Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{3}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{3}{5}\right)\\= \frac{-8}{3}- \frac{5}{5}+\frac{3}{5}\\=\frac{-8}{3}-\frac{1}{1}+\frac{3}{5}\\=\frac{-40}{15}-\frac{15}{15}+\frac{9}{15}\\=\frac{-40-15+9}{15}\\=\frac{-46}{15}\)
2. \(+\left(\frac{8}{9}\right) +\left(\frac{-4}{10}\right) +\left(\frac{-11}{3}\right)\\= \frac{8}{9}- \frac{4}{10}-\frac{11}{3}\\=\frac{8}{9}-\frac{2}{5}-\frac{11}{3}\\=\frac{40}{45}-\frac{18}{45}-\frac{165}{45}\\=\frac{40-18-165}{45}\\=\frac{-143}{45}\)
3. \(+\left(\frac{-7}{-8}\right) +\left(\frac{5}{-5}\right) -\left(\frac{10}{4}\right)\\= \frac{7}{8}- \frac{5}{5}-\frac{10}{4}\\=\frac{7}{8}-\frac{1}{1}-\frac{5}{2}\\=\frac{7-1-5}{8}\\=\frac{1}{8}\)
4. \(-\left(\frac{2}{3}\right) +\left(\frac{-10}{-4}\right) -\left(\frac{9}{7}\right)\\= \frac{-2}{3}+ \frac{10}{4}-\frac{9}{7}\\=\frac{-2}{3}+\frac{5}{2}-\frac{9}{7}\\=\frac{-28}{42}+\frac{105}{42}-\frac{54}{42}\\=\frac{-28+105-54}{42}\\=\frac{23}{42}\)
5. \(+\left(\frac{-7}{-2}\right) -\left(\frac{-9}{2}\right) +\left(\frac{10}{2}\right)\\= \frac{7}{2}+ \frac{9}{2}+\frac{10}{2}\\=\frac{7}{2}+\frac{9}{2}+\frac{5}{1}\\=\frac{7+9+5}{2}\\=\frac{21}{2}\)
6. \(-\left(\frac{7}{-2}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{12}{9}\right)\\= \frac{7}{2}+ \frac{7}{8}+\frac{12}{9}\\=\frac{7}{2}+\frac{7}{8}+\frac{4}{3}\\=\frac{84}{24}+\frac{21}{24}+\frac{32}{24}\\=\frac{84+21+32}{24}\\=\frac{137}{24}\)
7. \(-\left(\frac{8}{5}\right) -\left(\frac{8}{3}\right) -\left(\frac{12}{8}\right)\\= \frac{-8}{5}- \frac{8}{3}-\frac{12}{8}\\=\frac{-8}{5}-\frac{8}{3}-\frac{3}{2}\\=\frac{-48}{30}-\frac{80}{30}-\frac{45}{30}\\=\frac{-48-80-45}{30}\\=\frac{-173}{30}\)
8. \(-\left(\frac{8}{-3}\right) +\left(\frac{8}{-8}\right) -\left(\frac{2}{-7}\right)\\= \frac{8}{3}- \frac{8}{8}+\frac{2}{7}\\=\frac{8}{3}-\frac{1}{1}+\frac{2}{7}\\=\frac{56}{21}-\frac{21}{21}+\frac{6}{21}\\=\frac{56-21+6}{21}\\=\frac{41}{21}\)
9. \(-\left(\frac{10}{-7}\right) -\left(\frac{6}{-4}\right) -\left(\frac{10}{-10}\right)\\= \frac{10}{7}+ \frac{6}{4}+\frac{10}{10}\\=\frac{10}{7}+\frac{3}{2}+\frac{1}{1}\\=\frac{20}{14}+\frac{21}{14}+\frac{14}{14}\\=\frac{20+21+14}{14}\\=\frac{55}{14}\)
10. \(-\left(\frac{-5}{-2}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{4}{-11}\right)\\= \frac{-5}{2}- \frac{3}{7}+\frac{4}{11}\\=\frac{-385}{154}-\frac{66}{154}+\frac{56}{154}\\=\frac{-385-66+56}{154}\\=\frac{-395}{154}\)
11. \(-\left(\frac{8}{5}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-12}{5}\right)\\= \frac{-8}{5}- \frac{10}{6}+\frac{12}{5}\\=\frac{-8}{5}-\frac{5}{3}+\frac{12}{5}\\=\frac{-24}{15}-\frac{25}{15}+\frac{36}{15}\\=\frac{-24-25+36}{15}\\=\frac{-13}{15}\)
12. \(+\left(\frac{-8}{-3}\right) -\left(\frac{9}{-7}\right) +\left(\frac{5}{-5}\right)\\= \frac{8}{3}+ \frac{9}{7}-\frac{5}{5}\\=\frac{8}{3}+\frac{9}{7}-\frac{1}{1}\\=\frac{56}{21}+\frac{27}{21}-\frac{21}{21}\\=\frac{56+27-21}{21}\\=\frac{62}{21}\)