Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{3}\right) -\left(\frac{-4}{3}\right) +\left(\frac{9}{-5}\right)\\= \frac{2}{3}+ \frac{4}{3}-\frac{9}{5}\\=\frac{10}{15}+\frac{20}{15}-\frac{27}{15}\\=\frac{10+20-27}{15}\\=\frac{3}{15}\\=\frac{1}{5}\)
2. \(-\left(\frac{4}{-9}\right) +\left(\frac{5}{8}\right) -\left(\frac{3}{3}\right)\\= \frac{4}{9}+ \frac{5}{8}-\frac{3}{3}\\=\frac{4}{9}+\frac{5}{8}-\frac{1}{1}\\=\frac{32}{72}+\frac{45}{72}-\frac{72}{72}\\=\frac{32+45-72}{72}\\=\frac{5}{72}\)
3. \(-\left(\frac{10}{7}\right) +\left(\frac{3}{7}\right) +\left(\frac{9}{10}\right)\\= \frac{-10}{7}+ \frac{3}{7}+\frac{9}{10}\\=\frac{-100}{70}+\frac{30}{70}+\frac{63}{70}\\=\frac{-100+30+63}{70}\\=\frac{-7}{70}\\=\frac{-1}{10}\)
4. \(+\left(\frac{2}{-7}\right) -\left(\frac{10}{-4}\right) -\left(\frac{11}{8}\right)\\= \frac{-2}{7}+ \frac{10}{4}-\frac{11}{8}\\=\frac{-2}{7}+\frac{5}{2}-\frac{11}{8}\\=\frac{-16}{56}+\frac{140}{56}-\frac{77}{56}\\=\frac{-16+140-77}{56}\\=\frac{47}{56}\)
5. \(-\left(\frac{-6}{-7}\right) -\left(\frac{7}{2}\right) -\left(\frac{4}{-4}\right)\\= \frac{-6}{7}- \frac{7}{2}+\frac{4}{4}\\=\frac{-6}{7}-\frac{7}{2}+\frac{1}{1}\\=\frac{-12}{14}-\frac{49}{14}+\frac{14}{14}\\=\frac{-12-49+14}{14}\\=\frac{-47}{14}\)
6. \(+\left(\frac{-2}{9}\right) -\left(\frac{-9}{6}\right) -\left(\frac{-8}{-2}\right)\\= \frac{-2}{9}+ \frac{9}{6}-\frac{8}{2}\\=\frac{-2}{9}+\frac{3}{2}-\frac{4}{1}\\=\frac{-4}{18}+\frac{27}{18}-\frac{72}{18}\\=\frac{-4+27-72}{18}\\=\frac{-49}{18}\)
7. \(+\left(\frac{-3}{-7}\right) -\left(\frac{3}{3}\right) -\left(\frac{-12}{10}\right)\\= \frac{3}{7}- \frac{3}{3}+\frac{12}{10}\\=\frac{3}{7}-\frac{1}{1}+\frac{6}{5}\\=\frac{15}{35}-\frac{35}{35}+\frac{42}{35}\\=\frac{15-35+42}{35}\\=\frac{22}{35}\)
8. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-10}{7}\right) -\left(\frac{9}{4}\right)\\= \frac{6}{5}- \frac{10}{7}-\frac{9}{4}\\=\frac{168}{140}-\frac{200}{140}-\frac{315}{140}\\=\frac{168-200-315}{140}\\=\frac{-347}{140}\)
9. \(+\left(\frac{-8}{7}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{-12}{-11}\right)\\= \frac{-8}{7}+ \frac{4}{10}+\frac{12}{11}\\=\frac{-8}{7}+\frac{2}{5}+\frac{12}{11}\\=\frac{-440}{385}+\frac{154}{385}+\frac{420}{385}\\=\frac{-440+154+420}{385}\\=\frac{134}{385}\)
10. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-10}{-6}\right) -\left(\frac{2}{-5}\right)\\= \frac{4}{9}- \frac{10}{6}+\frac{2}{5}\\=\frac{4}{9}-\frac{5}{3}+\frac{2}{5}\\=\frac{20}{45}-\frac{75}{45}+\frac{18}{45}\\=\frac{20-75+18}{45}\\=\frac{-37}{45}\)
11. \(-\left(\frac{5}{2}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{-5}{-11}\right)\\= \frac{-5}{2}- \frac{9}{3}+\frac{5}{11}\\=\frac{-5}{2}-\frac{3}{1}+\frac{5}{11}\\=\frac{-55}{22}-\frac{66}{22}+\frac{10}{22}\\=\frac{-55-66+10}{22}\\=\frac{-111}{22}\)
12. \(+\left(\frac{10}{7}\right) +\left(\frac{7}{-3}\right) -\left(\frac{12}{-9}\right)\\= \frac{10}{7}- \frac{7}{3}+\frac{12}{9}\\=\frac{10}{7}-\frac{7}{3}+\frac{4}{3}\\=\frac{30}{21}-\frac{49}{21}+\frac{28}{21}\\=\frac{30-49+28}{21}\\=\frac{9}{21}\\=\frac{3}{7}\)