Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{3}\right) +\left(\frac{-4}{-5}\right) -\left(\frac{11}{-10}\right)\\= \frac{5}{3}+ \frac{4}{5}+\frac{11}{10}\\=\frac{50}{30}+\frac{24}{30}+\frac{33}{30}\\=\frac{50+24+33}{30}\\=\frac{107}{30}\)
2. \(+\left(\frac{4}{-3}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-3}{-2}\right)\\= \frac{-4}{3}- \frac{7}{5}-\frac{3}{2}\\=\frac{-40}{30}-\frac{42}{30}-\frac{45}{30}\\=\frac{-40-42-45}{30}\\=\frac{-127}{30}\)
3. \(-\left(\frac{2}{-3}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{11}{-12}\right)\\= \frac{2}{3}- \frac{3}{8}+\frac{11}{12}\\=\frac{16}{24}-\frac{9}{24}+\frac{22}{24}\\=\frac{16-9+22}{24}\\=\frac{29}{24}\)
4. \(-\left(\frac{-8}{-3}\right) +\left(\frac{10}{-3}\right) -\left(\frac{2}{-9}\right)\\= \frac{-8}{3}- \frac{10}{3}+\frac{2}{9}\\=\frac{-24}{9}-\frac{30}{9}+\frac{2}{9}\\=\frac{-24-30+2}{9}\\=\frac{-52}{9}\)
5. \(+\left(\frac{-2}{9}\right) +\left(\frac{9}{8}\right) -\left(\frac{10}{7}\right)\\= \frac{-2}{9}+ \frac{9}{8}-\frac{10}{7}\\=\frac{-112}{504}+\frac{567}{504}-\frac{720}{504}\\=\frac{-112+567-720}{504}\\=\frac{-265}{504}\)
6. \(+\left(\frac{2}{3}\right) -\left(\frac{5}{6}\right) +\left(\frac{-2}{-4}\right)\\= \frac{2}{3}- \frac{5}{6}+\frac{2}{4}\\=\frac{2}{3}-\frac{5}{6}+\frac{1}{2}\\=\frac{4}{6}-\frac{5}{6}+\frac{3}{6}\\=\frac{4-5+3}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
7. \(-\left(\frac{-10}{-7}\right) +\left(\frac{3}{4}\right) -\left(\frac{8}{11}\right)\\= \frac{-10}{7}+ \frac{3}{4}-\frac{8}{11}\\=\frac{-440}{308}+\frac{231}{308}-\frac{224}{308}\\=\frac{-440+231-224}{308}\\=\frac{-433}{308}\)
8. \(+\left(\frac{-8}{-3}\right) +\left(\frac{5}{-5}\right) -\left(\frac{-4}{-8}\right)\\= \frac{8}{3}- \frac{5}{5}-\frac{4}{8}\\=\frac{8}{3}-\frac{1}{1}-\frac{1}{2}\\=\frac{16}{6}-\frac{6}{6}-\frac{3}{6}\\=\frac{16-6-3}{6}\\=\frac{7}{6}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{10}{8}\right) +\left(\frac{-10}{-12}\right)\\= \frac{6}{5}+ \frac{10}{8}+\frac{10}{12}\\=\frac{6}{5}+\frac{5}{4}+\frac{5}{6}\\=\frac{72}{60}+\frac{75}{60}+\frac{50}{60}\\=\frac{72+75+50}{60}\\=\frac{197}{60}\)
10. \(+\left(\frac{-5}{2}\right) +\left(\frac{5}{-7}\right) -\left(\frac{7}{-9}\right)\\= \frac{-5}{2}- \frac{5}{7}+\frac{7}{9}\\=\frac{-315}{126}-\frac{90}{126}+\frac{98}{126}\\=\frac{-315-90+98}{126}\\=\frac{-307}{126}\)
11. \(+\left(\frac{9}{-2}\right) -\left(\frac{7}{-6}\right) +\left(\frac{4}{-5}\right)\\= \frac{-9}{2}+ \frac{7}{6}-\frac{4}{5}\\=\frac{-135}{30}+\frac{35}{30}-\frac{24}{30}\\=\frac{-135+35-24}{30}\\=\frac{-124}{30}\\=\frac{-62}{15}\)
12. \(-\left(\frac{-10}{7}\right) +\left(\frac{2}{-2}\right) +\left(\frac{-8}{2}\right)\\= \frac{10}{7}- \frac{2}{2}-\frac{8}{2}\\=\frac{10}{7}-\frac{1}{1}-\frac{4}{1}\\=\frac{10-1-4}{7}\\=\frac{5}{7}\)