{1}\\=\frac{-40}{28}+\frac{35}{28}+\frac{28}{28}\\=\frac{-40+35+28}{28}\\=\frac{23}{28}\)
4. \(+\left(\frac{9}{-2}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{10}{8}\right)\\= \frac{-9}{2}- \frac{3}{5}+\frac{10}{8}\\=\frac{-9}{2}-\frac{3}{5}+\frac{5}{4}\\=\frac{-90}{20}-\frac{12}{20}+\frac{25}{20}\\=\frac{-90-12+25}{20}\\=\frac{-77}{20}\)
5. \(-\left(\frac{-9}{-7}\right) -\left(\frac{10}{-10}\right) -\left(\frac{5}{-11}\right)\\= \frac{-9}{7}+ \frac{10}{10}+\frac{5}{11}\\=\frac{-9}{7}+\frac{1}{1}+\frac{5}{11}\\=\frac{-99}{77}+\frac{77}{77}+\frac{35}{77}\\=\frac{-99+77+35}{77}\\=\frac{13}{77}\)
6. \(-\left(\frac{5}{3}\right) -\left(\frac{-6}{7}\right) -\left(\frac{-3}{5}\right)\\= \frac{-5}{3}+ \frac{6}{7}+\frac{3}{5}\\=\frac{-175}{105}+\frac{90}{105}+\frac{63}{105}\\=\frac{-175+90+63}{105}\\=\frac{-22}{105}\)
7. \(+\left(\frac{9}{-4}\right) +\left(\frac{9}{-8}\right) +\left(\frac{5}{4}\right)\\= \frac{-9}{4}- \frac{9}{8}+\frac{5}{4}\\=\frac{-18}{8}-\frac{9}{8}+\frac{10}{8}\\=\frac{-18-9+10}{8}\\=\frac{-17}{8}\)
8. \(+\left(\frac{4}{-7}\right) -\left(\frac{3}{-8}\right) -\left(\frac{-11}{4}\right)\\= \frac{-4}{7}+ \frac{3}{8}+\frac{11}{4}\\=\frac{-32}{56}+\frac{21}{56}+\frac{154}{56}\\=\frac{-32+21+154}{56}\\=\frac{143}{56}\)
9. \(+\left(\frac{-3}{-4}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-12}{12}\right)\\= \frac{3}{4}+ \frac{8}{4}+\frac{12}{12}\\=\frac{3}{4}+\frac{2}{1}+\frac{1}{1}\\=\frac{3+2+1}{4}\\=\frac{6}{4}\\=\frac{3}{2}\)
10. \(+\left(\frac{8}{7}\right) +\left(\frac{10}{4}\right) -\left(\frac{-3}{-4}\right)\\= \frac{8}{7}+ \frac{10}{4}-\frac{3}{4}\\=\frac{8}{7}+\frac{5}{2}-\frac{3}{4}\\=\frac{32}{28}+\frac{70}{28}-\frac{21}{28}\\=\frac{32+70-21}{28}\\=\frac{81}{28}\)
11. \(-\left(\frac{-3}{-4}\right) -\left(\frac{-5}{7}\right) -\left(\frac{-2}{10}\right)\\= \frac{-3}{4}+ \frac{5}{7}+\frac{2}{10}\\=\frac{-3}{4}+\frac{5}{7}+\frac{1}{5}\\=\frac{-105}{140}+\frac{100}{140}+\frac{28}{140}\\=\frac{-105+100+28}{140}\\=\frac{23}{140}\)
12. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-5}{-7}\right) -\left(\frac{-7}{11}\right)\\= \frac{-4}{3}+ \frac{5}{7}+\frac{7}{11}\\=\frac{-308}{231}+\frac{165}{231}+\frac{147}{231}\\=\frac{-308+165+147}{231}\\=\frac{4}{231}\)