Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right) -\left(\frac{7}{-9}\right) +\left(\frac{-6}{6}\right)\\= \frac{6}{5}+ \frac{7}{9}-\frac{6}{6}\\=\frac{6}{5}+\frac{7}{9}-\frac{1}{1}\\=\frac{54}{45}+\frac{35}{45}-\frac{45}{45}\\=\frac{54+35-45}{45}\\=\frac{44}{45}\)
2. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-8}{10}\right) -\left(\frac{-12}{6}\right)\\= \frac{-10}{3}+ \frac{8}{10}+\frac{12}{6}\\=\frac{-10}{3}+\frac{4}{5}+\frac{2}{1}\\=\frac{-50}{15}+\frac{12}{15}+\frac{30}{15}\\=\frac{-50+12+30}{15}\\=\frac{-8}{15}\)
3. \(-\left(\frac{7}{-8}\right) -\left(\frac{5}{-7}\right) +\left(\frac{10}{12}\right)\\= \frac{7}{8}+ \frac{5}{7}+\frac{10}{12}\\=\frac{7}{8}+\frac{5}{7}+\frac{5}{6}\\=\frac{147}{168}+\frac{120}{168}+\frac{140}{168}\\=\frac{147+120+140}{168}\\=\frac{407}{168}\)
4. \(-\left(\frac{7}{-3}\right) -\left(\frac{5}{-8}\right) +\left(\frac{-12}{-11}\right)\\= \frac{7}{3}+ \frac{5}{8}+\frac{12}{11}\\=\frac{616}{264}+\frac{165}{264}+\frac{288}{264}\\=\frac{616+165+288}{264}\\=\frac{1069}{264}\)
5. \(-\left(\frac{3}{-4}\right) +\left(\frac{-5}{4}\right) +\left(\frac{-12}{8}\right)\\= \frac{3}{4}- \frac{5}{4}-\frac{12}{8}\\=\frac{3}{4}-\frac{5}{4}-\frac{3}{2}\\=\frac{3-5-3}{4}\\=\frac{-5}{4}\)
6. \(-\left(\frac{2}{3}\right) -\left(\frac{-5}{-4}\right) +\left(\frac{12}{7}\right)\\= \frac{-2}{3}- \frac{5}{4}+\frac{12}{7}\\=\frac{-56}{84}-\frac{105}{84}+\frac{144}{84}\\=\frac{-56-105+144}{84}\\=\frac{-17}{84}\)
7. \(-\left(\frac{3}{-2}\right) -\left(\frac{-2}{3}\right) +\left(\frac{-4}{7}\right)\\= \frac{3}{2}+ \frac{2}{3}-\frac{4}{7}\\=\frac{63}{42}+\frac{28}{42}-\frac{24}{42}\\=\frac{63+28-24}{42}\\=\frac{67}{42}\)
8. \(+\left(\frac{5}{3}\right) -\left(\frac{10}{-10}\right) +\left(\frac{4}{-6}\right)\\= \frac{5}{3}+ \frac{10}{10}-\frac{4}{6}\\=\frac{5}{3}+\frac{1}{1}-\frac{2}{3}\\=\frac{5+1-2}{3}\\=\frac{4}{3}\)
9. \(+\left(\frac{9}{4}\right) +\left(\frac{4}{-4}\right) +\left(\frac{-5}{5}\right)\\= \frac{9}{4}- \frac{4}{4}-\frac{5}{5}\\=\frac{9}{4}-\frac{1}{1}-\frac{1}{1}\\=\frac{9-1-1}{4}\\=\frac{7}{4}\)
10. \(+\left(\frac{-10}{7}\right) +\left(\frac{10}{-5}\right) +\left(\frac{-5}{12}\right)\\= \frac{-10}{7}- \frac{10}{5}-\frac{5}{12}\\=\frac{-10}{7}-\frac{2}{1}-\frac{5}{12}\\=\frac{-120}{84}-\frac{168}{84}-\frac{35}{84}\\=\frac{-120-168-35}{84}\\=\frac{-323}{84}\)
11. \(+\left(\frac{-3}{4}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{6}{7}\right)\\= \frac{-3}{4}+ \frac{2}{7}+\frac{6}{7}\\=\frac{-21}{28}+\frac{8}{28}+\frac{24}{28}\\=\frac{-21+8+24}{28}\\=\frac{11}{28}\)
12. \(-\left(\frac{6}{5}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{-7}{10}\right)\\= \frac{-6}{5}+ \frac{7}{8}+\frac{7}{10}\\=\frac{-48}{40}+\frac{35}{40}+\frac{28}{40}\\=\frac{-48+35+28}{40}\\=\frac{15}{40}\\=\frac{3}{8}\)