Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-7}\right) -\left(\frac{4}{-3}\right) -\left(\frac{8}{-11}\right)\\= \frac{8}{7}+ \frac{4}{3}+\frac{8}{11}\\=\frac{264}{231}+\frac{308}{231}+\frac{168}{231}\\=\frac{264+308+168}{231}\\=\frac{740}{231}\)
2. \(-\left(\frac{-7}{3}\right) +\left(\frac{8}{-8}\right) -\left(\frac{4}{-9}\right)\\= \frac{7}{3}- \frac{8}{8}+\frac{4}{9}\\=\frac{7}{3}-\frac{1}{1}+\frac{4}{9}\\=\frac{21}{9}-\frac{9}{9}+\frac{4}{9}\\=\frac{21-9+4}{9}\\=\frac{16}{9}\)
3. \(+\left(\frac{-9}{7}\right) -\left(\frac{-9}{8}\right) +\left(\frac{-5}{4}\right)\\= \frac{-9}{7}+ \frac{9}{8}-\frac{5}{4}\\=\frac{-72}{56}+\frac{63}{56}-\frac{70}{56}\\=\frac{-72+63-70}{56}\\=\frac{-79}{56}\)
4. \(+\left(\frac{-7}{-8}\right) +\left(\frac{8}{-3}\right) -\left(\frac{-10}{4}\right)\\= \frac{7}{8}- \frac{8}{3}+\frac{10}{4}\\=\frac{7}{8}-\frac{8}{3}+\frac{5}{2}\\=\frac{21}{24}-\frac{64}{24}+\frac{60}{24}\\=\frac{21-64+60}{24}\\=\frac{17}{24}\)
5. \(-\left(\frac{-8}{-3}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{-4}{10}\right)\\= \frac{-8}{3}- \frac{7}{5}-\frac{4}{10}\\=\frac{-8}{3}-\frac{7}{5}-\frac{2}{5}\\=\frac{-40}{15}-\frac{21}{15}-\frac{6}{15}\\=\frac{-40-21-6}{15}\\=\frac{-67}{15}\)
6. \(+\left(\frac{5}{-3}\right) +\left(\frac{-2}{8}\right) +\left(\frac{-12}{-3}\right)\\= \frac{-5}{3}- \frac{2}{8}+\frac{12}{3}\\=\frac{-5}{3}-\frac{1}{4}+\frac{4}{1}\\=\frac{-20}{12}-\frac{3}{12}+\frac{48}{12}\\=\frac{-20-3+48}{12}\\=\frac{25}{12}\)
7. \(-\left(\frac{-2}{-3}\right) +\left(\frac{7}{7}\right) +\left(\frac{-11}{-8}\right)\\= \frac{-2}{3}+ \frac{7}{7}+\frac{11}{8}\\=\frac{-2}{3}+\frac{1}{1}+\frac{11}{8}\\=\frac{-16}{24}+\frac{24}{24}+\frac{33}{24}\\=\frac{-16+24+33}{24}\\=\frac{41}{24}\)
8. \(+\left(\frac{-10}{-7}\right) +\left(\frac{3}{7}\right) +\left(\frac{4}{-8}\right)\\= \frac{10}{7}+ \frac{3}{7}-\frac{4}{8}\\=\frac{10}{7}+\frac{3}{7}-\frac{1}{2}\\=\frac{20}{14}+\frac{6}{14}-\frac{7}{14}\\=\frac{20+6-7}{14}\\=\frac{19}{14}\)
9. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-2}{3}\right) +\left(\frac{3}{8}\right)\\= \frac{-6}{5}- \frac{2}{3}+\frac{3}{8}\\=\frac{-144}{120}-\frac{80}{120}+\frac{45}{120}\\=\frac{-144-80+45}{120}\\=\frac{-179}{120}\)
10. \(+\left(\frac{8}{-3}\right) +\left(\frac{-7}{3}\right) +\left(\frac{-8}{4}\right)\\= \frac{-8}{3}- \frac{7}{3}-\frac{8}{4}\\=\frac{-8}{3}-\frac{7}{3}-\frac{2}{1}\\=\frac{-8-7-2}{3}\\=\frac{-17}{3}\)
11. \(-\left(\frac{-2}{-5}\right) -\left(\frac{7}{4}\right) -\left(\frac{-6}{5}\right)\\= \frac{-2}{5}- \frac{7}{4}+\frac{6}{5}\\=\frac{-8}{20}-\frac{35}{20}+\frac{24}{20}\\=\frac{-8-35+24}{20}\\=\frac{-19}{20}\)
12. \(-\left(\frac{9}{7}\right) +\left(\frac{8}{3}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-9}{7}+ \frac{8}{3}+\frac{7}{2}\\=\frac{-54}{42}+\frac{112}{42}+\frac{147}{42}\\=\frac{-54+112+147}{42}\\=\frac{205}{42}\)