Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{10}{-4}\right) +\left(\frac{-3}{6}\right)\\= \frac{10}{7}- \frac{10}{4}-\frac{3}{6}\\=\frac{10}{7}-\frac{5}{2}-\frac{1}{2}\\=\frac{20}{14}-\frac{35}{14}-\frac{7}{14}\\=\frac{20-35-7}{14}\\=\frac{-22}{14}\\=\frac{-11}{7}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{9}{-6}\right) -\left(\frac{11}{4}\right)\\= \frac{-6}{5}+ \frac{9}{6}-\frac{11}{4}\\=\frac{-6}{5}+\frac{3}{2}-\frac{11}{4}\\=\frac{-24}{20}+\frac{30}{20}-\frac{55}{20}\\=\frac{-24+30-55}{20}\\=\frac{-49}{20}\)
3. \(+\left(\frac{-5}{8}\right) -\left(\frac{-5}{8}\right) +\left(\frac{10}{-5}\right)\\= \frac{-5}{8}+ \frac{5}{8}-\frac{10}{5}\\=\frac{-5}{8}+\frac{5}{8}-\frac{2}{1}\\=\frac{-5+5-2}{8}\\=\frac{-2}{8}\\=\frac{-1}{4}\)
4. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-3}{-3}\right) -\left(\frac{-8}{10}\right)\\= \frac{10}{3}+ \frac{3}{3}+\frac{8}{10}\\=\frac{10}{3}+\frac{1}{1}+\frac{4}{5}\\=\frac{50}{15}+\frac{15}{15}+\frac{12}{15}\\=\frac{50+15+12}{15}\\=\frac{77}{15}\)
5. \(-\left(\frac{6}{5}\right) -\left(\frac{3}{2}\right) -\left(\frac{7}{8}\right)\\= \frac{-6}{5}- \frac{3}{2}-\frac{7}{8}\\=\frac{-48}{40}-\frac{60}{40}-\frac{35}{40}\\=\frac{-48-60-35}{40}\\=\frac{-143}{40}\)
6. \(-\left(\frac{2}{7}\right) +\left(\frac{-3}{7}\right) +\left(\frac{10}{7}\right)\\= \frac{-2}{7}- \frac{3}{7}+\frac{10}{7}\\=\frac{-2-3+10}{7}\\=\frac{5}{7}\)
7. \(-\left(\frac{-9}{-2}\right) -\left(\frac{-10}{2}\right) -\left(\frac{-12}{-9}\right)\\= \frac{-9}{2}+ \frac{10}{2}-\frac{12}{9}\\=\frac{-9}{2}+\frac{5}{1}-\frac{4}{3}\\=\frac{-27}{6}+\frac{30}{6}-\frac{8}{6}\\=\frac{-27+30-8}{6}\\=\frac{-5}{6}\)
8. \(+\left(\frac{8}{-3}\right) +\left(\frac{-9}{-7}\right) -\left(\frac{-10}{2}\right)\\= \frac{-8}{3}+ \frac{9}{7}+\frac{10}{2}\\=\frac{-8}{3}+\frac{9}{7}+\frac{5}{1}\\=\frac{-56}{21}+\frac{27}{21}+\frac{105}{21}\\=\frac{-56+27+105}{21}\\=\frac{76}{21}\)
9. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-4}{6}\right) +\left(\frac{-6}{11}\right)\\= \frac{10}{7}- \frac{4}{6}-\frac{6}{11}\\=\frac{10}{7}-\frac{2}{3}-\frac{6}{11}\\=\frac{330}{231}-\frac{154}{231}-\frac{126}{231}\\=\frac{330-154-126}{231}\\=\frac{50}{231}\)
10. \(+\left(\frac{10}{7}\right) -\left(\frac{-8}{5}\right) +\left(\frac{-11}{-5}\right)\\= \frac{10}{7}+ \frac{8}{5}+\frac{11}{5}\\=\frac{50}{35}+\frac{56}{35}+\frac{77}{35}\\=\frac{50+56+77}{35}\\=\frac{183}{35}\)
11. \(+\left(\frac{-9}{7}\right) +\left(\frac{-2}{-5}\right) +\left(\frac{-7}{7}\right)\\= \frac{-9}{7}+ \frac{2}{5}-\frac{7}{7}\\=\frac{-9}{7}+\frac{2}{5}-\frac{1}{1}\\=\frac{-45}{35}+\frac{14}{35}-\frac{35}{35}\\=\frac{-45+14-35}{35}\\=\frac{-66}{35}\)
12. \(-\left(\frac{-4}{5}\right) +\left(\frac{5}{8}\right) -\left(\frac{-9}{9}\right)\\= \frac{4}{5}+ \frac{5}{8}+\frac{9}{9}\\=\frac{4}{5}+\frac{5}{8}+\frac{1}{1}\\=\frac{32}{40}+\frac{25}{40}+\frac{40}{40}\\=\frac{32+25+40}{40}\\=\frac{97}{40}\)