Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-5}\right) -\left(\frac{-7}{7}\right) -\left(\frac{-6}{2}\right)\\= \frac{-4}{5}+ \frac{7}{7}+\frac{6}{2}\\=\frac{-4}{5}+\frac{1}{1}+\frac{3}{1}\\=\frac{-4+1+3}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)
2. \(-\left(\frac{9}{8}\right) -\left(\frac{-9}{8}\right) +\left(\frac{-4}{12}\right)\\= \frac{-9}{8}+ \frac{9}{8}-\frac{4}{12}\\=\frac{-9}{8}+\frac{9}{8}-\frac{1}{3}\\=\frac{-27}{24}+\frac{27}{24}-\frac{8}{24}\\=\frac{-27+27-8}{24}\\=\frac{-8}{24}\\=\frac{-1}{3}\)
3. \(+\left(\frac{3}{-2}\right) -\left(\frac{3}{4}\right) +\left(\frac{9}{-4}\right)\\= \frac{-3}{2}- \frac{3}{4}-\frac{9}{4}\\=\frac{-6}{4}-\frac{3}{4}-\frac{9}{4}\\=\frac{-6-3-9}{4}\\=\frac{-18}{4}\\=\frac{-9}{2}\)
4. \(-\left(\frac{9}{5}\right) +\left(\frac{-8}{-7}\right) +\left(\frac{8}{-10}\right)\\= \frac{-9}{5}+ \frac{8}{7}-\frac{8}{10}\\=\frac{-9}{5}+\frac{8}{7}-\frac{4}{5}\\=\frac{-63}{35}+\frac{40}{35}-\frac{28}{35}\\=\frac{-63+40-28}{35}\\=\frac{-51}{35}\)
5. \(+\left(\frac{-2}{-7}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{9}{11}\right)\\= \frac{2}{7}+ \frac{4}{3}+\frac{9}{11}\\=\frac{66}{231}+\frac{308}{231}+\frac{189}{231}\\=\frac{66+308+189}{231}\\=\frac{563}{231}\)
6. \(+\left(\frac{7}{-2}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{-11}{-2}\right)\\= \frac{-7}{2}- \frac{10}{6}+\frac{11}{2}\\=\frac{-7}{2}-\frac{5}{3}+\frac{11}{2}\\=\frac{-21}{6}-\frac{10}{6}+\frac{33}{6}\\=\frac{-21-10+33}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
7. \(+\left(\frac{8}{-3}\right) +\left(\frac{-8}{6}\right) +\left(\frac{6}{-6}\right)\\= \frac{-8}{3}- \frac{8}{6}-\frac{6}{6}\\=\frac{-8}{3}-\frac{4}{3}-\frac{1}{1}\\=\frac{-8-4-1}{3}\\=\frac{-13}{3}\)
8. \(-\left(\frac{-2}{-9}\right) -\left(\frac{7}{9}\right) -\left(\frac{-5}{4}\right)\\= \frac{-2}{9}- \frac{7}{9}+\frac{5}{4}\\=\frac{-8}{36}-\frac{28}{36}+\frac{45}{36}\\=\frac{-8-28+45}{36}\\=\frac{9}{36}\\=\frac{1}{4}\)
9. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{-5}{-2}\right)\\= \frac{-3}{2}- \frac{4}{5}+\frac{5}{2}\\=\frac{-15}{10}-\frac{8}{10}+\frac{25}{10}\\=\frac{-15-8+25}{10}\\=\frac{2}{10}\\=\frac{1}{5}\)
10. \(-\left(\frac{-3}{-4}\right) +\left(\frac{10}{-7}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-3}{4}- \frac{10}{7}-\frac{12}{5}\\=\frac{-105}{140}-\frac{200}{140}-\frac{336}{140}\\=\frac{-105-200-336}{140}\\=\frac{-641}{140}\)
11. \(+\left(\frac{10}{-9}\right) -\left(\frac{8}{-7}\right) -\left(\frac{-8}{-6}\right)\\= \frac{-10}{9}+ \frac{8}{7}-\frac{8}{6}\\=\frac{-10}{9}+\frac{8}{7}-\frac{4}{3}\\=\frac{-70}{63}+\frac{72}{63}-\frac{84}{63}\\=\frac{-70+72-84}{63}\\=\frac{-82}{63}\)
12. \(-\left(\frac{-9}{4}\right) +\left(\frac{-2}{-7}\right) -\left(\frac{-10}{-12}\right)\\= \frac{9}{4}+ \frac{2}{7}-\frac{10}{12}\\=\frac{9}{4}+\frac{2}{7}-\frac{5}{6}\\=\frac{189}{84}+\frac{24}{84}-\frac{70}{84}\\=\frac{189+24-70}{84}\\=\frac{143}{84}\)